diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term
index 71eae0b..8ec445d 100644
--- a/sage/.run.term-0.term
+++ b/sage/.run.term-0.term
@@ -1,44 +1,4 @@
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0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0]]]
@@ -19920,4 +19880,6872 @@ RModule of dimension 6 over GF(3),
 RModule of dimension 14 over GF(3)
 ]
 None
-[?2004h[?25l[?7lsage: [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ g
\ No newline at end of file
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git add -u
+]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ git commit -m ""o"b"l"i"c"z"e""a"n"i"e" "d"z"i"a"l"a"n"i"a" "n"a" "d"R" "c"h"y"b"a" "d"z"i"a"l"a"
+[master f7a04c6] obliczanie dzialania na dR chyba dziala
+ 3 files changed, 7256 insertions(+), 23 deletions(-)
+]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^3
+z1^2 - z1 = x^5
+
+(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x*z0 + x + z1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(z0 + 1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x*z0 + z1 + 1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(z0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+[
+RModule of dimension 1 over GF(2),
+RModule of dimension 4 over GF(2)
+]
+(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x*z0 + x + z1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(z0 + 1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x*z0 + z1 + 1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(z0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x^2) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(x) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(1) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+(0) * dx [(1) * dx, (x*z0 + z1) * dx, (z0) * dx, (x) * dx, (x^2) * dx]
+[
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A

+[?7h[?12l[?25h[?2004l[?7h[1 0 1 0 0 0 0 0 0 0]
+[0 1 0 0 0 0 0 0 0 0]
+[0 0 1 0 0 0 0 0 0 0]
+[0 1 0 1 0 0 0 0 0 1]
+[0 0 0 0 1 0 0 0 1 0]
+[0 0 0 0 0 1 0 1 0 0]
+[0 0 0 0 0 0 1 0 1 0]
+[0 0 0 0 0 0 0 1 0 0]
+[0 0 0 0 0 0 0 0 1 0]
+[0 0 0 0 0 0 0 0 0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l^2 == identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.coefficient_matrix()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.dimensions()

+[?7h[?12l[?25h[?2004l[?7h(10, 10)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.dimensions()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

+[?7h[?12l[?25h[?2004l[?7h5
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l.dimenions()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.dimensions()[?7h[?12l[?25h[?25l[?7lS.genu()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l^2 == identity_matrix(F, 6)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lid[?7h[?12l[?25h[?25l[?7lide[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A^p == identity_matrix(10)

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA^p == identity_matrix(10)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l^p = identity_matrix(10)[?7h[?12l[?25h[?25l[?7lB^p = identity_matrix(10)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: B^p == identity_matrix(10)

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA^p == identity_matrix(10)[?7h[?12l[?25h[?25l[?7l*BB*A[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l== B*A[?7h[?12l[?25h[?25l[?7lsage: A*B == B*A

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA*B == B*A[?7h[?12l[?25h[?25l[?7lB^pidentity_matrix(10)[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.dimenions()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^7
+z1^2 - z1 = x^5
+
+(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(z0 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^2*z1 + x*z0 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(z1 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x*z1 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^2*z1 + x^2 + x*z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+[
+RModule of dimension 1 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 4 over GF(2)
+]
+(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(z0 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^2*z1 + x*z0 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(z1 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x*z1 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^2*z1 + x^2 + x*z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x*z1) * dx, (x^2*z1 + x*z0) * dx, (x^2) * dx, (x^3) * dx]
+[
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^7
+z1^2 - z1 = x^9
+
+(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(z0 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^2*z0 + x^2 + x*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x*z0 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^3*z0 + x^3 + x^2*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(z1 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^2*z0 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x*z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^3*z0 + x^2*z1 + x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+[
+RModule of dimension 1 over GF(2),
+RModule of dimension 1 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 6 over GF(2)
+]
+(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(z0 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^2*z0 + x^2 + x*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x*z0 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^3*z0 + x^3 + x^2*z1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^5 + x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^3 + x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(z1 + 1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^2*z0 + x*z1 + x) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x*z0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^3*z0 + x^2*z1 + x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^4) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^5) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^3) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(x^2) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(0) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+(1) * dx [(1) * dx, (z1) * dx, (z0) * dx, (x) * dx, (x^2*z0 + x*z1) * dx, (x*z0) * dx, (x^2) * dx, (x^3*z0 + x^2*z1) * dx, (x^3) * dx, (x^4) * dx, (x^5) * dx]
+[
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lA*B == B*A[?7h[?12l[?25h[?25l[?7lB^pidentity_matrix(10)[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.dimenions()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lsage: A

+[?7h[?12l[?25h[?2004l[?7h22 x 22 dense matrix over Finite Field of size 2 (use the '.str()' method to see the entries)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^11
+z1^2 - z1 = x^9
+
+[
+RModule of dimension 1 over GF(2),
+RModule of dimension 1 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 6 over GF(2)
+]
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [11], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:16, in <module>
+
+File <string>:29, in group_action_matrices_dR(AS, threshold)
+
+File <string>:378, in de_rham_basis(self, threshold)
+
+File <string>:366, in lift_to_de_rham(self, fct, threshold)
+
+ValueError: Increase threshold!
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^11
+z1^2 - z1 = x^9
+
+[
+RModule of dimension 1 over GF(2),
+RModule of dimension 1 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 6 over GF(2)
+]
+[
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation:
+ z^5 - z = x^3
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:14, in <module>
+
+ValueError: not enough values to unpack (expected 2, got 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation:
+ z^5 - z = x^3
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [2], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:16, in <module>
+
+File /ext/sage/9.7/src/sage/matrix/special.py:922, in identity_matrix(ring, n, sparse)
+    920     n = ring
+    921     ring = ZZ
+--> 922 return matrix_space.MatrixSpace(ring, n, n, sparse)(1)
+
+File /ext/sage/9.7/src/sage/misc/classcall_metaclass.pyx:320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__()
+    318 """
+    319 if cls.classcall is not None:
+--> 320     return cls.classcall(cls, *args, **kwds)
+    321 else:
+    322     # Fast version of type.__call__(cls, *args, **kwds)
+
+File /ext/sage/9.7/src/sage/matrix/matrix_space.py:561, in MatrixSpace.__classcall__(cls, base_ring, nrows, ncols, sparse, implementation, **kwds)
+    516 """
+    517 Normalize the arguments to call the ``__init__`` constructor.
+    518 
+   (...)
+    558     False
+    559 """
+    560 if base_ring not in _Rings:
+--> 561     raise TypeError("base_ring (=%s) must be a ring"%base_ring)
+    562 nrows = int(nrows)
+    563 if ncols is None:
+
+TypeError: base_ring (=8) must be a ring
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equation:
+ z^5 - z = x^3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.dimensions()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l.dimensions()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [4], in <cell line: 1>()
+----> 1 A.jordan_form()
+
+AttributeError: 'list' object has no attribute 'jordan_form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form()[?7h[?12l[?25h[?25l[?7lsage: A

+[?7h[?12l[?25h[?2004l[?7h[
+[1 1 1 0 0 0 0 3]
+[0 1 2 0 0 0 0 4]
+[0 0 1 0 0 0 0 4]
+[0 0 0 1 4 1 3 0]
+[0 0 0 0 1 3 1 0]
+[0 0 0 0 0 1 4 0]
+[0 0 0 0 0 0 1 0]
+[0 0 0 0 0 0 0 1]
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l = AS.cohomology_of_structure_sheaf_basis()[1][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A = A[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = A[0][?7h[?12l[?25h[?25l[?7l.jordan_form()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldan_form()[?7h[?12l[?25h[?25l[?7lan_form()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form()

+[?7h[?12l[?25h[?2004l[?7h[1 1 0 0|0 0 0 0]
+[0 1 1 0|0 0 0 0]
+[0 0 1 1|0 0 0 0]
+[0 0 0 1|0 0 0 0]
+[-------+-------]
+[0 0 0 0|1 1 0 0]
+[0 0 0 0|0 1 1 0]
+[0 0 0 0|0 0 1 1]
+[0 0 0 0|0 0 0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lb()[?7h[?12l[?25h[?25l[?7ll()[?7h[?12l[?25h[?25l[?7lo()[?7h[?12l[?25h[?25l[?7lc()[?7h[?12l[?25h[?25l[?7lk()[?7h[?12l[?25h[?25l[?7ls()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_blocks()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [8], in <cell line: 1>()
+----> 1 A.jordan_blocks()
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float' object has no attribute 'jordan_blocks'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_blocks()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: A.jordan_blocks()

+  A.C                                 A.QR                                A.add_multiple_of_row               A.adjoint_classical                  

+  A.H                                 A.T                                 A.add_to_entry                      A.adjugate                           

+  A.LLL_gram                          A.act_on_polynomial                 A.additive_order                    A.anticommutator                    >

+  A.LU                                A.add_multiple_of_column            A.adjoint                           A.antitranspose                      

+ [?7h[?12l[?25h[?25l[?7lC

+ A.C                                

+

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lQR

+ A.C                                 A.QR                               [?7h[?12l[?25h[?25l[?7lC

+ A.C                                 A.QR                               [?7h[?12l[?25h[?25l[?7l

+

+

+

+

+[?7h[?12l[?25h[?25l[?7ljordan_blocks()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_blocks()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A.jordan_blocks()[0]

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [9], in <cell line: 1>()
+----> 1 A.jordan_blocks()[Integer(0)]
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float' object has no attribute 'jordan_blocks'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_blocks()[0][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7lf()[0][?7h[?12l[?25h[?25l[?7lo()[0][?7h[?12l[?25h[?25l[?7lr()[0][?7h[?12l[?25h[?25l[?7lm()[0][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form()[0]

+[?7h[?12l[?25h[?2004l[?7h(1, 1, 0, 0, 0, 0, 0, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form()[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm()[0][?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(sub

+ subdivide=  

+ subfactorial

+ subsets     

+

+ [?7h[?12l[?25h[?25l[?7ldivide=

+ subdivide=  

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l

+

+

+

+[?7h[?12l[?25h[?25l[?7lT[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lTrue[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(subdivide=True)

+[?7h[?12l[?25h[?2004l[?7h[1 1 0 0|0 0 0 0]
+[0 1 1 0|0 0 0 0]
+[0 0 1 1|0 0 0 0]
+[0 0 0 1|0 0 0 0]
+[-------+-------]
+[0 0 0 0|1 1 0 0]
+[0 0 0 0|0 1 1 0]
+[0 0 0 0|0 0 1 1]
+[0 0 0 0|0 0 0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(subdivide=True)[0]

+[?7h[?12l[?25h[?2004l[?7h(1, 1, 0, 0, 0, 0, 0, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(subdivide=True)

+[?7h[?12l[?25h[?2004l[?7h[1 1 0 0|0 0 0 0]
+[0 1 1 0|0 0 0 0]
+[0 0 1 1|0 0 0 0]
+[0 0 0 1|0 0 0 0]
+[-------+-------]
+[0 0 0 0|1 1 0 0]
+[0 0 0 0|0 1 1 0]
+[0 0 0 0|0 0 1 1]
+[0 0 0 0|0 0 0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l()[0][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A.jordan_form(subdivide=True)

+[?7h[?12l[?25h[?2004l[?7h[1 1 0 0|0 0 0 0]
+[0 1 1 0|0 0 0 0]
+[0 0 1 1|0 0 0 0]
+[0 0 0 1|0 0 0 0]
+[-------+-------]
+[0 0 0 0|1 1 0 0]
+[0 0 0 0|0 1 1 0]
+[0 0 0 0|0 0 1 1]
+[0 0 0 0|0 0 0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lyA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lpA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7leA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form(subdivide=True))

+[?7h[?12l[?25h[?2004l[?7h<class 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float'>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form(subdivide=True))[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form(subdivide=True))[0]

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [16], in <cell line: 1>()
+----> 1 type(A.jordan_form(subdivide=True))[Integer(0)]
+
+TypeError: 'sage.misc.inherit_comparison.InheritComparisonMetaclass' object is not subscriptable
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form(subdivide=True))[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lTru[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form(

+  base_ring=                                   subdivide=                                   AA                                            

+  check_input=                                 transformation=                              AS                                            

+  eigenvalues=                                 %%!                                          AbelianGroup                                 >

+  sparse=                                      A                                            AbelianGroupMorphism                          

+ [?7h[?12l[?25h[?25l[?7lbase_ring=

+ base_ring=                                  

+

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lsubdivde

+ base_ring=                                   subdivide=                                  [?7h[?12l[?25h[?25l[?7lAA

+ subdivide=                                   AA                                          [?7h[?12l[?25h[?25l[?7lbelianGroupWithValues

+ subdivdeAA        belianGroupWithValues

+ transformaion=AS             belianVariety

+<%%!         AbelianGroupdditiveAbelianGroup

+ A      belianGroupMorphismdditiveAbelianGroupWrapper[?7h[?12l[?25h[?25l[?7ldditiveAbelianGroupWrapperElement

+AA        belianGroupWithValuesdditiveAbelianGroupWrapperElement

+AS             belianVarietydditiveMagmas

+AbelianGroupdditiveAbelianGroupffneCryptosystem  

+belianGroupMorphismdditiveAbelianGroupWrapperffneGroup                [?7h[?12l[?25h[?25l[?7lbelianGroupWithValues

+ AbelianGroupWithValues                       AdditiveAbelianGroupWrapperElement          [?7h[?12l[?25h[?25l[?7ldditiveAbelianGroupWrapperElement

+ AbelianGroupWithValues                       AdditiveAbelianGroupWrapperElement          [?7h[?12l[?25h[?25l[?7lffneHypersurface

+belianGroupWithValuesdditiveAbelianGroupWrapperElementffneHypersurface                

+belianVarietydditiveMagmasffneNilTeperleyLiebTypeA

+dditiveAbelianGroupffneCryptosystem  PermutationGroup

+dditiveAbelianGroupWrapperffneGroup                Space[?7h[?12l[?25h[?25l[?7lToricVaiety

+dditiveAbelianGroupWrapperElementffneHypersurface                ToricVaiety

+dditiveMagmasffneNilTeperleyLiebTypeAWeylGroups           

+ffneCryptosystem  PermutationGrouplarmInterrup        

+ffneGroup                Spacelgebra    [?7h[?12l[?25h[?25l[?7llgebraIdeals

+ffneHypersurface                ToricVaietylgebraIdeals     

+ffneNilTeperleyLiebTypeAWeylGroups           lgebraModules  

+PermutationGrouplarmInterrup        gebraicField

+Spacelgebra    icNumber[?7h[?12l[?25h[?25l[?7licReal

+ToricVaietylgebraIdeals     icReal

+WeylGroups           lgebraModules  icRealField

+larmInterrup        gebraicFields      

+lgebra    icNumbersWithBasis[?7h[?12l[?25h[?25l[?7llCusps

+lgebraIdeals     icReallCusps     

+lgebraModules  icRealFieldlExactCovers    

+gebraicFields      phabet

+icNumbersWithBasisphabeticString[?7h[?12l[?25h[?25l[?7lternatingGroup

+icReallCusps     ternatingGroup

+icRealFieldlExactCovers    ternaingSignMatrices

+s      phabetternaingSignMatrix

+sWithBasisphabeticStringrithmEror  [?7h[?12l[?25h[?25l[?7llCusps

+ AllCusps                                     AlternatingGroup                            [?7h[?12l[?25h[?25l[?7lternatingGroup

+ AllCusps                                     AlternatingGroup                            [?7h[?12l[?25h[?25l[?7lrithmecSubgroup_Permutation

+lCusps     ternatingGrouprithmecSubgroup_Permutation

+lExactCovers    ternaingSignMatricesrrangemets           

+phabetternaingSignMatrixrinGroup           

+phabeticStringrithmEror  ssertionEror [?7h[?12l[?25h[?25l[?7lssionGroupS

+ternatingGrouprithmecSubgroup_PermutationssionGroupS                  

+ternaingSignMatricesrrangemets           ssionGroupU

+ternaingSignMatrixrinGroup           symptoticRing

+rithmEror  ssertionEror tkinModulaCorrespondenceDatabase[?7h[?12l[?25h[?25l[?7lrithmeticSubgroup_Permutation

+ ArithmeticSubgroup_Permutation               AssionGroupS                                [?7h[?12l[?25h[?25l[?7llternangGroup

+ AlternatingGroup                             ArithmeticSubgroup_Permutation              [?7h[?12l[?25h[?25l[?7lrithmecSubgroup_Permutation

+ AlternatingGroup                             ArithmeticSubgroup_Permutation              [?7h[?12l[?25h[?25l[?7lssionGroupS

+ ArithmeticSubgroup_Permutation               AssionGroupS                                [?7h[?12l[?25h[?25l[?7ltknModularPolynomialDatabase

+rithmecSubgroup_PermutationssionGroupS                  tknModularPolynomialDatabase

+rrangemets           ssionGroupUttributeError

+rinGroup           symptoticRingugentedLatticeDiagramFilling

+ssertionEror tkinModulaCorrespondenceDatabaseutomaton                         [?7h[?12l[?25h[?25l[?7lxiom

+ssionGroupS                  tknModularPolynomialDatabasexiom                         

+ssionGroupUttributeErrorBackslashOperator

+symptoticRingugentedLatticeDiagramFillingBaseExcption                 

+tkinModulaCorrespondenceDatabaseutomaton                         BaxterPermutations[?7h[?12l[?25h[?25l[?7lBerkovich_Cp_Affine

+tknModularPolynomialDatabasexiom                         Berkovich_Cp_Affine

+ttributeErrorBackslashOperatorerovic_Cp_Prjective

+ugentedLatticeDiagramFillingBaseExcption                 esel       

+utomaton                         BaxterPermutationsezoutianQadraticForm[?7h[?12l[?25h[?25l[?7lialgebras

+xiom                         Berkovich_Cp_Affineialgebras         

+BackslashOperatorerovic_Cp_PrjectiveialgebrasWithBasis    

+BaseExcption                 esel       imodules

+BaxterPermutationsezoutianQadraticForminaryQF              [?7h[?12l[?25h[?25l[?7lnaryQF_reduced_representatives

+Berkovich_Cp_Affineialgebras         naryQF_reduced_representatives

+erovic_Cp_PrjectiveialgebrasWithBasis    naryRecurrenceSequence

+esel       imodulesnaryStrings

+ezoutianQadraticForminaryQF              Tree[?7h[?12l[?25h[?25l[?7lTrees

+ialgebras         naryQF_reduced_representativesTrees                     

+ialgebrasWithBasis    naryRecurrenceSequenceptiteGaph          

+imodulesnaryStringstset       

+inaryQF              TreelockDesign[?7h[?12l[?25h[?25l[?7lBlockingIOError

+naryQF_reduced_representativesTrees                     lockingIOError

+naryRecurrenceSequenceptiteGaph          ooleanPolynomialRing

+naryStringstset       raidGroup

+TreelockDesignranchingRule[?7h[?12l[?25h[?25l[?7lBrandtModule

+Trees                     lockingIOErrorrandtModule   

+ptiteGaph          ooleanPolynomialRingraurAlgebra        

+tset       raidGroupokenPipeError

+lockDesignranchingRuleuhatTitsQuotient[?7h[?12l[?25h[?25l[?7lBufferError

+lockingIOErrorrandtModule   ufferError 

+ooleanPolynomialRingraurAlgebra        ytesWarning 

+raidGroupokenPipeErrorCBF            

+ranchingRuleuhatTitsQuotientCC                [?7h[?12l[?25h[?25l[?7lCDF

+randtModule   ufferError CDF        

+raurAlgebra        ytesWarning CFiniteSequence

+okenPipeErrorCBF            FiniteSequences

+uhatTitsQuotientCC                IF[?7h[?12l[?25h[?25l[?7lL

+ufferError CDF        L

+ytesWarning CFiniteSequencePRFanoToricVariety

+CBF            FiniteSequencesRT             

+CC                IFRT_basis[?7h[?12l[?25h[?25l[?7lRT_list

+CDF        LRT_list

+CFiniteSequencePRFanoToricVarietyRT_vects        

+FiniteSequencesRT             _super

+IFRT_basisachedFunction[?7h[?12l[?25h[?25l[?7lallableSymbolicExpressionRing

+LRT_listallableSymbolicExpressionRing

+PRFanoToricVarietyRT_vects        artanMatix

+RT             _superartanType

+RT_basisachedFunctiontegory      [?7h[?12l[?25h[?25l[?7lhainComplex

+RT_listallableSymbolicExpressionRinghainComplex                  

+RT_vects        artanMatixhainCompleMorphism

+_superartanTypehainComlexes

+achedFunctiontegory      hi     [?7h[?12l[?25h[?25l[?7lChildProcessError

+allableSymbolicExpressionRinghainComplex                  ildProcessError

+artanMatixhainCompleMorphismi                  

+artanTypehainComlexeslssFunction 

+tegory      hi     lassicalCrystals[?7h[?12l[?25h[?25l[?7lClassicalModularPolynomialDatabase

+hainComplex                  ildProcessErrorlassicalModularPolynomialDatabase

+hainCompleMorphismi                  liffordAlgebra

+hainComlexeslssFunction uterAlgebra

+hi     lassicalCrystalsuterComplex   [?7h[?12l[?25h[?25l[?7luterQuiver

+ildProcessErrorlassicalModularPolynomialDatabaseuterQuiver                     

+i                  liffordAlgebrausteSeed    

+lssFunction uterAlgebraoalgbras    

+lassicalCrystalsuterComplex   oalgbrasWithBasis[?7h[?12l[?25h[?25l[?7lolor

+lassicalModularPolynomialDatabaseuterQuiver                     olor        

+liffordAlgebrausteSeed    olordPrmutations

+uterAlgebraoalgbras    mbinations

+uterComplex   oalgbrasWithBasismbinatorialCls [?7h[?12l[?25h[?25l[?7lmbinatorialFreeModule

+uterQuiver                     olor        mbinatorialFreeModule

+usteSeed    olordPrmutationsmbinatoialObject

+oalgbras    mbinationsorialPolyhedron

+oalgbrasWithBasismbinatorialCls Species[?7h[?12l[?25h[?25l[?7lmutiveAdditiveGroups

+olor        mbinatorialFreeModulemutiveAdditiveGroups

+olordPrmutationsmbinatoialObjectmutiveAdditiveMonoids

+mbinationsorialPolyhedronmutiveAdditivSemigroups

+mbinatorialCls SpeciesmutiveAgebraElement[?7h[?12l[?25h[?25l[?7llgebraIdeals

+mbinatorialFreeModulemutiveAdditiveGroupslgebraIdeals 

+mbinatoialObjectmutiveAdditiveMonoidslgebras       

+orialPolyhedronmutiveAdditivSemigroupsRing              

+SpeciesmutiveAgebraElementRingElement   [?7h[?12l[?25h[?25l[?7lRingIdeals

+mutiveAdditiveGroupslgebraIdeals RingIdeals   

+mutiveAdditiveMonoidslgebras       Rings   

+mutiveAdditivSemigroupsRing              pleteDiscreteValuationFields

+mutiveAgebraElementRingElement   pleteDiscreteValuaionRings[?7h[?12l[?25h[?25l[?7lAlgebraIdeals

+ CommutativeAlgebraIdeals                     CommutativeRingIdeals                       [?7h[?12l[?25h[?25l[?7ldditiveGroups

+ CommutativeAdditiveGroups                    CommutativeAlgebraIdeals                    [?7h[?12l[?25h[?25l[?7lbinorialFreeModule

+binorialFreeModule  dditiveGroupsAlgebraIdeals

+binorialObject       dditiveMonoidsAlgebras

+binorialPolyhdron      AdditiveSemigroupsmutativeRing                

+binoriaSpecies     AlgebraElementmutativeRingElemen        [?7h[?12l[?25h[?25l[?7llor

+lor                  binorialFreeModule  dditiveGroups

+loredPemutationsbinorialObject       dditiveMonoids

+ions           binorialPolyhdron      AdditiveSemigroups

+Class  binoriaSpecies     AlgebraElement[?7h[?12l[?25h[?25l[?7llusterQuiver

+lusterQuiverlor                  binorialFreeModule  

+lustrSed        loredPemutationsbinorialObject       

+algebras  ions           binorialPolyhdron      

+algebrasWithBisClass  binoriaSpecies     [?7h[?12l[?25h[?25l[?7lasicalModularPolynomialDatabase

+asicalModularPolynomialDatabaselusterQuiverlor                  

+iffodAlgebralustrSed        loredPemutations

+lustrAlgebraalgebras  ions           

+lustrComplex     algebrasWithBisClass  [?7h[?12l[?25h[?25l[?7lChildProcessError

+hildProcessError                 asicalModularPolynomialDatabaselusterQuiver

+i             iffodAlgebralustrSed        

+asFunction lustrAlgebraalgebras  

+asicalCrystalslustrComplex     algebrasWithBis[?7h[?12l[?25h[?25l[?7lChainComplex

+ainComplex     hildProcessError                 asicalModularPolynomialDatabase

+hainComplexMorphismi             iffodAlgebra

+hinComplexesasFunction lustrAlgebra

+hi              asicalCrystalslustrComplex     [?7h[?12l[?25h[?25l[?7lallableSymbolicExpressionRing

+allableSymbolicExpressionRingainComplex     hildProcessError                 

+artanMatri        hainComplexMorphismi             

+artanTye    hinComplexesasFunction 

+ategoryhi              asicalCrystals[?7h[?12l[?25h[?25l[?7lRT_list

+RT_list                      allableSymbolicExpressionRingainComplex     

+RT_vectos artanMatri        hainComplexMorphism

+_super   artanTye    hinComplexes

+chedFunctionategoryhi              [?7h[?12l[?25h[?25l[?7lLF

+LF     RT_list                      allableSymbolicExpressionRing

+PRFanoTicVarietyRT_vectos artanMatri        

+RT    _super   artanTye    

+RT_basis     chedFunctionategory[?7h[?12l[?25h[?25l[?7lD

+DLF     RT_list                      

+FiniteSequence    PRFanoTicVarietyRT_vectos 

+FiniteSequencesRT    _super   

+IF      RT_basis     chedFunction[?7h[?12l[?25h[?25l[?7lBufferError

+BufferErrorDLF     

+BytesWarning   FiniteSequence    PRFanoTicVariety

+BF             FiniteSequencesRT    

+C IF      RT_basis     [?7h[?12l[?25h[?25l[?7lBrandtModule

+randtModuleBufferErrorD

+rauerAlgebraBytesWarning   FiniteSequence    

+BrokenPipeErrorBF             FiniteSequences

+BruhatTitsQuotientC IF      [?7h[?12l[?25h[?25l[?7lBlockingIOError

+lockingIOErrorrandtModuleBufferError

+oolanPolynomialRingrauerAlgebraBytesWarning   

+aidGroup     BrokenPipeErrorBF             

+anchingRule     BruhatTitsQuotientC [?7h[?12l[?25h[?25l[?7lBlockingIOErro

+

+

+

+

+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lvision([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form().subdivision())

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [17], in <cell line: 1>()
+----> 1 type(A.jordan_form().subdivision())
+
+File /ext/sage/9.7/src/sage/matrix/matrix2.pyx:8845, in sage.matrix.matrix2.Matrix.subdivision()
+   8843         self._subdivisions = (l_row, l_col)
+   8844 
+-> 8845 def subdivision(self, i, j):
+   8846     """
+   8847     Returns an immutable copy of the (i,j)th submatrix of self,
+
+TypeError: subdivision() takes exactly 2 positional arguments (0 given)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form().subdivision())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7li))[?7h[?12l[?25h[?25l[?7l,))[?7h[?12l[?25h[?25l[?7l ))[?7h[?12l[?25h[?25l[?7li))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, i)[?7h[?12l[?25h[?25l[?7l1, i)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l))[?7h[?12l[?25h[?25l[?7l1))[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: type(A.jordan_form().subdivision(1, 1))

+[?7h[?12l[?25h[?2004l[?7h<class 'sage.matrix.matrix_modn_dense_float.Matrix_modn_dense_float'>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7ltyp(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7lt(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7lstr(A.jordan_form().subdivision(1, 1))[?7h[?12l[?25h[?25l[?7lsage: str(A.jordan_form().subdivision(1, 1))

+[?7h[?12l[?25h[?2004l[?7h'[1 1 0 0]\n[0 1 1 0]\n[0 0 1 1]\n[0 0 0 1]'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equation:
+ z^2 - z = x^3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
+z0^2 - z0 = x^3
+z1^2 - z1 = a*x^3
+
+/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
+********************************************************************************
+Denominators of fraction field elements are sometimes dropped without warning.
+This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
+********************************************************************************
+>> A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1
+                                  ^
+User error: Identifier 'a' has not been declared or assigned
+>> , 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);Indecomposab
+                                                               ^
+User error: Identifier 'A' has not been declared or assigned
+>> ,6), A);IndecomposableSummands(M);
+                                  ^
+User error: Identifier 'M' has not been declared or assigned
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
+z0^2 - z0 = x^3
+z1^2 - z1 = a*x^3
+
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [3], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:19, in <module>
+
+NameError: name 'T' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^2 with the equations:
+z0^2 - z0 = x^3
+z1^2 - z1 = a*x^3
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA.jordan_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lsage: A

+[?7h[?12l[?25h[?2004l[?7h[    1 a + 1     0     0     0     a]
+[    0     1     0     0     0     0]
+[    0     0     1     0     a     0]
+[    0     0     0     1     1     0]
+[    0     0     0     0     1     0]
+[    0     0     0     0     0     1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB^p == identity_matrix(10)[?7h[?12l[?25h[?25l[?7lsage: B

+[?7h[?12l[?25h[?2004l[?7h[1 1 0 0 0 1]
+[0 1 0 0 0 0]
+[0 0 1 0 1 0]
+[0 0 0 1 a 0]
+[0 0 0 0 1 0]
+[0 0 0 0 0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, text=True)

+[?7h[?12l[?25h[?2004l[?7h'A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);IndecomposableSummands(M);'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

+[?7h[?12l[?25h[?2004l[?7h3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^3
+z1^2 - z1 = x^13
+
+[
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lare_equivalent_matrix(A1, A2, q)[?7h[?12l[?25h[?25l[?7lsage: q = 5

+....: p = q.factor()[0][0]

+....: n = 2

+....: A1 = matrix(ZZ, [[1, 3], [3, 4]])

+....: A2 = matrix(ZZ, [[2, 3], [2, 2]])

+....: print((identity_matrix(n) + A1.transpose()*A1).determinant()%p)

+....: print((identity_matrix(n) + A2.transpose()*A2).determinant()%p)[?7h[?12l[?25h[?25l[?7lare_equivalent_matrix(A1, A2, q)

+ 

+ 

+ 

+ 

+ 

+ [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista_np = [2*i+1 for i in range(q//2)][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
+z0^3 - z0 = x^2
+z1^3 - z1 = x^5
+
+[
+RModule of dimension 6 over GF(3),
+RModule of dimension 6 over GF(3),
+RModule of dimension 14 over GF(3)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA2 = matrix(ZZ, [[2, 3], [2, 2]])[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

+[?7h[?12l[?25h[?2004l[?7h[x^4*z0 + x^3*z1 + z0^2*z1^2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lare_equivalent_matrix(A1, A2, q)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lno  20 -th root; divide by 2
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [3], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:13, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lno  14 -th root; divide by 2
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [4], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:13, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
+z0^3 - z0 = x^5
+z1^3 - z1 = x^11
+
+I haven't found all forms.
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [5], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:17, in <module>
+
+File <string>:29, in group_action_matrices_dR(AS, threshold)
+
+File <string>:145, in holomorphic_differentials_basis(self, threshold)
+
+NameError: name 'holomorphic_differentials_basis' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
+z0^3 - z0 = x^5
+z1^3 - z1 = x^11
+
+I haven't found all forms.
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [6], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:17, in <module>
+
+File <string>:29, in group_action_matrices_dR(AS, threshold)
+
+File <string>:145, in holomorphic_differentials_basis(self, threshold)
+
+NameError: name 'holomorphic_differentials_basis' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
+z0^3 - z0 = x^5
+z1^3 - z1 = x^11
+
+I haven't found all forms.
+---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [7], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:17, in <module>
+
+File <string>:29, in group_action_matrices_dR(AS, threshold)
+
+File <string>:145, in holomorphic_differentials_basis(self, threshold)
+
+NameError: name 'holomorphic_differentials_basis' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lno  20 -th root; divide by 2
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [8], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:13, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
+z0^3 - z0 = x^2
+z1^3 - z1 = 2*x^8
+
+[
+RModule of dimension 6 over GF(3),
+RModule of dimension 6 over GF(3),
+RModule of dimension 6 over GF(3),
+RModule of dimension 6 over GF(3),
+RModule of dimension 6 over GF(3),
+RModule of dimension 14 over GF(3)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equations:
+z0^3 - z0 = x^2
+z1^3 - z1 = 2*x^11
+
+[
+RModule of dimension 6 over GF(3),
+RModule of dimension 6 over GF(3),
+RModule of dimension 6 over GF(3),
+RModule of dimension 6 over GF(3),
+RModule of dimension 6 over GF(3),
+RModule of dimension 6 over GF(3),
+RModule of dimension 6 over GF(3),
+RModule of dimension 6 over GF(3),
+RModule of dimension 14 over GF(3)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equations:
+z0^5 - z0 = x^2
+z1^5 - z1 = x^7
+
+
+
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equations:
+z0^5 - z0 = x^2
+z1^5 - z1 = x^7
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

+[?7h[?12l[?25h[?2004l[?7h[x^6*z0^3 + x^5*z0^2*z1 + z0^4*z1^4 + x^4*z0*z1^2 + x^3*z1^3]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rhmbasis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
+ ( (z1) * dx, 0 ),
+ ( (z1^2) * dx, 0 ),
+ ( (z1^3) * dx, 0 ),
+ ( (2*x^4*z0^4 - 2*x^3*z0^3*z1 - x^2*z0^2*z1^2 + z1^4) * dx, 0 ),
+ ( (z0) * dx, 0 ),
+ ( (z0*z1) * dx, 0 ),
+ ( (z0*z1^2) * dx, 0 ),
+ ( (z0*z1^3) * dx, 0 ),
+ ( (x^3*z0^4*z1 + x^2*z0^3*z1^2 + x^6 + x*z0^2*z1^3 + z0*z1^4) * dx, 0 ),
+ ( (z0^2) * dx, 0 ),
+ ( (z0^2*z1) * dx, 0 ),
+ ( (z0^2*z1^2) * dx, 0 ),
+ ( (-x^5 + z0^2*z1^3) * dx, 0 ),
+ ( (z0^3) * dx, 0 ),
+ ( (z0^3*z1) * dx, 0 ),
+ ( (z0^3*z1^2) * dx, 0 ),
+ ( (2*x^5*z0 + z0^3*z1^3 + 2*x^4*z1) * dx, 0 ),
+ ( (z0^4) * dx, 0 ),
+ ( (z0^4*z1) * dx, 0 ),
+ ( (z0^4*z1^2) * dx, 0 ),
+ ( (-x^5*z0^2 + z0^4*z1^3 - 2*x^4*z0*z1 + 2*x^3*z1^2) * dx, 0 ),
+ ( (x) * dx, 0 ),
+ ( (x*z1) * dx, 0 ),
+ ( (x*z1^2) * dx, 0 ),
+ ( (-x^4*z0^3 + x*z1^3) * dx, 0 ),
+ ( (x*z0) * dx, 0 ),
+ ( (x*z0*z1) * dx, 0 ),
+ ( (x*z0*z1^2) * dx, 0 ),
+ ( (-x^4*z0^4 - 2*x^3*z0^3*z1 + 2*x^2*z0^2*z1^2 + x*z0*z1^3) * dx, 0 ),
+ ( (x*z0^2) * dx, 0 ),
+ ( (x*z0^2*z1) * dx, 0 ),
+ ( (x*z0^2*z1^2) * dx, 0 ),
+ ( (x*z0^3) * dx, 0 ),
+ ( (x*z0^3*z1) * dx, 0 ),
+ ( (x*z0^3*z1^2 - x^5) * dx, 0 ),
+ ( (x*z0^4) * dx, 0 ),
+ ( (x*z0^4*z1) * dx, 0 ),
+ ( (x*z0^4*z1^2 + x^5*z0 - 2*x^4*z1) * dx, 0 ),
+ ( (x^2) * dx, 0 ),
+ ( (x^2*z1) * dx, 0 ),
+ ( (x^2*z1^2) * dx, 0 ),
+ ( (x^2*z0) * dx, 0 ),
+ ( (x^2*z0*z1) * dx, 0 ),
+ ( (-x^4*z0^3 + x^2*z0*z1^2) * dx, 0 ),
+ ( (x^2*z0^2) * dx, 0 ),
+ ( (x^2*z0^2*z1) * dx, 0 ),
+ ( (x^2*z0^3) * dx, 0 ),
+ ( (x^2*z0^3*z1) * dx, 0 ),
+ ( (x^2*z0^4) * dx, 0 ),
+ ( (x^2*z0^4*z1 - x^5) * dx, 0 ),
+ ( (x^3) * dx, 0 ),
+ ( (x^3*z1) * dx, 0 ),
+ ( (x^3*z0) * dx, 0 ),
+ ( (x^3*z0*z1) * dx, 0 ),
+ ( (x^3*z0^2) * dx, 0 ),
+ ( (-x^4*z0^3 + x^3*z0^2*z1) * dx, 0 ),
+ ( (x^3*z0^3) * dx, 0 ),
+ ( (x^3*z0^4) * dx, 0 ),
+ ( (x^4) * dx, 0 ),
+ ( (x^4*z0) * dx, 0 ),
+ ( (x^4*z0^2) * dx, 0 ),
+ ( (-2*x^5) * dx, z1/x ),
+ ( (x^5*z1) * dx, z1^2/x ),
+ ( (-x^5*z1^2) * dx, z1^3/x ),
+ ( (2*x^5*z1^3) * dx, z1^4/x ),
+ ( (-2*x^5*z0) * dx, z0*z1/x ),
+ ( (x^5*z0*z1) * dx, z0*z1^2/x ),
+ ( (-x^5*z0*z1^2) * dx, z0*z1^3/x ),
+ ( (2*x^5*z0*z1^3 - x^4*z0^4 + x^3*z0^3*z1 - 2*x^2*z0^2*z1^2) * dx, z0*z1^4/x ),
+ ( (-2*x^5*z0^2) * dx, z0^2*z1/x ),
+ ( (x^5*z0^2*z1) * dx, z0^2*z1^2/x ),
+ ( (-x^5*z0^2*z1^2) * dx, z0^2*z1^3/x ),
+ ( (2*x^5*z0^2*z1^3 - x^3*z0^4*z1 - x^2*z0^3*z1^2 - x^6 - x*z0^2*z1^3) * dx, z0^2*z1^4/x ),
+ ( (0) * dx, z0^3/x ),
+ ( (-2*x^5*z0^3) * dx, z0^3*z1/x ),
+ ( (x^5*z0^3*z1) * dx, z0^3*z1^2/x ),
+ ( (-x^5*z0^3*z1^2 - x^5) * dx, z0^3*z1^3/x ),
+ ( (2*x^5*z0^3*z1^3 - z0^2*z1^4) * dx, z0^3*z1^4/x ),
+ ( (0) * dx, z0^4/x ),
+ ( (-2*x^5*z0^4) * dx, z0^4*z1/x ),
+ ( (x^5*z0^4*z1) * dx, z0^4*z1^2/x ),
+ ( (-x^5*z0^4*z1^2 + x^5*z0 + x^4*z1) * dx, z0^4*z1^3/x ),
+ ( (2*x^5*z0^4*z1^3 - x^4*z0^3 + 2*z0^3*z1^4) * dx, z0^4*z1^4/x ),
+ ( (x^4*z1) * dx, z1^2/x^2 ),
+ ( (-x^4*z1^2) * dx, z1^3/x^2 ),
+ ( (2*x^4*z1^3) * dx, z1^4/x^2 ),
+ ( (x^4*z0*z1) * dx, z0*z1^2/x^2 ),
+ ( (-x^4*z0*z1^2) * dx, z0*z1^3/x^2 ),
+ ( (2*x^4*z0*z1^3) * dx, z0*z1^4/x^2 ),
+ ( (x^4*z0^2*z1) * dx, z0^2*z1^2/x^2 ),
+ ( (-x^4*z0^2*z1^2) * dx, z0^2*z1^3/x^2 ),
+ ( (2*x^4*z0^2*z1^3 + x^5) * dx, z0^2*z1^4/x^2 ),
+ ( (-2*x^4*z0^3) * dx, z0^3*z1/x^2 ),
+ ( (x^4*z0^3*z1) * dx, z0^3*z1^2/x^2 ),
+ ( (-x^4*z0^3*z1^2) * dx, z0^3*z1^3/x^2 ),
+ ( (2*x^4*z0^3*z1^3 - 2*x^5*z0 + x^4*z1) * dx, z0^3*z1^4/x^2 ),
+ ( (-2*x^4*z0^4) * dx, z0^4*z1/x^2 ),
+ ( (x^4*z0^4*z1) * dx, z0^4*z1^2/x^2 ),
+ ( (-x^4*z0^4*z1^2) * dx, z0^4*z1^3/x^2 ),
+ ( (2*x^4*z0^4*z1^3 + x^5*z0^2 - x^4*z0*z1 + 2*x^3*z1^2) * dx, z0^4*z1^4/x^2 ),
+ ( (-x^3*z1^2) * dx, z1^3/x^3 ),
+ ( (2*x^3*z1^3) * dx, z1^4/x^3 ),
+ ( (-x^3*z0*z1^2) * dx, z0*z1^3/x^3 ),
+ ( (2*x^3*z0*z1^3) * dx, z0*z1^4/x^3 ),
+ ( (-x^3*z0^2*z1^2) * dx, z0^2*z1^3/x^3 ),
+ ( (2*x^3*z0^2*z1^3) * dx, z0^2*z1^4/x^3 ),
+ ( (x^3*z0^3*z1) * dx, z0^3*z1^2/x^3 ),
+ ( (-x^3*z0^3*z1^2) * dx, z0^3*z1^3/x^3 ),
+ ( (2*x^3*z0^3*z1^3) * dx, z0^3*z1^4/x^3 ),
+ ( (x^3*z0^4*z1) * dx, z0^4*z1^2/x^3 ),
+ ( (-x^3*z0^4*z1^2) * dx, z0^4*z1^3/x^3 ),
+ ( (2*x^3*z0^4*z1^3) * dx, z0^4*z1^4/x^3 ),
+ ( (2*x^2*z1^3) * dx, z1^4/x^4 ),
+ ( (2*x^2*z0*z1^3) * dx, z0*z1^4/x^4 ),
+ ( (-x^2*z0^2*z1^2) * dx, z0^2*z1^3/x^4 ),
+ ( (2*x^2*z0^2*z1^3) * dx, z0^2*z1^4/x^4 ),
+ ( (-x^2*z0^3*z1^2) * dx, z0^3*z1^3/x^4 ),
+ ( (2*x^2*z0^3*z1^3) * dx, z0^3*z1^4/x^4 ),
+ ( (-x^2*z0^4*z1^2) * dx, z0^4*z1^3/x^4 ),
+ ( (2*x^2*z0^4*z1^3) * dx, z0^4*z1^4/x^4 ),
+ ( (2*x*z0^2*z1^3) * dx, z0^2*z1^4/x^5 ),
+ ( (2*x*z0^3*z1^3) * dx, z0^3*z1^4/x^5 ),
+ ( (2*x*z0^4*z1^3) * dx, z0^4*z1^4/x^5 )]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l_(AS)[?7h[?12l[?25h[?25l[?7ld(AS)[?7h[?12l[?25h[?25l[?7lr(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7lR(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS); magma

+ magma     

+ magma_free

+ magmathis 

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+ magma     

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_free

+ magma     

+ magma_free[?7h[?12l[?25h[?25l[?7lthis

+

+ magma_free

+ magmathis [?7h[?12l[?25h[?25l[?7l

+

+

+

+[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS); magmathis(A, B)

+[?7h[?12l[?25h[?2004l
+
+^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[24;1R^[[25;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R
+
+^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[24;1R^[[25;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[28;1R^[[2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [1;3S[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^3
+z1^2 - z1 = x^5
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS); magmathis(A, B)[?7h[?12l[?25h[?25l[?7lS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ljumps[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: AS.jumps

+[?7h[?12l[?25h[?2004l[?7h[[3, 7]]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lraification_jumps()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lfication_jumps()[?7h[?12l[?25h[?25l[?7lsage: AS.ramification_jumps()

+[?7h[?12l[?25h[?2004l[?7h[3, 7]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.ramification_jumps()[?7h[?12l[?25h[?25l[?7ljups[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^3
+z1^2 - z1 = x^7
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.ramification_jumps()[?7h[?12l[?25h[?25l[?7ljups[?7h[?12l[?25h[?25l[?7lsage: AS.jumps

+[?7h[?12l[?25h[?2004l[?7h[[3, 11]]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 3 [[3, 11]] 1 5
+^C---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [6], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:16, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+File <string>:134, in artin_schreier_transform(power_series, prec)
+
+File <string>:12, in new_reverse(power_series, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1829 if x:
+   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
+-> 1831 a = self(kwds[name])
+   1832 del kwds[name]
+   1833 try:
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1850         x = x[0]
+   1851 
+-> 1852     return self.__u(*x)*(x[0]**self.__n)
+   1853 
+   1854 def __pari__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
+    363         x[0] = a
+    364         x = tuple(x)
+--> 365     return self.__f(x)
+    366 
+    367 def _unsafe_mutate(self, i, value):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
+    896             return result
+    897         pol._compiled = CompiledPolynomialFunction(pol.list())
+--> 898     return pol._compiled.eval(a)
+    899 
+    900 def compose_trunc(self, Polynomial other, long n):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
+    123 cdef object temp
+    124 try:
+--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
+    126     temp = self._dag.value               #for an explanation
+    127     pd_clean(self._dag)                  #of these 3 lines
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (96 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (95 times)]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    507 pd_eval(self.left, vars, coeffs)
+    508 pd_eval(self.right, vars, coeffs)
+--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
+    510 pd_clean(self.left)
+    511 pd_clean(self.right)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1233, in sage.structure.element.Element.__add__()
+   1231 # Left and right are Sage elements => use coercion model
+   1232 if BOTH_ARE_ELEMENT(cl):
+-> 1233     return coercion_model.bin_op(left, right, add)
+   1234 
+   1235 cdef long value
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1204, in sage.structure.coerce.CoercionModel.bin_op()
+   1202     self._record_exception()
+   1203 else:
+-> 1204     return PyObject_CallObject(op, xy)
+   1205 
+   1206 if op is mul:
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1230, in sage.structure.element.Element.__add__()
+   1228 cdef int cl = classify_elements(left, right)
+   1229 if HAVE_SAME_PARENT(cl):
+-> 1230     return (<Element>left)._add_(right)
+   1231 # Left and right are Sage elements => use coercion model
+   1232 if BOTH_ARE_ELEMENT(cl):
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:764, in sage.rings.laurent_series_ring_element.LaurentSeries._add_()
+    762 elif self.__n > right.__n:
+    763     m = right.__n
+--> 764     f1 = self.__u << self.__n - m
+    765     f2 = right.__u
+    766 else:
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:583, in sage.rings.power_series_poly.PowerSeries_poly.__lshift__()
+    581 """
+    582 if n:
+--> 583     return PowerSeries_poly(self._parent, self.__f << n, self._prec + n)
+    584 else:
+    585     return self
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
+     42     ValueError: series has negative valuation
+     43 """
+---> 44 R = parent._poly_ring()
+     45 if isinstance(f, Element):
+     46     if (<Element>f)._parent is R:
+
+File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
+    958         pass
+    959     return False
+--> 961 def _poly_ring(self):
+    962     """
+    963     Return the underlying polynomial ring used to represent elements of
+    964     this power series ring.
+   (...)
+    970         Univariate Polynomial Ring in t over Integer Ring
+    971     """
+    972     return self.__poly_ring
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 3 [[3, 11]] 1 5
+1 5 [[3, 11]] 1 9
+1 7 [[3, 11]] 1 13
+1 9 [[3, 11]] 1 17
+1 11 [[3, 11]] 1 21
+1 13 [[3, 11]] 1 25
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+7 9 [[3, 11]] 7 11
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+7 13 [[3, 11]] 7 19
+9 11 [[3, 11]] 9 13
+9 13 [[3, 11]] 9 17
+11 13 [[3, 11]] 11 15
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
+1 5 [[1, 9]] 1 9
+1 7 [[1, 13]] 1 13
+1 9 [[1, 17]] 1 17
+1 11 [[1, 21]] 1 21
+1 13 [[1, 25]] 1 25
+3 5 [[3, 7]] 3 7
+3 7 [[3, 11]] 3 11
+3 9 [[3, 15]] 3 15
+3 11 [[3, 19]] 3 19
+3 13 [[3, 23]] 3 23
+5 7 [[5, 9]] 5 9
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+5 11 [[5, 17]] 5 17
+5 13 [[5, 21]] 5 21
+7 9 [[7, 11]] 7 11
+7 11 [[7, 15]] 7 15
+7 13 [[7, 19]] 7 19
+9 11 [[9, 13]] 9 13
+9 13 [[9, 17]] 9 17
+11 13 [[11, 15]] 11 15
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^11
+z1^2 - z1 = x^13
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.jumps[?7h[?12l[?25h[?25l[?7lraification_jumps()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lfication_jumps()[?7h[?12l[?25h[?25l[?7lsage: AS.ramification_jumps()

+[?7h[?12l[?25h[?2004l[?7h[11, 15]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.ramification_jumps()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

+[?7h[?12l[?25h[?2004l[?7h37
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
+3 7
+1 5 [[1, 9]] 1 9
+7 11
+1 7 [[1, 13]] 1 13
+11 15
+1 9 [[1, 17]] 1 17
+15 19
+1 11 [[1, 21]] 1 21
+19 23
+1 13 [[1, 25]] 1 25
+23 27
+3 5 [[3, 7]] 3 7
+9 13
+3 7 [[3, 11]] 3 11
+13 17
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+17 21
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+21 25
+3 13 [[3, 23]] 3 23
+25 29
+5 7 [[5, 9]] 5 9
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+23 27
+5 13 [[5, 21]] 5 21
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+29 33
+9 11 [[9, 13]] 9 13
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+31 35
+11 13 [[11, 15]] 11 15
+33 37
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
+7 7
+1 5 [[1, 9]] 1 9
+11 11
+1 7 [[1, 13]] 1 13
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+27 27
+5 13 [[5, 21]] 5 21
+31 31
+7 9 [[7, 11]] 7 11
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+33 33
+9 11 [[9, 13]] 9 13
+31 31
+9 13 [[9, 17]] 9 17
+35 35
+11 13 [[11, 15]] 11 15
+37 37
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lzmag = AS.magical_element(threshold = 18)[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l.jorda_form(subdivide=True)[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[1]^2/AS.x*AS.dx[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: AS.z[0]*AS.z[1]

+[?7h[?12l[?25h[?2004l[?7hz0*z1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]).norm()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [15], in <cell line: 1>()
+----> 1 (AS.z[Integer(0)]*AS.z[Integer(1)]).norm()
+
+AttributeError: 'as_function' object has no attribute 'norm'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lprint((identity_matrix(n) + A2.transpose()*A2).determinant()%p)[?7h[?12l[?25h[?25l[?7l = q.factor()[0][0][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]*AS.z[1][?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lal_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

+[?7h[?12l[?25h[?2004l[?7h[]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element(threshold=20)

+[?7h[?12l[?25h[?2004l[?7h[x^12 + z0*z1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lare_equivalent_matrix(A1, A2, q)[?7h[?12l[?25h[?25l[?7lsage: a

+[?7h[?12l[?25h[?2004l[?7h13
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: b

+[?7h[?12l[?25h[?2004l[?7h13
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]*AS.z[1]).norm()[?7h[?12l[?25h[?25l[?7la^8 + a^7 + a^5 + a^3 + a^2)^2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (a+b)/2

+[?7h[?12l[?25h[?2004l[?7h13
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^11
+z1^2 - z1 = x^13
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a+b)/2[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (11+13)/2

+[?7h[?12l[?25h[?2004l[?7h12
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
+7 7
+1 5 [[1, 9]] 1 9
+11 11
+1 7 [[1, 13]] 1 13
+15 15
+1 9 [[1, 17]] 1 17
+19 19
+1 11 [[1, 21]] 1 21
+23 23
+1 13 [[1, 25]] 1 25
+27 27
+3 5 [[3, 7]] 3 7
+13 13
+3 7 [[3, 11]] 3 11
+17 17
+3 9 [[3, 15]] 3 15
+21 21
+3 11 [[3, 19]] 3 19
+25 25
+3 13 [[3, 23]] 3 23
+29 29
+5 7 [[5, 9]] 5 9
+19 19
+5 9 [[5, 13]] 5 13
+23 23
+5 11 [[5, 17]] 5 17
+27 27
+5 13 [[5, 21]] 5 21
+31 31
+7 9 [[7, 11]] 7 11
+25 25
+7 11 [[7, 15]] 7 15
+29 29
+7 13 [[7, 19]] 7 19
+33 33
+9 11 [[9, 13]] 9 13
+31 31
+9 13 [[9, 17]] 9 17
+35 35
+11 13 [[11, 15]] 11 15
+37 37
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element(threshold=20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

+[?7h[?12l[?25h[?2004l[?7h[(a + 1)*x^3 + z0*z1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l16.factor()[0][0][?7h[?12l[?25h[?25l[?7l/(a^13 + a^12 + a^11 + a^9 + a^8 + a^4 + a^3 + a)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 1/(a+1)

+[?7h[?12l[?25h[?2004l[?7ha
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[x^6*z0 + x^5*z1 + x^4*z0 + x^4*z2 + z0*z1*z2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[x^7*z0 + x^6*z1 + x^5*z0 + x^4*z2 + z0*z1*z2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[x^7*z0 + x^6*z0 + x^6*z1 + x^5*z0 + x^5*z1 + x^4*z2 + z0*z1*z2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
+********************************************************************************
+Denominators of fraction field elements are sometimes dropped without warning.
+This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
+********************************************************************************
+>> A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1
+                                  ^
+User error: Identifier 'a' has not been declared or assigned
+>> , 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);Indecomposab
+                                                               ^
+User error: Identifier 'A' has not been declared or assigned
+>> ,6), A);IndecomposableSummands(M);
+                                  ^
+User error: Identifier 'M' has not been declared or assigned
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 3 over GF(2^2),
+RModule of dimension 3 over GF(2^2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [4], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:16, in <module>
+
+TypeError: group_action_matrices_holo() got an unexpected keyword argument 'threshold'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 1 over GF(2^2),
+RModule of dimension 2 over GF(2^2)
+]
+[
+RModule of dimension 3 over GF(2^2),
+RModule of dimension 3 over GF(2^2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 1 over GF(2^2),
+RModule of dimension 2 over GF(2^2),
+RModule of dimension 3 over GF(2^2)
+]
+[
+RModule of dimension 3 over GF(2^2),
+RModule of dimension 3 over GF(2^2),
+RModule of dimension 3 over GF(2^2),
+RModule of dimension 3 over GF(2^2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 1 over GF(2^2),
+RModule of dimension 1 over GF(2^2),
+RModule of dimension 2 over GF(2^2),
+RModule of dimension 2 over GF(2^2),
+RModule of dimension 3 over GF(2^2)
+]
+[
+RModule of dimension 3 over GF(2^2),
+RModule of dimension 3 over GF(2^2),
+RModule of dimension 3 over GF(2^2),
+RModule of dimension 3 over GF(2^2),
+RModule of dimension 3 over GF(2^2),
+RModule of dimension 3 over GF(2^2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 1 over GF(2^2),
+RModule of dimension 2 over GF(2^2)
+]
+[
+RModule of dimension 3 over GF(2^2),
+RModule of dimension 3 over GF(2^2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 1 over GF(2^2),
+RModule of dimension 2 over GF(2^2)
+]
+F<a> := GF(4);A := MatrixAlgebra<GF(4),6|[1, a + 1, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(4),6), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 1 over GF(2),
+RModule of dimension 4 over GF(2)
+]
+F<a> := GF(4);A := MatrixAlgebra<GF(2),10|[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(2),10), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 1 over GF(2),
+RModule of dimension 4 over GF(2)
+]
+[
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 1 over GF(2),
+RModule of dimension 4 over GF(2)
+]
+A := MatrixAlgebra<GF(2),10|[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(2),10), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004lWARNING: your terminal doesn't support cursor position requests (CPR).

+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 1 over GF(2),
+RModule of dimension 4 over GF(2)
+]
+^C^C
+KeyboardInterrupt
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 3 [[1, 5]] 1 5
+7 7
+1 5 [[1, 9]] 1 9
+11 11
+1 7 [[1, 13]] 1 13
+15 15
+^C---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
+    279 try:
+--> 280     if a.parent() is not K:
+    281         a = K.coerce(a)
+
+AttributeError: 'tuple' object has no attribute 'parent'
+
+During handling of the above exception, another exception occurred:
+
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [2], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+File <string>:134, in artin_schreier_transform(power_series, prec)
+
+File <string>:12, in new_reverse(power_series, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1829 if x:
+   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
+-> 1831 a = self(kwds[name])
+   1832 del kwds[name]
+   1833 try:
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1850         x = x[0]
+   1851 
+-> 1852     return self.__u(*x)*(x[0]**self.__n)
+   1853 
+   1854 def __pari__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
+    363         x[0] = a
+    364         x = tuple(x)
+--> 365     return self.__f(x)
+    366 
+    367 def _unsafe_mutate(self, i, value):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
+    281         a = K.coerce(a)
+    282 except (TypeError, AttributeError, NotImplementedError):
+--> 283     return Polynomial.__call__(self, a)
+    284 
+    285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
+    896             return result
+    897         pol._compiled = CompiledPolynomialFunction(pol.list())
+--> 898     return pol._compiled.eval(a)
+    899 
+    900 def compose_trunc(self, Polynomial other, long n):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
+    123 cdef object temp
+    124 try:
+--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
+    126     temp = self._dag.value               #for an explanation
+    127     pd_clean(self._dag)                  #of these 3 lines
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (10 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (9 times)]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    507 pd_eval(self.left, vars, coeffs)
+    508 pd_eval(self.right, vars, coeffs)
+--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
+    510 pd_clean(self.left)
+    511 pd_clean(self.right)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:912, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
+    910 """
+    911 cdef LaurentSeries right = <LaurentSeries>right_r
+--> 912 return type(self)(self._parent,
+    913                   self.__u * right.__u,
+    914                   self.__n + right.__n)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:165, in sage.rings.laurent_series_ring_element.LaurentSeries.__init__()
+    163         self.__u = f
+    164 else:
+--> 165     val = f.valuation()
+    166     if val is infinity:
+    167         self.__n = 0
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:134, in sage.rings.power_series_poly.PowerSeries_poly.valuation()
+    132         return self._prec
+    133 
+--> 134     return self.__f.valuation()
+    135 
+    136 def degree(self):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:9215, in sage.rings.polynomial.polynomial_element.Polynomial.valuation()
+   9213 if p is None:
+   9214     for k from 0 <= k <= self.degree():
+-> 9215         if self.get_unsafe(k):
+   9216             return ZZ(k)
+   9217 if isinstance(p, Polynomial):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:179, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.get_unsafe()
+    177     self._parent._modulus.restore()
+    178     cdef ZZ_pE_c c_pE = ZZ_pEX_coeff(self.x, i)
+--> 179     return self._parent._base(ZZ_pE_c_to_list(c_pE))
+    180 
+    181 cpdef list list(self, bint copy=True):
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/finite_field_givaro.py:229, in FiniteField_givaro._element_constructor_(self, e)
+    211     """
+    212     Return a random element of ``self``.
+    213 
+   (...)
+    225         True
+    226     """
+    227     return self._cache.random_element()
+--> 229 def _element_constructor_(self, e):
+    230     """
+    231     Coerces several data types to ``self``.
+    232 
+   (...)
+    368         2*a4^3 + 2*a4^2 + 1
+    369     """
+    370     return self._cache.element_from_data(e)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 2 [[1, 4]] 1 4
+7 14
+1 4 [[1, 10]] 1 10
+13 26
+^C---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
+    279 try:
+--> 280     if a.parent() is not K:
+    281         a = K.coerce(a)
+
+AttributeError: 'tuple' object has no attribute 'parent'
+
+During handling of the above exception, another exception occurred:
+
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [3], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+File <string>:134, in artin_schreier_transform(power_series, prec)
+
+File <string>:12, in new_reverse(power_series, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1829 if x:
+   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
+-> 1831 a = self(kwds[name])
+   1832 del kwds[name]
+   1833 try:
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1850         x = x[0]
+   1851 
+-> 1852     return self.__u(*x)*(x[0]**self.__n)
+   1853 
+   1854 def __pari__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
+    363         x[0] = a
+    364         x = tuple(x)
+--> 365     return self.__f(x)
+    366 
+    367 def _unsafe_mutate(self, i, value):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
+    281         a = K.coerce(a)
+    282 except (TypeError, AttributeError, NotImplementedError):
+--> 283     return Polynomial.__call__(self, a)
+    284 
+    285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
+    896             return result
+    897         pol._compiled = CompiledPolynomialFunction(pol.list())
+--> 898     return pol._compiled.eval(a)
+    899 
+    900 def compose_trunc(self, Polynomial other, long n):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
+    123 cdef object temp
+    124 try:
+--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
+    126     temp = self._dag.value               #for an explanation
+    127     pd_clean(self._dag)                  #of these 3 lines
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (13 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (12 times)]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    507 pd_eval(self.left, vars, coeffs)
+    508 pd_eval(self.right, vars, coeffs)
+--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
+    510 pd_clean(self.left)
+    511 pd_clean(self.right)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
+    911 cdef LaurentSeries right = <LaurentSeries>right_r
+    912 return type(self)(self._parent,
+--> 913                   self.__u * right.__u,
+    914                   self.__n + right.__n)
+    915 
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:539, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
+    537     19*w^10 + 323*w^11 + O(w^12)
+    538 """
+--> 539 prec = self._mul_prec(right_r)
+    540 return PowerSeries_poly(self._parent,
+    541                         self.__f * (<PowerSeries_poly>right_r).__f,
+
+File /ext/sage/9.7/src/sage/rings/power_series_ring_element.pyx:949, in sage.rings.power_series_ring_element.PowerSeries._mul_prec()
+    947         prec = sp + right.valuation()
+    948     else:
+--> 949         prec = min(rp + self.valuation(), sp + right.valuation())
+    950 # endif
+    951 return prec
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:131, in sage.rings.power_series_poly.PowerSeries_poly.valuation()
+    129     +Infinity
+    130 """
+--> 131 if self.__f == 0:
+    132     return self._prec
+    133 
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1112, in sage.structure.element.Element.__richcmp__()
+   1110         return (<Element>self)._richcmp_(other, op)
+   1111     else:
+-> 1112         return coercion_model.richcmp(self, other, op)
+   1113 
+   1114 cpdef _richcmp_(left, right, int op):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1973, in sage.structure.coerce.CoercionModel.richcmp()
+   1971 # Coerce to a common parent
+   1972 try:
+-> 1973     x, y = self.canonical_coercion(x, y)
+   1974 except (TypeError, NotImplementedError):
+   1975     pass
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
+   1313     x_elt = x
+   1314 if y_map is not None:
+-> 1315     y_elt = (<Map>y_map)._call_(y)
+   1316 else:
+   1317     y_elt = y
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:1692, in sage.categories.map.FormalCompositeMap._call_()
+   1690 """
+   1691 for f in self.__list:
+-> 1692     x = f._call_(x)
+   1693 return x
+   1694 
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:153, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    151 argument is assumed to be bound to the codomain).
+    152 """
+--> 153 cpdef Element _call_(self, x):
+    154     cdef Parent C = self._codomain
+    155     try:
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/finite_field_givaro.py:229, in FiniteField_givaro._element_constructor_(self, e)
+    211     """
+    212     Return a random element of ``self``.
+    213 
+   (...)
+    225         True
+    226     """
+    227     return self._cache.random_element()
+--> 229 def _element_constructor_(self, e):
+    230     """
+    231     Coerces several data types to ``self``.
+    232 
+   (...)
+    368         2*a4^3 + 2*a4^2 + 1
+    369     """
+    370     return self._cache.element_from_data(e)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [4] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:21 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:28
+    print((p-_sage_const_1 )*(a+p*b, AS.exponent_of_different_prim())
+         ^
+SyntaxError: '(' was never closed
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 2 [[1, 4]] 1 4
+14 14
+1 4 [[1, 10]] 1 10
+26 26
+1 5 [[1, 13]] 1 13
+32 32
+1 7 [[1, 19]] 1 19
+44 44
+1 8 [[1, 22]] 1 22
+50 50
+1 10 [[1, 28]] 1 28
+62 62
+1 11 [[1, 31]] 1 31
+68 68
+^C---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
+    279 try:
+--> 280     if a.parent() is not K:
+    281         a = K.coerce(a)
+
+AttributeError: 'tuple' object has no attribute 'parent'
+
+During handling of the above exception, another exception occurred:
+
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [5], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+File <string>:134, in artin_schreier_transform(power_series, prec)
+
+File <string>:12, in new_reverse(power_series, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1829 if x:
+   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
+-> 1831 a = self(kwds[name])
+   1832 del kwds[name]
+   1833 try:
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1850         x = x[0]
+   1851 
+-> 1852     return self.__u(*x)*(x[0]**self.__n)
+   1853 
+   1854 def __pari__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
+    363         x[0] = a
+    364         x = tuple(x)
+--> 365     return self.__f(x)
+    366 
+    367 def _unsafe_mutate(self, i, value):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
+    281         a = K.coerce(a)
+    282 except (TypeError, AttributeError, NotImplementedError):
+--> 283     return Polynomial.__call__(self, a)
+    284 
+    285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
+    896             return result
+    897         pol._compiled = CompiledPolynomialFunction(pol.list())
+--> 898     return pol._compiled.eval(a)
+    899 
+    900 def compose_trunc(self, Polynomial other, long n):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
+    123 cdef object temp
+    124 try:
+--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
+    126     temp = self._dag.value               #for an explanation
+    127     pd_clean(self._dag)                  #of these 3 lines
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (5 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (4 times)]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    507 pd_eval(self.left, vars, coeffs)
+    508 pd_eval(self.right, vars, coeffs)
+--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
+    510 pd_clean(self.left)
+    511 pd_clean(self.right)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1233, in sage.structure.element.Element.__add__()
+   1231 # Left and right are Sage elements => use coercion model
+   1232 if BOTH_ARE_ELEMENT(cl):
+-> 1233     return coercion_model.bin_op(left, right, add)
+   1234 
+   1235 cdef long value
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1200, in sage.structure.coerce.CoercionModel.bin_op()
+   1198 # Now coerce to a common parent and do the operation there
+   1199 try:
+-> 1200     xy = self.canonical_coercion(x, y)
+   1201 except TypeError:
+   1202     self._record_exception()
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1315, in sage.structure.coerce.CoercionModel.canonical_coercion()
+   1313     x_elt = x
+   1314 if y_map is not None:
+-> 1315     y_elt = (<Map>y_map)._call_(y)
+   1316 else:
+   1317     y_elt = y
+
+File /ext/sage/9.7/src/sage/categories/morphism.pyx:601, in sage.categories.morphism.SetMorphism._call_()
+    599         3
+    600     """
+--> 601     return self._function(x)
+    602 
+    603 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:919, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_()
+    917     return type(self)(self._parent, self.__u._rmul_(c), self.__n)
+    918 
+--> 919 cpdef _lmul_(self, Element c):
+    920     return type(self)(self._parent, self.__u._lmul_(c), self.__n)
+    921 
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:920, in sage.rings.laurent_series_ring_element.LaurentSeries._lmul_()
+    918 
+    919     cpdef _lmul_(self, Element c):
+--> 920         return type(self)(self._parent, self.__u._lmul_(c), self.__n)
+    921 
+    922     def __pow__(_self, r, dummy):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:569, in sage.rings.power_series_poly.PowerSeries_poly._lmul_()
+    567         2 + 6*t^4 + O(t^120)
+    568     """
+--> 569     return PowerSeries_poly(self._parent, c * self.__f, self._prec, check=False)
+    570 
+    571 def __lshift__(PowerSeries_poly self, n):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1516, in sage.structure.element.Element.__mul__()
+   1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+-> 1516     return coercion_model.bin_op(left, right, mul)
+   1517 
+   1518 cdef long value
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1194, in sage.structure.coerce.CoercionModel.bin_op()
+   1192 if action is not None:
+   1193     if (<Action>action)._is_left:
+-> 1194         return (<Action>action)._act_(x, y)
+   1195     else:
+   1196         return (<Action>action)._act_(y, x)
+
+File /ext/sage/9.7/src/sage/structure/coerce_actions.pyx:612, in sage.structure.coerce_actions.LeftModuleAction._act_()
+    610 if self.extended_base is not None:
+    611     a = <ModuleElement?>self.extended_base(a)
+--> 612 return (<ModuleElement>a)._rmul_(<Element>g)  # g * a
+    613 
+    614 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:400, in sage.rings.polynomial.polynomial_element.Polynomial._rmul_()
+    398     if not right:
+    399         return self._parent.zero()
+--> 400     return self * self._parent(right)
+    401 
+    402 def subs(self, *x, **kwds):
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:12221, in sage.rings.polynomial.polynomial_element.PolynomialBaseringInjection._call_()
+  12219         Univariate Polynomial Ring in x over Integer Ring
+  12220     """
+> 12221     return self._new_constant_poly_(x, self._codomain)
+  12222 
+  12223 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:5449, in sage.rings.polynomial.polynomial_element.Polynomial._new_constant_poly()
+   5447     return self.get_unsafe(0)
+   5448 
+-> 5449 cpdef Polynomial _new_constant_poly(self, a, Parent P):
+   5450     """
+   5451     Create a new constant polynomial from a in P, which MUST be an
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:5463, in sage.rings.polynomial.polynomial_element.Polynomial._new_constant_poly()
+   5461     """
+   5462     t = type(self)
+-> 5463     return t(P, [a] if a else [], check=False)
+   5464 
+   5465 def is_monic(self):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:151, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__init__()
+    149     # not do K.coerce(e) but K(e).
+    150     e = K(e)
+--> 151     d = parent._modulus.ZZ_pE(list(e.polynomial()))
+    152     ZZ_pEX_SetCoeff(self.x, i, d.x)
+    153 return
+
+File /ext/sage/9.7/src/sage/libs/ntl/ntl_ZZ_pEContext.pyx:149, in sage.libs.ntl.ntl_ZZ_pEContext.ntl_ZZ_pEContext_class.ZZ_pE()
+    147     [4 3]
+    148 """
+--> 149 from .ntl_ZZ_pE import ntl_ZZ_pE
+    150 return ntl_ZZ_pE(v,modulus=self)
+    151 
+
+File <frozen importlib._bootstrap>:404, in parent(self)
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l1 2 [[1, 6]] 1 6
+44 44
+1 3 [[1, 11]] 1 11
+64 64
+1 4 [[1, 16]] 1 16
+84 84
+1 6 [[1, 26]] 1 26
+124 124
+1 7 [[1, 31]] 1 31
+144 144
+no  36 -th root; divide by 2
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [6], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:26, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 5^2 with the equations:
+z0^5 - z0 = x
+z1^5 - z1 = x^7
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 5^2 with the equations:
+z0^5 - z0 = x
+z1^5 - z1 = x^7
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lz[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0]*AS.z[1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]^*AS.z[1][?7h[?12l[?25h[?25l[?7l(*AS.z[1][?7h[?12l[?25h[?25l[?7l()*AS.z[1][?7h[?12l[?25h[?25l[?7l()p*AS.z[1][?7h[?12l[?25h[?25l[?7l-*AS.z[1][?7h[?12l[?25h[?25l[?7l*AS.z[1][?7h[?12l[?25h[?25l[?7l()*AS.z[1][?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)*AS.z[1][?7h[?12l[?25h[?25l[?7l-)*AS.z[1][?7h[?12l[?25h[?25l[?7l1)*AS.z[1][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lno  8 -th root; divide by 2
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [9], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:37, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 5 with the equations:
+z0^5 - z0 = x^3
+z1^5 - z1 = 3*x^4
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lz[0]*AS.z[1][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[]*AS.z[1][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.z[0]^(p-1)*AS.z[1]^(p-1)

+[?7h[?12l[?25h[?2004l[?7hz0^4*z1^4
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]^(p-1)*AS.z[1]^(p-1)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [13], in <cell line: 1>()
+----> 1 AS.z[Integer(0)]**(p-Integer(1))*AS.z[Integer(1)]**(p-Integer(1)).valuation()
+
+TypeError: Integer.valuation() takes exactly one argument (0 given)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).valuation()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^(p-1)*AS.z[1]^(p-1)).valuation()

+[?7h[?12l[?25h[?2004l[?7h-140
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4*Q[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lcal_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

+[?7h[?12l[?25h[?2004l[?7h[z0^4*z1^4 + 2*x^3*z0^3*z1 - 2*x^2*z0^2*z1^3 + x^5*z0 - x^4*z1^2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

+[?7h[?12l[?25h[?2004l[?7h92
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lA)[?7h[?12l[?25h[?25l[?7lS)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lz)[?7h[?12l[?25h[?25l[?7l[)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^3*AS.z[1]).valuation()

+[?7h[?12l[?25h[?2004l[?7h-65
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*AS.z[1]).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l^).valuation()[?7h[?12l[?25h[?25l[?7l3).valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l2*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^2*AS.z[1]^3).valuation()

+[?7h[?12l[?25h[?2004l[?7h-90
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lno  18 -th root; divide by 3
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [19], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:37, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l\[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l\[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[0]^2*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l3).valuation()[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

+[?7h[?12l[?25h[?2004l[?7h132
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lcal_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

+[?7h[?12l[?25h[?2004l[?7h[x^6*z0^2 - x^3*z0^3*z1^2 + z0^4*z1^4 - 2*x^6*z1 + 2*x^3*z0*z1^3]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^2*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.z[0]^2*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l3*AS.z[1]^3).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l2).valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^3*AS.z[1]^2).valuation()

+[?7h[?12l[?25h[?2004l[?7h-105
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*AS.z[1]^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element()[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element()

+[?7h[?12l[?25h[?2004l[?7h[]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ld)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element(threshold=20)

+[?7h[?12l[?25h[?2004l[?7h[x^8 + x^6*z0*z1 + x^4*z0^2*z1^2 + x^2*z0^3*z1^3 + z0^4*z1^4]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*AS.z[1]^2).valuation()[?7h[?12l[?25h[?25l[?7lAS.magical_element()[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

+[?7h[?12l[?25h[?2004l[?7h152
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lmagical_element(threshold=20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[0]^3*AS.z[1]^2).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l3).valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]^3*AS.z[1]^3).valuation()

+[?7h[?12l[?25h[?2004l[?7h-150
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lmagical_element(threshold=20)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element(threshold=20)

+[?7h[?12l[?25h[?2004l[?7h[x^8 + x^4*z0*z1 + z0^2*z1^2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lexponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different_prim()

+[?7h[?12l[?25h[?2004l[?7h52
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different_prim()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()).valuation()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[]*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(().valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l().valuation()[?7h[?12l[?25h[?25l[?7l).valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]).valuation()

+[?7h[?12l[?25h[?2004l[?7h-36
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(AS.z[0]*AS.z[1]).valuation()[?7h[?12l[?25h[?25l[?7lAS.exponent_of_differen_prim()[?7h[?12l[?25h[?25l[?7lmagical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lsage: AS.magical_element(threshold=20)

+[?7h[?12l[?25h[?2004l[?7h[x^6*z0 + x^5*z1 + z0^2*z1^2]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.magical_element(threshold=20)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentias_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?7h[(1) * dx,
+ (x^3*z0 + z1) * dx,
+ (z0) * dx,
+ (x) * dx,
+ (x*z0) * dx,
+ (x^2) * dx,
+ (x^2*z0) * dx,
+ (x^3) * dx,
+ (x^4) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 2 with the equations:
+z0^2 - z0 = x^3
+z1^2 - z1 = x^9
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lus()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

+[?7h[?12l[?25h[?2004l[?7h3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?7h[(1) * dx, ((a + 1)*z0 + z1) * dx, (x) * dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

+[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
+********************************************************************************
+Denominators of fraction field elements are sometimes dropped without warning.
+This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
+********************************************************************************
+[?7h[( (1) * dx, 0 ),
+ ( ((a + 1)*z0 + z1) * dx, 0 ),
+ ( (x) * dx, 0 ),
+ ( (0) * dx, z1/x ),
+ ( (a*x*z0 + x*z1) * dx, z0*z1/x ),
+ ( (a*z0 + z1) * dx, z0*z1/x^2 )]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a+1)[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l(+1)[?7h[?12l[?25h[?25l[?7lsage: 1/(a+1)

+[?7h[?12l[?25h[?2004l[?7ha
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a+1)[?7h[?12l[?25h[?25l[?7lsage: 1/(a+1)

+[?7h[?12l[?25h[?2004l[?7ha
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a+1)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lno  3 -th root; divide by a^2 + a + 1
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [4], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:14, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

+[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
+********************************************************************************
+Denominators of fraction field elements are sometimes dropped without warning.
+This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
+********************************************************************************
+[?7h[( (1) * dx, 0 ),
+ ( ((a^2 + a)*z0 + z1) * dx, 0 ),
+ ( (x) * dx, 0 ),
+ ( (0) * dx, z1/x ),
+ ( (a*x*z0 + x*z1) * dx, z0*z1/x ),
+ ( (a*z0 + z1) * dx, z0*z1/x^2 )]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a+1)[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^3 + a^12 + a^11 + a^9 + a^8 + a^4 + a^3 + a)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: 1/(a^2+a)

+[?7h[?12l[?25h[?2004l[?7ha + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^3[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: a^2

+[?7h[?12l[?25h[?2004l[?7ha^2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^2[?7h[?12l[?25h[?25l[?7l1/(a^2+a)[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: 1/(a^2+a)^2

+[?7h[?12l[?25h[?2004l[?7ha^2 + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a^2+a)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(a^2+a)^2[?7h[?12l[?25h[?25l[?7l(a^2+a)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (a^2+a)^2

+[?7h[?12l[?25h[?2004l[?7ha
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: AS.dx

+[?7h[?12l[?25h[?2004l[?7h(1) * dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.dx.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7h(a + 1)*t^4 + a*t^16 + t^22 + a^2*t^52 + t^64 + (a^2 + 1)*t^70 + (a^2 + a + 1)*t^76 + (a + 1)*t^88 + a^2*t^94 + (a^2 + 1)*t^196 + (a^2 + a)*t^208 + (a + 1)*t^214 + (a^2 + a + 1)*t^244 + (a + 1)*t^256 + a^2*t^262 + a*t^268 + (a^2 + 1)*t^280 + (a^2 + a + 1)*t^286 + (a^2 + a)*t^292 + O(t^295)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^3 with the equations:
+z0^2 - z0 = x^3
+z1^2 - z1 = a*x^3
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: AS.x.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ha*t^-4 + t^2 + (a + 1)*t^5 + (a^2 + 1)*t^8 + a*t^17 + (a^2 + a)*t^20 + t^23 + t^44 + (a^2 + 1)*t^50 + a^2*t^53 + (a^2 + a + 1)*t^56 + t^65 + (a^2 + 1)*t^71 + a^2*t^74 + (a^2 + a + 1)*t^77 + a*t^80 + (a + 1)*t^89 + (a^2 + 1)*t^92 + a^2*t^95 + (a^2 + a)*t^188 + (a + 1)*t^194 + (a^2 + 1)*t^197 + a^2*t^200 + (a^2 + a)*t^209 + t^212 + (a + 1)*t^215 + (a + 1)*t^236 + a^2*t^242 + (a^2 + a + 1)*t^245 + a*t^248 + (a + 1)*t^257 + a^2*t^263 + (a^2 + a + 1)*t^266 + a*t^269 + (a^2 + a)*t^272 + (a^2 + 1)*t^281 + (a^2 + a + 1)*t^287 + a*t^290 + (a^2 + a)*t^293 + O(t^296)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lexponet_fdifferent_prim()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonent_of_different_prim()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_differen()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [15], in <cell line: 1>()
+----> 1 AS.exponent_of_differen()
+
+AttributeError: 'as_cover' object has no attribute 'exponent_of_differen'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_differen()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7lsage: AS.exponent_of_different()

+[?7h[?12l[?25h[?2004l[?7h12
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_different()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lS.exponent_of_different()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[0]^(p-1)*AS.z[1]^(p-1).valuation()[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: AS.z[0].valuation()

+[?7h[?12l[?25h[?2004l[?7h-6
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[0].valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l].valuation()[?7h[?12l[?25h[?25l[?7l1].valuation()[?7h[?12l[?25h[?25l[?7lsage: AS.z[1].valuation()

+[?7h[?12l[?25h[?2004l[?7h-6
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1].valuation()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.z[1].valuation()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: AS.z[1]/AS.x

+[?7h[?12l[?25h[?2004l[?7hz1/x
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]/AS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]/AS.x).diffn()

+[?7h[?12l[?25h[?2004l[?7h((a*x^3 + z1)/x^2) * dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.z[1]/AS.x[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^3 with the equations:
+z0^2 - z0 = x^3
+z1^2 - z1 = a*x^3
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn()[?7h[?12l[?25h[?25l[?7lAS.z[1]/AS.x[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()aa[?7h[?12l[?25h[?25l[?7laa[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l.dx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.exponent_of_differen()[?7h[?12l[?25h[?25l[?7lt()[?7h[?12l[?25h[?25l[?7lz[0].valuation()[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/AS.x[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltio[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[1]/AS.x).diffn().valuation()

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn().valuation()[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn().valuation()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l]/AS.x).difn([?7h[?12l[?25h[?25l[?7l0]/AS.x).difn([?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[]*/AS.x).difn([?7h[?12l[?25h[?25l[?7lA/AS.x).difn([?7h[?12l[?25h[?25l[?7lS/AS.x).difn([?7h[?12l[?25h[?25l[?7l./AS.x).difn([?7h[?12l[?25h[?25l[?7lz/AS.x).difn([?7h[?12l[?25h[?25l[?7l[/AS.x).difn([?7h[?12l[?25h[?25l[?7l1/AS.x).difn([?7h[?12l[?25h[?25l[?7l[]/AS.x).difn([?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)([?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]/AS.x).diffn()

+[?7h[?12l[?25h[?2004l[?7h((a*x^3*z0 + x^3*z1 + z0*z1)/x^2) * dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[0]*AS.z[1]/AS.x).diffn()[?7h[?12l[?25h[?25l[?7l1/x).diffn(valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x).diffn().valuation()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l0*z[1]/AS.xdiffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.x).difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()^.difn()[?7h[?12l[?25h[?25l[?7l2.difn()[?7h[?12l[?25h[?25l[?7l(2).difn()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: (AS.z[0]*AS.z[1]/(AS.x)^2).diffn()

+[?7h[?12l[?25h[?2004l[?7h(a*z0 + z1) * dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(AS); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(); magmathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_dR(AS)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lsage: A

+[?7h[?12l[?25h[?2004l[?7h[      1 a^2 + a       0       0       0       a]
+[      0       1       0       0       0       0]
+[      0       0       1       0       a       0]
+[      0       0       0       1       1       0]
+[      0       0       0       0       1       0]
+[      0       0       0       0       0       1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lenumerate(lll)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lz[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lAx)[?7h[?12l[?25h[?25l[?7lSx)[?7h[?12l[?25h[?25l[?7l.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(AS.z[1]/AS.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e1 = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1 = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: e1

+[?7h[?12l[?25h[?2004l[?7h( (0) * dx, z1^2/x^2 )
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: e1.coordinates()

+[?7h[?12l[?25h[?2004l[?7h(a, 0, 0, 0, 0, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l0]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[]*/AS.x)^2)[?7h[?12l[?25h[?25l[?7lA/AS.x)^2)[?7h[?12l[?25h[?25l[?7lS/AS.x)^2)[?7h[?12l[?25h[?25l[?7l./AS.x)^2)[?7h[?12l[?25h[?25l[?7lz/AS.x)^2)[?7h[?12l[?25h[?25l[?7lp/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[/AS.x)^2)[?7h[?12l[?25h[?25l[?7l/AS.x)^2)[?7h[?12l[?25h[?25l[?7l/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[/AS.x)^2)[?7h[?12l[?25h[?25l[?7l1/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e1 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l.coordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7lsage: e1 = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le1 = as_cech(AS, 0*AS.dx, (AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l0*z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l2 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e2 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le2 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ldinates[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: e2.coordinates()

+[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, 0, 0, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le2.coordinates()[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7las_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7las[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le2.coordinates()[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x)^2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^)^2)[?7h[?12l[?25h[?25l[?7l2)^2)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x^2)^2)[?7h[?12l[?25h[?25l[?7l3 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x^2)^2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: e3 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x^2)^2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le3 = as_cech(AS, 0*AS.dx, (AS.z[0]*AS.z[1]/AS.x^2)^2)[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: e3.coordinates()

+[?7h[?12l[?25h[?2004l[?7h(0, 0, 0, a^2 + a + 1, 0, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^2 + a + 1[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: (a^2 + a + 1)^2

+[?7h[?12l[?25h[?2004l[?7ha + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l/(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7lsage: 1/(a^2 + a + 1)^2

+[?7h[?12l[?25h[?2004l[?7ha^2 + a
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1/(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.z[1]/AS.x[?7h[?12l[?25h[?25l[?7ldx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
+ ( ((a^2 + a)*z0 + z1) * dx, 0 ),
+ ( (x) * dx, 0 ),
+ ( (0) * dx, z1/x ),
+ ( (a*x*z0 + x*z1) * dx, z0*z1/x ),
+ ( (a*z0 + z1) * dx, z0*z1/x^2 )]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmatrix(v0).transpose()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgmathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A, B, text=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lTru)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lG")[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l,")[?7h[?12l[?25h[?25l[?7la")[?7h[?12l[?25h[?25l[?7l.")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l<")[?7h[?12l[?25h[?25l[?7la")[?7h[?12l[?25h[?25l[?7l>?")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l ")[?7h[?12l[?25h[?25l[?7l:")[?7h[?12l[?25h[?25l[?7l=")[?7h[?12l[?25h[?25l[?7l ")[?7h[?12l[?25h[?25l[?7lG")[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l(")[?7h[?12l[?25h[?25l[?7l4")[?7h[?12l[?25h[?25l[?7l()")[?7h[?12l[?25h[?25l[?7l();")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(4);")

+[?7h[?12l[?25h[?2004l[?7h>> F<a> := GF(4);A := MatrixAlgebra<GF(8),6|[1, a^2 + a, 0, 0, 0, a, 0, 1, 0,
+                                   ^
+Runtime error in MatrixAlgebra< ... >: Rhs argument 1 is invalid for this constructor
+>> RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);
+                            ^
+User error: Identifier 'A' has not been declared or assigned
+>> RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);
+                                                      ^
+User error: Identifier 'M' has not been declared or assigned
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^3 with the equations:
+z0^2 - z0 = x^3
+z1^2 - z1 = a*x^3
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(4);")[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(4);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l);")[?7h[?12l[?25h[?25l[?7l8);")[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(8);")

+[?7h[?12l[?25h[?2004l[?7h[
+RModule of dimension 3 over GF(2^3),
+RModule of dimension 3 over GF(2^3)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lsage: A

+[?7h[?12l[?25h[?2004l[?7h[      1 a^2 + a       0       0       0       a]
+[      0       1       0       0       0       0]
+[      0       0       1       0       a       0]
+[      0       0       0       1       1       0]
+[      0       0       0       0       1       0]
+[      0       0       0       0       0       1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lsage: B

+[?7h[?12l[?25h[?2004l[?7h[    1     1     0     0     0     1]
+[    0     1     0     0     0     0]
+[    0     0     1     0     1     0]
+[    0     0     0     1 a + 1     0]
+[    0     0     0     0     1     0]
+[    0     0     0     0     0     1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lt=)[?7h[?12l[?25h[?25l[?7lT)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lTrue)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(8);", text=True)

+[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),6|[1, a^2 + a, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a + 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l1 = matrix(ZZ, [[1, 3], [3, 4]])[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7lh(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7ll(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(8);", text=True)

+[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),6|[1, a^2 + a, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a + 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lTru)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B, prefix="F<a> := GF(8);")

+[?7h[?12l[?25h[?2004l[?7h[
+RModule of dimension 3 over GF(2^3),
+RModule of dimension 3 over GF(2^3)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A, B, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, B, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l1, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);")

+[?7h[?12l[?25h[?2004l[?7h[
+RModule of dimension 1 over GF(2^3),
+RModule of dimension 2 over GF(2^3)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lxt)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7lT)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lTrue)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)

+[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l, B, prefix="F<a> := GF(8);")[?7h[?12l[?25h[?25l[?7l, text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)

+[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a + 1, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7ld(AS)[?7h[?12l[?25h[?25l[?7lR(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_dR(AS)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)

+[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),6|[1, a^2 + a + 1, 0, 0, 0, a + 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a + 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a^2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_dR(AS)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)

+[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),6|[1, a^2 + a, 0, 0, 0, a, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, a, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1],[1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, a + 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);IndecomposableSummands(M);'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7lh(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7ll(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)

+[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lsage: A1, B1 = group_action_matrices_holo(AS)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A1, B1, prefix="F<a> := GF(8);", text=True)

+[?7h[?12l[?25h[?2004l[?7h'F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a + 1, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA1, B1 = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: AS.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[( (1) * dx, 0 ),
+ ( ((a^2 + a)*z0 + z1) * dx, 0 ),
+ ( (x) * dx, 0 ),
+ ( (0) * dx, z1/x ),
+ ( (a*x*z0 + x*z1) * dx, z0*z1/x ),
+ ( (a*z0 + z1) * dx, z0*z1/x^2 )]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le3.coordinates()[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lrham_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: eta6 = AS.de_rham_basis()[5]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta6 = AS.de_rham_basis()[5][?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l6[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: eta6.group_action([1, 0]).coordinates()

+[?7h[?12l[?25h[?2004l[?7h(a, 0, 0, 0, 0, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7leta6.group_action([1, 0]).coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l0, 0]).cordinates()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l]).cordinates()[?7h[?12l[?25h[?25l[?7l1]).cordinates()[?7h[?12l[?25h[?25l[?7lsage: eta6.group_action([0, 1]).coordinates()

+[?7h[?12l[?25h[?2004l[?7h(1, 0, 0, 0, 0, 1)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule M of dimension 2 over GF(2^2)
+]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lF<a> := GF(4);A := MatrixAlgebra<GF(4),2|[1, 1, 0, 1],[1, a, 0, 1]>;M := RModule(RSpace(GF(4),2), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lF<a> := GF(4);A := MatrixAlgebra<GF(4),2|[1, 0, 1, 1],[1, 0, a, 1]>;M := RModule(RSpace(GF(4),2), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
+********************************************************************************
+Denominators of fraction field elements are sometimes dropped without warning.
+This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
+********************************************************************************
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB[?7h[?12l[?25h[?25l[?7l = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l(); magmathis(A, B)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lagmathis(A, B)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l<")[?7h[?12l[?25h[?25l[?7l>")[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la>")[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l:")[?7h[?12l[?25h[?25l[?7l=")[?7h[?12l[?25h[?25l[?7lG")[?7h[?12l[?25h[?25l[?7lF")[?7h[?12l[?25h[?25l[?7l(")[?7h[?12l[?25h[?25l[?7l4")[?7h[?12l[?25h[?25l[?7l()")[?7h[?12l[?25h[?25l[?7l();")[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l);")[?7h[?12l[?25h[?25l[?7l8);")[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7let6.group_action([0, 1]).coordinates()[?7h[?12l[?25h[?25l[?7llod('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la^2[?7h[?12l[?25h[?25l[?7lsage: a

+[?7h[?12l[?25h[?2004l[?7ha
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.square_root()

+[?7h[?12l[?25h[?2004l[?7ha^2 + a
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+a)^2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l)^2[?7h[?12l[?25h[?25l[?7lsage: (a^2+a)^2

+[?7h[?12l[?25h[?2004l[?7ha
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lF<a> := GF(4);A := MatrixAlgebra<GF(8),2|[1, 1, 0, 1],[1, a, 0, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lF<a> := GF(4);A := MatrixAlgebra<GF(8),2|[1, 0, 1, 1],[1, 0, a^2 + 1, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),2|[1, 1, 0, 1],[1, a^2 + 1, 0, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
+F<a> := GF(8);A := MatrixAlgebra<GF(8),2|[1, 0, 1, 1],[1, 0, a^2 + 1, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lF<a> := GF(8);A := MatrixAlgebra<GF(8),2|[1, 1, 0, 1],[1, a, 0, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
+F<a> := GF(8);A := MatrixAlgebra<GF(8),2|[1, 0, 1, 1],[1, 0, a, 1]>;M := RModule(RSpace(GF(8),2), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
+********************************************************************************
+Denominators of fraction field elements are sometimes dropped without warning.
+This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
+********************************************************************************
+F<a> := GF(8);A := MatrixAlgebra<GF(8),3|[1, a^2 + a, 0, 0, 1, 0, 0, 0, 1],[1, 1, 0, 0, 1, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),3), A);IndecomposableSummands(M);
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l{
+[  1]
+}
+{
+[  1 a^4]
+[  0   1],
+[  1   1]
+[  0   1]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l/ext/sage/9.7/src/sage/rings/polynomial/polynomial_singular_interface.py:372:
+********************************************************************************
+Denominators of fraction field elements are sometimes dropped without warning.
+This issue is being tracked at https://trac.sagemath.org/sage_trac/ticket/17696.
+********************************************************************************
+{
+[  1]
+}
+{
+[  1 a^4]
+[  0   1],
+[  1   1]
+[  0   1]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l{
+[1]
+}
+{
+[1 0 1 0]
+[0 1 0 0]
+[0 0 1 0]
+[0 1 0 1],
+[1 1 0 0]
+[0 1 0 0]
+[0 0 1 0]
+[0 0 0 1]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 1 over GF(2),
+RModule of dimension 4 over GF(2)
+]
+{
+[1]
+}
+{
+[1 0 1 0]
+[0 1 0 0]
+[0 0 1 0]
+[0 1 0 1],
+[1 1 0 0]
+[0 1 0 0]
+[0 0 1 0]
+[0 0 0 1]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 2 over GF(2),
+RModule of dimension 2 over GF(2),
+RModule of dimension 3 over GF(2),
+RModule of dimension 3 over GF(2)
+]
+{
+[1 1]
+[0 1],
+[1 0]
+[0 1]
+}
+{
+[1 0]
+[1 1],
+[1 0]
+[0 1]
+}
+{
+[1 1 0]
+[0 1 0]
+[0 0 1],
+[1 1 1]
+[0 1 0]
+[0 0 1]
+}
+{
+[1 0 1]
+[0 1 0]
+[0 0 1],
+[1 0 1]
+[0 1 1]
+[0 0 1]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lno  7 -th root; divide by a
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [5], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lno  7 -th root; divide by a + 1
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [6], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lno  7 -th root; divide by a + 1
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [7], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lno  7 -th root; divide by a + 1
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [8], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lno  7 -th root; divide by a^2
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [9], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lno  7 -th root; divide by a^2 + a
+---------------------------------------------------------------------------
+ValueError                                Traceback (most recent call last)
+Input In [10], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+ValueError: not enough values to unpack (expected 4, got 2)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 2 over GF(2^3),
+RModule of dimension 2 over GF(2^3),
+RModule of dimension 2 over GF(2^3),
+RModule of dimension 2 over GF(2^3),
+RModule of dimension 3 over GF(2^3),
+RModule of dimension 3 over GF(2^3)
+]
+{
+[  1   0]
+[a^2   1],
+[  1   0]
+[  0   1]
+}
+{
+[  1   0]
+[a^6   1],
+[  1   0]
+[  0   1]
+}
+{
+[  1   0]
+[a^2   1],
+[  1   0]
+[  0   1]
+}
+{
+[  1   0]
+[a^6   1],
+[  1   0]
+[  0   1]
+}
+{
+[  1 a^2   1]
+[  0   1   0]
+[  0   0   1],
+[  1   1   0]
+[  0   1   0]
+[  0   0   1]
+}
+{
+[  1   0 a^5]
+[  0   1 a^6]
+[  0   0   1],
+[  1   0 a^4]
+[  0   1 a^4]
+[  0   0   1]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.square_root()[?7h[?12l[?25h[?25l[?7lsage: a

+[?7h[?12l[?25h[?2004l[?7ha
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lmin[?7h[?12l[?25h[?25l[?7lmini[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: minimal_polynomial(a)

+[?7h[?12l[?25h[?2004l[?7hx^3 + x + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lminimal_polynomial(a)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(a^2+a)^2[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 2 over GF(2^4),
+RModule of dimension 2 over GF(2^4),
+RModule of dimension 2 over GF(2^4),
+RModule of dimension 2 over GF(2^4),
+RModule of dimension 3 over GF(2^4),
+RModule of dimension 3 over GF(2^4)
+]
+{
+[   1    0]
+[   0    1],
+[   1    0]
+[   a    1]
+}
+{
+[   1    0]
+[   0    1],
+[   1    0]
+[   1    1]
+}
+{
+[   1  a^2]
+[   0    1],
+[   1    0]
+[   0    1]
+}
+{
+[   1    0]
+[a^14    1],
+[   1    0]
+[   0    1]
+}
+{
+[   1    1    0]
+[   0    1    0]
+[   0    0    1],
+[   1  a^5    1]
+[   0    1    0]
+[   0    0    1]
+}
+{
+[   1    0 a^12]
+[   0    1    0]
+[   0    0    1],
+[   1    0    a]
+[   0    1 a^14]
+[   0    0    1]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.de_rham_basis()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ljumps[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: AS.jumps

+[?7h[?12l[?25h[?2004l[?7h[[3, 11]]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.jumps[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lraification_jumps()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lmification_jumps()[?7h[?12l[?25h[?25l[?7lsage: AS.ramification_jumps()

+[?7h[?12l[?25h[?2004l[?7h[3, 11]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l>> F<a> := GF(16);A := MatrixAlgebra<GF(8),12|[1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0
+                                    ^
+Runtime error in MatrixAlgebra< ... >: Rhs argument 1 is invalid for this constructor
+>> ;M := RModule(RSpace(GF(8),12), A);L := IndecomposableSummands(M); L;for i
+                                   ^
+User error: Identifier 'A' has not been declared or assigned
+>> ;M := RModule(RSpace(GF(8),12), A);L := IndecomposableSummands(M); L;for i
+                                                                  ^
+User error: Identifier 'M' has not been declared or assigned
+>> ;M := RModule(RSpace(GF(8),12), A);L := IndecomposableSummands(M); L;for i
+                                                                      ^
+User error: Identifier 'L' has not been declared or assigned
+>> ummands(M); L;for i in [1 .. #L] do print(Generators(Action(L[i]))); end fo
+                                 ^
+User error: Identifier 'L' has not been declared or assigned
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[
+RModule of dimension 3 over GF(2^3),
+RModule of dimension 3 over GF(2^3),
+RModule of dimension 3 over GF(2^3),
+RModule of dimension 3 over GF(2^3)
+]
+{
+[  1   0 a^5]
+[  0   1 a^4]
+[  0   0   1],
+[  1   0 a^3]
+[  0   1 a^5]
+[  0   0   1]
+}
+{
+[  1   0 a^3]
+[  0   1 a^2]
+[  0   0   1],
+[  1   0   1]
+[  0   1   a]
+[  0   0   1]
+}
+{
+[  1   0   1]
+[  0   1   0]
+[  0   0   1],
+[  1   1   0]
+[  0   1   0]
+[  0   0   1]
+}
+{
+[  1   0   1]
+[  0   1   0]
+[  0   0   1],
+[  1   1   0]
+[  0   1   0]
+[  0   0   1]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.ramification_jumps()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7lsage: AS

+[?7h[?12l[?25h[?2004l[?7h(Z/p)^2-cover of Superelliptic curve with the equation y^1 = x over Finite Field in a of size 2^3 with the equations:
+z0^2 - z0 = x^5
+z1^2 - z1 = a*x^5 + x^3
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.ramification_jumps()[?7h[?12l[?25h[?25l[?7lgenus()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lus()[?7h[?12l[?25h[?25l[?7lsage: AS.genus()

+[?7h[?12l[?25h[?2004l[?7h6
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7lS[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAS.genus()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lB = group_action_matrices_dR(AS)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l(AS)[?7h[?12l[?25h[?25l[?7l_(AS)[?7h[?12l[?25h[?25l[?7lh(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7ll(AS)[?7h[?12l[?25h[?25l[?7lo(AS)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_holo(AS)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lminimal_polynomial(a)[?7h[?12l[?25h[?25l[?7lagmathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lathis(A1, B1, prefix="F<a> := GF(8);", text=True)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lTru)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, B)[?7h[?12l[?25h[?25l[?7l, B)[?7h[?12l[?25h[?25l[?7lA, B)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

+[?7h[?12l[?25h[?2004l[?7h>> 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, a^2 + a, 0, 0, 0, 0, 0, 1, 0, 0, 0,
+                                          ^
+User error: Identifier 'a' has not been declared or assigned
+>>  0, 0, 1, 0, 0, 0, 0, 0, 0, 1]>;M := RModule(RSpace(GF(8),6), A);L := Indec
+                                                                 ^
+User error: Identifier 'A' has not been declared or assigned
+>> 8),6), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Gen
+                                         ^
+User error: Identifier 'M' has not been declared or assigned
+>> 8),6), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Gen
+                                             ^
+User error: Identifier 'L' has not been declared or assigned
+>> 8),6), A);L := IndecomposableSummands(M); L;for i in [1 .. #L] do print(Gen
+                                                               ^
+User error: Identifier 'L' has not been declared or assigned
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: A

+[?7h[?12l[?25h[?2004l[?7h[      1       0       1       0       0       0]
+[      0       1       0       0       0       0]
+[      0       0       1       0       0       0]
+[      0       0       0       1 a^2 + a       0]
+[      0       0       0       0       1       0]
+[      0       0       0       0       0       1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(A).base_ring().order()[?7h[?12l[?25h[?25l[?7lsage: parent(A).base_ring().order()

+[?7h[?12l[?25h[?2004l[?7h8
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l^C---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:280, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
+    279 try:
+--> 280     if a.parent() is not K:
+    281         a = K.coerce(a)
+
+AttributeError: 'tuple' object has no attribute 'parent'
+
+During handling of the above exception, another exception occurred:
+
+KeyboardInterrupt                         Traceback (most recent call last)
+Input In [25], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:15, in <module>
+
+File <string>:44, in __init__(self, C, list_of_fcts, prec)
+
+File <string>:134, in artin_schreier_transform(power_series, prec)
+
+File <string>:12, in new_reverse(power_series, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1831, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1829 if x:
+   1830     raise ValueError("must not specify %s keyword and positional argument" % name)
+-> 1831 a = self(kwds[name])
+   1832 del kwds[name]
+   1833 try:
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:1852, in sage.rings.laurent_series_ring_element.LaurentSeries.__call__()
+   1850         x = x[0]
+   1851 
+-> 1852     return self.__u(*x)*(x[0]**self.__n)
+   1853 
+   1854 def __pari__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:365, in sage.rings.power_series_poly.PowerSeries_poly.__call__()
+    363         x[0] = a
+    364         x = tuple(x)
+--> 365     return self.__f(x)
+    366 
+    367 def _unsafe_mutate(self, i, value):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zz_pex.pyx:283, in sage.rings.polynomial.polynomial_zz_pex.Polynomial_ZZ_pEX.__call__()
+    281         a = K.coerce(a)
+    282 except (TypeError, AttributeError, NotImplementedError):
+--> 283     return Polynomial.__call__(self, a)
+    284 
+    285 _a = self._parent._modulus.ZZ_pE(list(a.polynomial()))
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:898, in sage.rings.polynomial.polynomial_element.Polynomial.__call__()
+    896             return result
+    897         pol._compiled = CompiledPolynomialFunction(pol.list())
+--> 898     return pol._compiled.eval(a)
+    899 
+    900 def compose_trunc(self, Polynomial other, long n):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:125, in sage.rings.polynomial.polynomial_compiled.CompiledPolynomialFunction.eval()
+    123 cdef object temp
+    124 try:
+--> 125     pd_eval(self._dag, x, self._coeffs)  #see further down
+    126     temp = self._dag.value               #for an explanation
+    127     pd_clean(self._dag)                  #of these 3 lines
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+    [... skipping similar frames: sage.rings.polynomial.polynomial_compiled.pd_eval at line 353 (47 times), sage.rings.polynomial.polynomial_compiled.abc_pd.eval at line 507 (46 times)]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:507, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    505 
+    506     cdef int eval(abc_pd self, object vars, object coeffs) except -2:
+--> 507         pd_eval(self.left, vars, coeffs)
+    508         pd_eval(self.right, vars, coeffs)
+    509         self.value = self.left.value * self.right.value + coeffs[self.index]
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:353, in sage.rings.polynomial.polynomial_compiled.pd_eval()
+    351 cdef inline int pd_eval(generic_pd pd, object vars, object coeffs) except -2:
+    352     if pd.value is None:
+--> 353         pd.eval(vars, coeffs)
+    354     pd.hits += 1
+    355 
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_compiled.pyx:509, in sage.rings.polynomial.polynomial_compiled.abc_pd.eval()
+    507 pd_eval(self.left, vars, coeffs)
+    508 pd_eval(self.right, vars, coeffs)
+--> 509 self.value = self.left.value * self.right.value + coeffs[self.index]
+    510 pd_clean(self.left)
+    511 pd_clean(self.right)
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:913, in sage.rings.laurent_series_ring_element.LaurentSeries._mul_()
+    911 cdef LaurentSeries right = <LaurentSeries>right_r
+    912 return type(self)(self._parent,
+--> 913                   self.__u * right.__u,
+    914                   self.__n + right.__n)
+    915 
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:1514, in sage.structure.element.Element.__mul__()
+   1512 cdef int cl = classify_elements(left, right)
+   1513 if HAVE_SAME_PARENT(cl):
+-> 1514     return (<Element>left)._mul_(right)
+   1515 if BOTH_ARE_ELEMENT(cl):
+   1516     return coercion_model.bin_op(left, right, mul)
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:540, in sage.rings.power_series_poly.PowerSeries_poly._mul_()
+    538 """
+    539 prec = self._mul_prec(right_r)
+--> 540 return PowerSeries_poly(self._parent,
+    541                         self.__f * (<PowerSeries_poly>right_r).__f,
+    542                         prec=prec,
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:44, in sage.rings.power_series_poly.PowerSeries_poly.__init__()
+     42     ValueError: series has negative valuation
+     43 """
+---> 44 R = parent._poly_ring()
+     45 if isinstance(f, Element):
+     46     if (<Element>f)._parent is R:
+
+File /ext/sage/9.7/src/sage/rings/power_series_ring.py:961, in PowerSeriesRing_generic._poly_ring(self)
+    958         pass
+    959     return False
+--> 961 def _poly_ring(self):
+    962     """
+    963     Return the underlying polynomial ring used to represent elements of
+    964     this power series ring.
+   (...)
+    970         Univariate Polynomial Ring in t over Integer Ring
+    971     """
+    972     return self.__poly_ring
+
+File src/cysignals/signals.pyx:310, in cysignals.signals.python_check_interrupt()
+
+KeyboardInterrupt: 
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lparent(A).base_ring().order()[?7h[?12l[?25h[?25l[?7lmgmahis(A, B)[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lS.genus()[?7h[?12l[?25h[?25l[?7l, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lsage: A, B = group_action_matrices_holo(AS)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA, B = group_action_matrices_holo(AS)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lparent(A).base_ring().order()[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7lmagmathis(A, B)[?7h[?12l[?25h[?25l[?7lsage: magmathis(A, B)

+[?7h[?12l[?25h[?2004l[?7h[
+RModule of dimension 1 over GF(2^3),
+RModule of dimension 2 over GF(2^3),
+RModule of dimension 3 over GF(2^3)
+]
+{
+[  1]
+}
+{
+[  1 a^4]
+[  0   1],
+[  1   1]
+[  0   1]
+}
+{
+[  1   0   1]
+[  0   1   0]
+[  0   0   1],
+[  1   1   0]
+[  0   1   0]
+[  0   0   1]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l12.factor()[1][0][?7h[?12l[?25h[?25l[?7l/(a^2 + a + 1)^2[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 1/a

+[?7h[?12l[?25h[?2004l[?7ha^2 + 1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l^2[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l8[?7h[?12l[?25h[?25l[?7lsage: a^8

+[?7h[?12l[?25h[?2004l[?7ha
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ losage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x-x^3)^2 - x^2[?7h[?12l[?25h[?25l[?7l(x-x^3) + (-x^3)^3)^2-x^2[?7h[?12l[?25h[?25l[?7lR.<x> = PolynomialRing(QQ)[?7h[?12l[?25h[?25l[?7l((x-x^3) + (x-x^3)^3)^2-x^2[?7h[?12l[?25h[?25l[?7lx-x^3)^2 - ^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7lpatil_fraction_decomposition()[?7h[?12l[?25h[?25l[?7l = (x^2 + 1)/(x^2*(x^3 - x))[?7h[?12l[?25h[?25l[?7lsage: F.<x> = PolynomialRing(GF(3))

+....: FF = FractionField(F)[?7h[?12l[?25h[?25l[?7lf = (x^2 + 1)/(x^2*(x^3 - x)

+ [?7h[?12l[?25h[?25l[?7l.partial_fraction_decomposition()[?7h[?12l[?25h[?25l[?7ldeivtive()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l = (x^2 + 1)/(x^2*(x^3 - x))[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: f = C.y

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [2], in <cell line: 1>()
+----> 1 f = C.y
+
+NameError: name 'C' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lsage: C_super

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C_super.x

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [4], in <cell line: 1>()
+----> 1 C_super.x
+
+AttributeError: 'superelliptic' object has no attribute 'x'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C_super.x

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y, z0, z1 = Rxyz.gens()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxC_super.x[?7h[?12l[?25h[?25l[?7lxC_super.x[?7h[?12l[?25h[?25l[?7l,C_super.x[?7h[?12l[?25h[?25l[?7l C_super.x[?7h[?12l[?25h[?25l[?7lyC_super.x[?7h[?12l[?25h[?25l[?7lyC_super.x[?7h[?12l[?25h[?25l[?7l C_super.x[?7h[?12l[?25h[?25l[?7l=C_super.x[?7h[?12l[?25h[?25l[?7l C_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, C.super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = C_super.x, C.super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, y = C_super.x, C.super.y[?7h[?12l[?25h[?25l[?7lsage: x, y = C_super.x, C.super.y

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [7], in <cell line: 1>()
+----> 1 x, y = C_super.x, C.super.y
+
+NameError: name 'C' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C.super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper.y[?7h[?12l[?25h[?25l[?7l_super.y[?7h[?12l[?25h[?25l[?7lsage: x, y = C_super.x, C_super.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = C.y[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lsage: f = y+y/x^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y+y/x^2[?7h[?12l[?25h[?25l[?7l.derivative()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7liscrimnant()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lerivative()[?7h[?12l[?25h[?25l[?7lrivative()[?7h[?12l[?25h[?25l[?7lsage: f.derivative()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [10], in <cell line: 1>()
+----> 1 f.derivative()
+
+AttributeError: 'superelliptic_function' object has no attribute 'derivative'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld = f.degree()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: diffn(f)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [11], in <cell line: 1>()
+----> 1 diffn(f)
+
+NameError: name 'diffn' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn(f)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7liscrimnant()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()

+[?7h[?12l[?25h[?2004l[?7h((-1)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7ldiffn(f)[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l = y+y/x^2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly/x^2[?7h[?12l[?25h[?25l[?7l-y/x^2[?7h[?12l[?25h[?25l[?7lsage: f = y-y/x^2

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y-y/x^2[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7l = y-y/x^2[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2/x^3+1/x^5)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [15], in <cell line: 1>()
+----> 1 f = y*(x**Integer(3) + Integer(2)*x+Integer(2)/x**Integer(3)+Integer(1)/x**Integer(5))
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
+   1962         return y
+   1963 
+-> 1964     return coercion_model.bin_op(left, right, operator.mul)
+   1965 
+   1966 cpdef _mul_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
+   1246     # We should really include the underlying error.
+   1247     # This causes so much headache.
+-> 1248     raise bin_op_exception(op, x, y)
+   1249 
+   1250 cpdef canonical_coercion(self, x, y):
+
+TypeError: unsupported operand parent(s) for *: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2/x^3+1/x^5)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [16], in <cell line: 1>()
+----> 1 f = y*(x**Integer(3) + Integer(2)*x+Integer(2)/x**Integer(3)+Integer(1)/x**Integer(5))
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
+   1962         return y
+   1963 
+-> 1964     return coercion_model.bin_op(left, right, operator.mul)
+   1965 
+   1966 cpdef _mul_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
+   1246     # We should really include the underlying error.
+   1247     # This causes so much headache.
+-> 1248     raise bin_op_exception(op, x, y)
+   1249 
+   1250 cpdef canonical_coercion(self, x, y):
+
+TypeError: unsupported operand parent(s) for *: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7l = y-y/x^2[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ldiffn(f)[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l = y+y/x^2[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7lsage: x, y = C_super.x, C_super.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2/x^3+1/x^5)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [19], in <cell line: 1>()
+----> 1 f = y*(x**Integer(3) + Integer(2)*x+Integer(2)/x**Integer(3)+Integer(1)/x**Integer(5))
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__()
+   1962         return y
+   1963 
+-> 1964     return coercion_model.bin_op(left, right, operator.mul)
+   1965 
+   1966 cpdef _mul_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op()
+   1240 mul_method = getattr(y, '__r%s__'%op_name, None)
+   1241 if mul_method is not None:
+-> 1242     res = mul_method(x)
+   1243     if res is not None and res is not NotImplemented:
+   1244         return res
+
+File <string>:53, in __rmul__(self, constant)
+
+File <string>:6, in __init__(self, C, g)
+
+AttributeError: 'superelliptic' object has no attribute 'height'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7lx, y = C_super., C_super.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7lx, y = C_super., C_super.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7l = y-y/x^2[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ldiffn(f)[?7h[?12l[?25h[?25l[?7lf.derivative()[?7h[?12l[?25h[?25l[?7l = y+y/x^2[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7lsage: x, y = C_super.x, C_super.y

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2/x^3+1/x^5)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [22], in <cell line: 1>()
+----> 1 f = y*(x**Integer(3) + Integer(2)*x+Integer(2)/x**Integer(3)+Integer(1)/x**Integer(5))
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:2037, in sage.rings.integer.Integer.__truediv__()
+   2035         return y
+   2036 
+-> 2037     return coercion_model.bin_op(left, right, operator.truediv)
+   2038 
+   2039 cpdef _div_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
+   1246     # We should really include the underlying error.
+   1247     # This causes so much headache.
+-> 1248     raise bin_op_exception(op, x, y)
+   1249 
+   1250 cpdef canonical_coercion(self, x, y):
+
+TypeError: unsupported operand parent(s) for /: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_function(C, g)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_, g)[?7h[?12l[?25h[?25l[?7ls, g)[?7h[?12l[?25h[?25l[?7lu, g)[?7h[?12l[?25h[?25l[?7lp, g)[?7h[?12l[?25h[?25l[?7le, g)[?7h[?12l[?25h[?25l[?7lr, g)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7lsage: f1 = superelliptic_function(C_super, 1)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = superelliptic_function(C_super, 1)[?7h[?12l[?25h[?25l[?7l = y*(x^3 + 2*x+2/x^3+1/x^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1/x^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^3+f1/x^5)[?7h[?12l[?25h[?25l[?7lx^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l1x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2f1/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l*f1/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x+2*f1/x^3+f1/x^5)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x+2*f1/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = y*(x^3 + 2*x+2*f1/x^3+f1/x^5)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: f = y*(x^3 + 2*x)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = y*(x^3 + 2*x)[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: f.diffn()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lrham_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C_super.de_rham_basis()

+[?7h[?12l[?25h[?2004lsage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
+  """
+sage/rings/polynomial/polynomial_zmod_flint.pyx:7: DeprecationWarning: invalid escape sequence '\Z'
+  """
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [28], in <cell line: 1>()
+----> 1 C_super.de_rham_basis()
+
+File <string>:94, in de_rham_basis(self)
+
+File <string>:86, in basis_de_rham_degrees(self)
+
+File <string>:150, in cut(f, i)
+
+File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
+    583     return expression.sum(*args, **kwds)
+    584 elif max(len(args),len(kwds)) <= 1:
+--> 585     return sum(expression, *args, **kwds)
+    586 else:
+    587     from sage.symbolic.ring import SR
+
+File <string>:150, in <genexpr>(.0)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring.py:469, in PolynomialRing_general._element_constructor_(self, x, check, is_gen, construct, **kwds)
+    467 elif isinstance(x, sage.rings.power_series_ring_element.PowerSeries):
+    468     x = x.truncate()
+--> 469 return C(self, x, check, is_gen, construct=construct, **kwds)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:129, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__()
+    127         except AttributeError:
+    128             pass
+--> 129     Polynomial_template.__init__(self, parent, x, check, is_gen, construct)
+    130 
+    131 cdef Polynomial_template _new(self):
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_template.pxi:176, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__()
+    174     self.__class__.__init__(self, parent, x, check=check, is_gen=is_gen, construct=construct)
+    175 else:
+--> 176     x = parent.base_ring()(x)
+    177     self.__class__.__init__(self, parent, x, check=check, is_gen=is_gen, construct=construct)
+    178 
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod_ring.py:1185, in IntegerModRing_generic._element_constructor_(self, x)
+   1143 """
+   1144 TESTS::
+   1145 
+   (...)
+   1182     True
+   1183 """
+   1184 try:
+-> 1185     return integer_mod.IntegerMod(self, x)
+   1186 except (NotImplementedError, PariError):
+   1187     raise TypeError("error coercing to finite field")
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:201, in sage.rings.finite_rings.integer_mod.IntegerMod()
+    199         return a
+    200 t = modulus.element_class()
+--> 201 return t(parent, value)
+    202 
+    203 
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:391, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    389             z = value % self.__modulus.sageInteger
+    390         else:
+--> 391             raise
+    392 self.set_from_mpz(z.value)
+    393 
+
+File /ext/sage/9.7/src/sage/rings/finite_rings/integer_mod.pyx:380, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__()
+    378 else:
+    379     try:
+--> 380         z = integer_ring.Z(value)
+    381     except (TypeError, ValueError):
+    382         from sage.structure.element import Expression
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    159             print(type(C), C)
+    160             print(type(C._element_constructor), C._element_constructor)
+--> 161         raise
+    162 
+    163 cpdef Element _call_with_args(self, x, args=(), kwds={}):
+
+File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_()
+    154 cdef Parent C = self._codomain
+    155 try:
+--> 156     return C._element_constructor(x)
+    157 except Exception:
+    158     if print_warnings:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:717, in sage.rings.integer.Integer.__init__()
+    715                 return
+    716 
+--> 717             raise TypeError("unable to coerce %s to an integer" % type(x))
+    718 
+    719 def __reduce__(self):
+
+TypeError: unable to coerce <class '__main__.superelliptic_function'> to an integer
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC_super.de_rham_basis()[?7h[?12l[?25h[?25l[?7lsage: C_super.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lff.discriminant()%8[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista += [[e, f, g]][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [1], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:10, in <module>
+
+AttributeError: 'superelliptic' object has no attribute 'holo_basis'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.de_rham_basis()[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C_super.

+  C_super.a_number                               C_super.cartier_matrix                         C_super.degrees_de_rham1                        

+  C_super.base_ring                              C_super.characteristic                         C_super.degrees_holomorphic_differentials       

+  C_super.basis_de_rham_degrees                  C_super.de_rham_basis                          C_super.exponent                               >

+  C_super.basis_holomorphic_differentials_degree C_super.degrees_de_rham0                       C_super.final_type                              

+ [?7h[?12l[?25h[?25l[?7la_number

+ C_super.a_number                              

+

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lcartier_matrix

+ C_super.a_number                               C_super.cartier_matrix                        [?7h[?12l[?25h[?25l[?7ldegresde_ham1

+ C_super.cartier_matrix                         C_super.degrees_de_rham1                      [?7h[?12l[?25h[?25l[?7lfrobnius_matrix

+ cartier_matrixdegresde_ham1frobnius_matrix

+ characteristicdegees_holomorphic_differentialsgnus                            

+<de_rham_basis        exponent     holmorphic_differentials_basis

+ degrees_de_rham0                      final_typ      is_smooth [?7h[?12l[?25h[?25l[?7lpolynomial

+degresde_ham1frobnius_matrixpolynomial       

+degees_holomorphic_differentialsgnus                            vrschiebung_matrix 

+exponent     holmorphic_differentials_basisx                               

+final_typ      is_smooth y         [?7h[?12l[?25h[?25l[?7lfrobenius_matrix

+ C_super.frobenius_matrix                       C_super.polynomial                            [?7h[?12l[?25h[?25l[?7linal_type

+ C_super.frobenius_matrix                      

+

+

+ C_super.final_type                            [?7h[?12l[?25h[?25l[?7lrobenius_matrix

+ C_super.frobenius_matrix                      

+

+

+ C_super.final_type                            [?7h[?12l[?25h[?25l[?7lgenus

+ C_super.frobenius_matrix                      

+ C_super.genus                                 [?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis

+

+ C_super.genus                                 

+ C_super.holomorphic_differentials_basis       [?7h[?12l[?25h[?25l[?7l

+

+

+

+

+[?7h[?12l[?25h[?25l[?7lsage: C_super.holomorphic_differentials_basis

+[?7h[?12l[?25h[?2004l[?7h<bound method superelliptic.holomorphic_differentials_basis of Superelliptic curve with the equation y^2 = x^15 + x^13 + x^11 + 2*x^9 + 2*x^7 + 2*x^5 + 1 over Finite Field of size 3>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+ [?7h[?12l[?25h[?25l[?7lC_super.holomorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C_super.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?7h[(1/y) dx,
+ (x/y) dx,
+ (x^2/y) dx,
+ (x^3/y) dx,
+ (x^4/y) dx,
+ (x^5/y) dx,
+ (x^6/y) dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lAC_super.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C_super.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l=C_super.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7l C_super.holomorphic_diferentials_basis()[?7h[?12l[?25h[?25l[?7lsage: A = C_super.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[:, 2] = vector([1, 1, 1])[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A[0]

+[?7h[?12l[?25h[?2004l[?7h(1/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lrun.term-0.term[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrun.term-0.term[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom, f = AS.de_rham_basis()[16][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l = AS.holomophic_differentials_basis()[5]; om.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: om = A[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = A[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.serre_duality_pairing(A)[?7h[?12l[?25h[?25l[?7lsage: om.serre_duality_pairing(A)

+ om.cartier              om.expansion_at_infty   om.is_regular_on_Uinfty

+ om.coordinates          om.form                 om.jth_component       

+ om.curve                om.is_regular_on_U0                            

+

+ [?7h[?12l[?25h[?25l[?7lcartier

+ om.cartier             

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lexpansion_at_infty

+ om.cartier              om.expansion_at_infty  [?7h[?12l[?25h[?25l[?7lis_regular_on_Uinfty

+ om.expansion_at_infty   om.is_regular_on_Uinfty[?7h[?12l[?25h[?25l[?7ljth_component

+ om.is_regular_on_Uinfty

+ om.jth_component       [?7h[?12l[?25h[?25l[?7lform

+

+ om.form                 om.jth_component       [?7h[?12l[?25h[?25l[?7lis_regular_on_U0

+

+ om.form                

+ om.is_regular_on_U0    [?7h[?12l[?25h[?25l[?7lform

+

+ om.form                

+ om.is_regular_on_U0    [?7h[?12l[?25h[?25l[?7lexpansion_at_infty

+ om.expansion_at_infty  

+ om.form                [?7h[?12l[?25h[?25l[?7lcartier

+ om.cartier              om.expansion_at_infty  [?7h[?12l[?25h[?25l[?7lexpansion_at_infty

+ om.cartier              om.expansion_at_infty  [?7h[?12l[?25h[?25l[?7lform

+ om.expansion_at_infty  

+ om.form                [?7h[?12l[?25h[?25l[?7l

+

+

+

+[?7h[?12l[?25h[?25l[?7lsage: om.form

+[?7h[?12l[?25h[?2004l[?7h1/y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [8] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:21 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:15
+    return superelliptic_form(C1, f(x=x+_sage_const_1 , y))
+                                                         ^
+SyntaxError: positional argument follows keyword argument
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[(1/y) dx, (x/y) dx, (x^2/y) dx, (x^3/y) dx, (x^4/y) dx, (x^5/y) dx, (x^6/y) dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la_lead = f.coefficients(sparse=False)[d][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.form[?7h[?12l[?25h[?25l[?7l = A[0][?7h[?12l[?25h[?25l[?7lA[0][?7h[?12l[?25h[?25l[?7l = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: A = C_super.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lom.form[?7h[?12l[?25h[?25l[?7l = A[0][?7h[?12l[?25h[?25l[?7lA[0][?7h[?12l[?25h[?25l[?7lom = A[0][?7h[?12l[?25h[?25l[?7lsage: om = A[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la_lead = f.coefficients(sparse=False)[d][?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: autom(om)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [12], in <cell line: 1>()
+----> 1 autom(om)
+
+File <string>:15, in autom(omega)
+
+NameError: name 'y' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lautom(om)[?7h[?12l[?25h[?25l[?7lom = A[0][?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [13] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:21 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:21
+    print [autom(omm) for omm in A]
+    ^
+SyntaxError: Missing parentheses in call to 'print'. Did you mean print(...)?
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [14], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File <string>:21, in <listcomp>(.0)
+
+File <string>:16, in autom(omega)
+
+File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__()
+    895 if mor is not None:
+    896     if no_extra_args:
+--> 897         return mor._call_(x)
+    898     else:
+    899         return mor._call_with_args(x, args, kwds)
+
+File /ext/sage/9.7/src/sage/categories/map.pyx:788, in sage.categories.map.Map._call_()
+    786     return self._call_with_args(x, args, kwds)
+    787 
+--> 788 cpdef Element _call_(self, x):
+    789     """
+    790     Call method with a single argument, not implemented in the base class.
+
+File /ext/sage/9.7/src/sage/rings/fraction_field.py:1254, in FractionFieldEmbeddingSection._call_(self, x, check)
+   1249     return num
+   1250 if check and not den.is_unit():
+   1251     # This should probably be a ValueError.
+   1252     # However, too much existing code is expecting this to throw a
+   1253     # TypeError, so we decided to keep it for the time being.
+-> 1254     raise TypeError("fraction must have unit denominator")
+   1255 return num * den.inverse_of_unit()
+
+TypeError: fraction must have unit denominator
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
+[(1, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0), (1, 2, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0), (1, 1, 0, 1, 1, 0, 0), (1, 2, 1, 1, 2, 1, 0), (1, 0, 0, 2, 0, 0, 1)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
+[(1, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0), (1, 2, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0), (1, 1, 0, 1, 1, 0, 0), (1, 2, 1, 1, 2, 1, 0), (1, 0, 0, 2, 0, 0, 1)]
+[1 1 1 1 1 1 1]
+[0 1 2 0 1 2 0]
+[0 0 1 0 0 1 0]
+[0 0 0 1 1 1 2]
+[0 0 0 0 1 2 0]
+[0 0 0 0 0 1 0]
+[0 0 0 0 0 0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: M

+[?7h[?12l[?25h[?2004l[?7h[1 1 1 1 1 1 1]
+[0 1 2 0 1 2 0]
+[0 0 1 0 0 1 0]
+[0 0 0 1 1 1 2]
+[0 0 0 0 1 2 0]
+[0 0 0 0 0 1 0]
+[0 0 0 0 0 0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l.determinant()[?7h[?12l[?25h[?25l[?7lj[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.jordan_form()

+[?7h[?12l[?25h[?2004l[?7h[1 1 0|0 0 0|0]
+[0 1 1|0 0 0|0]
+[0 0 1|0 0 0|0]
+[-----+-----+-]
+[0 0 0|1 1 0|0]
+[0 0 0|0 1 1|0]
+[0 0 0|0 0 1|0]
+[-----+-----+-]
+[0 0 0|0 0 0|1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^15 + x^13 + x^11 + 2*x^9 + 2*x^7 + 2*x^5 + 1 over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
+[(1, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0), (1, 2, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0), (1, 1, 0, 1, 1, 0, 0), (1, 2, 1, 1, 2, 1, 0), (1, 0, 0, 2, 0, 0, 1)]
+[1 1 1 1 1 1 1]
+[0 1 2 0 1 2 0]
+[0 0 1 0 0 1 0]
+[0 0 0 1 1 1 2]
+[0 0 0 0 1 2 0]
+[0 0 0 0 0 1 0]
+[0 0 0 0 0 0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: Cf

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^5 + 1 over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Cf.genus()

+[?7h[?12l[?25h[?2004l[?7h2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCf.genus()[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Cf.is_smooth()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lCf.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lschiebung_matrix[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.verschiebung_matrix()

+[?7h[?12l[?25h[?2004l[?7h[0 2 0 1 0 0 0 0 0 0 0 0 0 0]
+[0 0 2 0 1 0 0 0 0 0 0 0 0 0]
+[1 0 0 2 0 1 0 0 0 0 0 0 0 0]
+[0 0 2 0 1 0 0 0 0 0 0 0 0 0]
+[0 0 0 2 0 1 0 0 0 0 0 0 0 0]
+[0 1 0 0 2 0 1 0 0 0 0 0 0 0]
+[0 0 0 2 0 1 0 0 0 0 0 0 0 0]
+[0 1 0 2 0 0 0 0 0 0 0 0 0 0]
+[2 0 1 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[1 0 2 0 0 0 0 0 0 0 0 0 0 0]
+[0 1 2 0 1 0 0 0 0 0 0 0 0 0]
+[0 1 0 2 0 0 0 0 0 0 0 0 0 0]
+[0 2 1 0 2 0 0 0 0 0 0 0 0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.verschiebung_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltier_matrix[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.cartier_matrix()

+[?7h[?12l[?25h[?2004l[?7h[0 2 0 1 0 0 0]
+[0 0 2 0 1 0 0]
+[1 0 0 2 0 1 0]
+[0 0 2 0 1 0 0]
+[0 0 0 2 0 1 0]
+[0 1 0 0 2 0 1]
+[0 0 0 2 0 1 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 7[?7h[?12l[?25h[?25l[?7lagmathis(A, B)[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7lmathis(A, B)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[(1/y) dx, ((x + 1)/y) dx, ((x^2 - x + 1)/y) dx, ((x^3 + 1)/y) dx, ((x^4 + x^3 + x + 1)/y) dx, ((x^5 - x^4 + x^3 + x^2 - x + 1)/y) dx, ((x^6 - x^3 + 1)/y) dx]
+[(1, 0, 0, 0, 0, 0, 0), (1, 1, 0, 0, 0, 0, 0), (1, 2, 1, 0, 0, 0, 0), (1, 0, 0, 1, 0, 0, 0), (1, 1, 0, 1, 1, 0, 0), (1, 2, 1, 1, 2, 1, 0), (1, 0, 0, 2, 0, 0, 1)]
+[1 1 1 1 1 1 1]
+[0 1 2 0 1 2 0]
+[0 0 1 0 0 1 0]
+[0 0 0 1 1 1 2]
+[0 0 0 0 1 2 0]
+[0 0 0 0 0 1 0]
+[0 0 0 0 0 0 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[1 1 1 1 1 1 1]
+[0 1 2 0 1 2 0]
+[0 0 1 0 0 1 0]
+[0 0 0 1 1 1 2]
+[0 0 0 0 1 2 0]
+[0 0 0 0 0 1 0]
+[0 0 0 0 0 0 1]
+[
+RModule M of dimension 7 over GF(3)
+]
+{
+[1 1 1 1 1 1 1]
+[0 1 2 0 1 2 0]
+[0 0 1 0 0 1 0]
+[0 0 0 1 1 1 2]
+[0 0 0 0 1 2 0]
+[0 0 0 0 0 1 0]
+[0 0 0 0 0 0 1],
+[0 2 0 1 0 0 0]
+[0 0 2 0 1 0 0]
+[1 0 0 2 0 1 0]
+[0 0 2 0 1 0 0]
+[0 0 0 2 0 1 0]
+[0 1 0 0 2 0 1]
+[0 0 0 2 0 1 0]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA = C_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l[0][?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A[0].cartier()

+[?7h[?12l[?25h[?2004l[?7h((x^3 - x)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[0].cartier()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: A[0].cartier().coordinates()

+[?7h[?12l[?25h[?2004l[?7h(0, 2, 0, 1, 0, 0, 0)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[1 1 1 1 1 1 1]
+[0 1 2 0 1 2 0]
+[0 0 1 0 0 1 0]
+[0 0 0 1 1 1 2]
+[0 0 0 0 1 2 0]
+[0 0 0 0 0 1 0]
+[0 0 0 0 0 0 1]
+[
+RModule M of dimension 7 over GF(3)
+]
+{
+[1 1 1 1 1 1 1]
+[0 1 2 0 1 2 0]
+[0 0 1 0 0 1 0]
+[0 0 0 1 1 1 2]
+[0 0 0 0 1 2 0]
+[0 0 0 0 0 1 0]
+[0 0 0 0 0 0 1],
+[0 0 1 0 0 0 0]
+[2 0 0 0 0 1 0]
+[0 2 0 2 0 0 0]
+[1 0 2 0 2 0 2]
+[0 1 0 1 0 2 0]
+[0 0 1 0 1 0 1]
+[0 0 0 0 0 1 0]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.cartier_matrix()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.de_rham_basis()

+[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
+ ((x/y) dx, 0, (x/y) dx),
+ ((x^2/y) dx, 0, (x^2/y) dx),
+ ((x^3/y) dx, 0, (x^3/y) dx),
+ ((x^4/y) dx, 0, (x^4/y) dx),
+ ((x^5/y) dx, 0, (x^5/y) dx),
+ ((x^6/y) dx, 0, (x^6/y) dx),
+ (((x^13 - x^11 - x^7 + x^5)/y) dx, 2/x*y, ((-1)/(x^2*y)) dx),
+ (((-x^12 + x^8 + x^6 - x^2)/y) dx, 2/x^2*y, (1/(x^3*y)) dx),
+ (((x^9 - x^7 - x^3 + x)/y) dx, 2/x^3*y, 0 dx),
+ (((x^10 - x^8 - x^4 + x^2)/y) dx, 2/x^4*y, ((-1)/(x^5*y)) dx),
+ (((-x^9 + x^5 + x^3)/y) dx, 2/x^5*y, ((x^5 + 1)/(x^6*y)) dx),
+ (((x^6 - x^4 - 1)/y) dx, 2/x^6*y, ((-1)/(x^2*y)) dx),
+ (((x^7 - x^5 - x)/y) dx, 2/x^7*y, ((-x^7 - 1)/(x^8*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [33], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:29, in <module>
+
+File <string>:17, in autom(omega)
+
+AttributeError: 'superelliptic_cech' object has no attribute 'form'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7lsage: A

+[?7h[?12l[?25h[?2004l[?7h[((1/y) dx, 0, (1/y) dx),
+ ((x/y) dx, 0, (x/y) dx),
+ ((x^2/y) dx, 0, (x^2/y) dx),
+ ((x^3/y) dx, 0, (x^3/y) dx),
+ ((x^4/y) dx, 0, (x^4/y) dx),
+ ((x^5/y) dx, 0, (x^5/y) dx),
+ ((x^6/y) dx, 0, (x^6/y) dx),
+ (((x^13 - x^11 - x^7 + x^5)/y) dx, 2/x*y, ((-1)/(x^2*y)) dx),
+ (((-x^12 + x^8 + x^6 - x^2)/y) dx, 2/x^2*y, (1/(x^3*y)) dx),
+ (((x^9 - x^7 - x^3 + x)/y) dx, 2/x^3*y, 0 dx),
+ (((x^10 - x^8 - x^4 + x^2)/y) dx, 2/x^4*y, ((-1)/(x^5*y)) dx),
+ (((-x^9 + x^5 + x^3)/y) dx, 2/x^5*y, ((x^5 + 1)/(x^6*y)) dx),
+ (((x^6 - x^4 - 1)/y) dx, 2/x^6*y, ((-1)/(x^2*y)) dx),
+ (((x^7 - x^5 - x)/y) dx, 2/x^7*y, ((-x^7 - 1)/(x^8*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A[0]

+[?7h[?12l[?25h[?2004l[?7h((1/y) dx, 0, (1/y) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm = 7[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: mm = A[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmm = A[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: mm.

+ mm.coordinates  mm.frobenius    mm.omega8      

+ mm.curve        mm.is_cocycle   mm.verschiebung

+ mm.f            mm.omega0                      

+

+ [?7h[?12l[?25h[?25l[?7lf

+

+

+[?7h[?12l[?25h[?25l[?7lsage: mm.f

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lA[0][?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: A[-1]

+[?7h[?12l[?25h[?2004l[?7h(((x^7 - x^5 - x)/y) dx, 2/x^7*y, ((-x^7 - 1)/(x^8*y)) dx)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lA[-1][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lsage: A[-1].f

+[?7h[?12l[?25h[?2004l[?7h2/x^7*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[-1].f[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lsage: A[-1].f.fct

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [40], in <cell line: 1>()
+----> 1 A[-Integer(1)].f.fct
+
+AttributeError: 'superelliptic_function' object has no attribute 'fct'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lA[-1].f.fct[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7luct[?7h[?12l[?25h[?25l[?7lnct[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsage: A[-1].f.function

+[?7h[?12l[?25h[?2004l[?7h2/x^7*y
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lset(*lista2)[?7h[?12l[?25h[?25l[?7lubset_um_quadratic_form(A0, q)[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lsage: ?superelliptic_cech

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+OSError                                   Traceback (most recent call last)
+Input In [42], in <cell line: 1>()
+----> 1 get_ipython().run_line_magic('pinfo', 'superelliptic_cech')
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:2305, in InteractiveShell.run_line_magic(self, magic_name, line, _stack_depth)
+   2303     kwargs['local_ns'] = self.get_local_scope(stack_depth)
+   2304 with self.builtin_trap:
+-> 2305     result = fn(*args, **kwargs)
+   2306 return result
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/magics/namespace.py:58, in NamespaceMagics.pinfo(self, parameter_s, namespaces)
+     56     self.psearch(oname)
+     57 else:
+---> 58     self.shell._inspect('pinfo', oname, detail_level=detail_level,
+     59                         namespaces=namespaces)
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:1685, in InteractiveShell._inspect(self, meth, oname, namespaces, **kw)
+   1683     pmethod(info.obj, oname, formatter)
+   1684 elif meth == 'pinfo':
+-> 1685     pmethod(
+   1686         info.obj,
+   1687         oname,
+   1688         formatter,
+   1689         info,
+   1690         enable_html_pager=self.enable_html_pager,
+   1691         **kw,
+   1692     )
+   1693 else:
+   1694     pmethod(info.obj, oname)
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:698, in Inspector.pinfo(self, obj, oname, formatter, info, detail_level, enable_html_pager, omit_sections)
+    665 def pinfo(
+    666     self,
+    667     obj,
+   (...)
+    673     omit_sections=(),
+    674 ):
+    675     """Show detailed information about an object.
+    676 
+    677     Optional arguments:
+   (...)
+    696     - omit_sections: set of section keys and titles to omit
+    697     """
+--> 698     info = self._get_info(
+    699         obj, oname, formatter, info, detail_level, omit_sections=omit_sections
+    700     )
+    701     if not enable_html_pager:
+    702         del info['text/html']
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:591, in Inspector._get_info(self, obj, oname, formatter, info, detail_level, omit_sections)
+    571 def _get_info(
+    572     self, obj, oname="", formatter=None, info=None, detail_level=0, omit_sections=()
+    573 ):
+    574     """Retrieve an info dict and format it.
+    575 
+    576     Parameters
+   (...)
+    588         Titles or keys to omit from output (can be set, tuple, etc., anything supporting `in`)
+    589     """
+--> 591     info = self.info(obj, oname=oname, info=info, detail_level=detail_level)
+    593     _mime = {
+    594         'text/plain': [],
+    595         'text/html': '',
+    596     }
+    598     def append_field(bundle, title:str, key:str, formatter=None):
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/oinspect.py:762, in Inspector.info(self, obj, oname, info, detail_level)
+    760             ds += "\nDocstring:\n" + obj.__doc__
+    761 else:
+--> 762     ds = getdoc(obj)
+    763     if ds is None:
+    764         ds = '<no docstring>'
+
+File /ext/sage/9.7/src/sage/misc/lazy_import.pyx:391, in sage.misc.lazy_import.LazyImport.__call__()
+    389         True
+    390     """
+--> 391     return self.get_object()(*args, **kwds)
+    392 
+    393 def __repr__(self):
+
+File /ext/sage/9.7/src/sage/misc/sageinspect.py:2107, in sage_getdoc(obj, obj_name, embedded)
+   2105 r = sage_getdoc_original(obj)
+   2106 s = sage.misc.sagedoc.format(r, embedded=embedded)
+-> 2107 f = sage_getfile(obj)
+   2108 if f and os.path.exists(f):
+   2109     from sage.doctest.control import skipfile
+
+File /ext/sage/9.7/src/sage/misc/sageinspect.py:1414, in sage_getfile(obj)
+   1412 # No go? fall back to inspect.
+   1413 try:
+-> 1414     sourcefile = inspect.getabsfile(obj)
+   1415 except TypeError: # this happens for Python builtins
+   1416     return ''
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:844, in getabsfile(object, _filename)
+    839 """Return an absolute path to the source or compiled file for an object.
+    840 
+    841 The idea is for each object to have a unique origin, so this routine
+    842 normalizes the result as much as possible."""
+    843 if _filename is None:
+--> 844     _filename = getsourcefile(object) or getfile(object)
+    845 return os.path.normcase(os.path.abspath(_filename))
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:817, in getsourcefile(object)
+    813 def getsourcefile(object):
+    814     """Return the filename that can be used to locate an object's source.
+    815     Return None if no way can be identified to get the source.
+    816     """
+--> 817     filename = getfile(object)
+    818     all_bytecode_suffixes = importlib.machinery.DEBUG_BYTECODE_SUFFIXES[:]
+    819     all_bytecode_suffixes += importlib.machinery.OPTIMIZED_BYTECODE_SUFFIXES[:]
+
+File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/inspect.py:785, in getfile(object)
+    783             return module.__file__
+    784         if object.__module__ == '__main__':
+--> 785             raise OSError('source code not available')
+    786     raise TypeError('{!r} is a built-in class'.format(object))
+    787 if ismethod(object):
+
+OSError: source code not available
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l?superelliptic_cech[?7h[?12l[?25h[?25l[?7lA[-1].f.function[?7h[?12l[?25h[?25l[?7l?superelliptic_cech[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+UnboundLocalError                         Traceback (most recent call last)
+Input In [43], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:44, in <module>
+
+File <string>:33, in automdR(omega)
+
+UnboundLocalError: local variable 'om8' referenced before assignment
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[1 1 1 1 1 1 1 0 0 0 0 0 0 0]
+[0 1 2 0 1 2 0 0 0 0 0 0 0 0]
+[0 0 1 0 0 1 0 0 0 0 0 0 0 0]
+[0 0 0 1 1 1 2 0 0 0 0 0 0 0]
+[0 0 0 0 1 2 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 1 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 1 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0 0 0 0 0]
+[
+RModule of dimension 1 over GF(3),
+RModule of dimension 1 over GF(3),
+RModule of dimension 1 over GF(3),
+RModule of dimension 1 over GF(3),
+RModule of dimension 10 over GF(3)
+]
+{
+[0]
+}
+{
+[0]
+}
+{
+[0]
+}
+{
+[0]
+}
+{
+[1 1 1 1 1 1 1 0 0 0]
+[0 1 2 0 1 2 0 0 0 0]
+[0 0 1 0 0 1 0 0 0 0]
+[0 0 0 1 1 1 2 0 0 0]
+[0 0 0 0 1 2 0 0 0 0]
+[0 0 0 0 0 1 0 0 0 0]
+[0 0 0 0 0 0 1 0 0 0]
+[0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0],
+[0 0 1 0 0 0 0 0 2 0]
+[2 0 0 0 0 1 0 1 0 1]
+[0 2 0 2 0 0 0 0 1 2]
+[1 0 2 0 2 0 2 2 0 0]
+[0 1 0 1 0 2 0 0 0 1]
+[0 0 1 0 1 0 1 0 0 0]
+[0 0 0 0 0 1 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0]
+[0 0 0 0 0 0 0 0 0 0]
+}
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [45], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:43, in <module>
+
+File <string>:75, in coordinates(self)
+
+File <string>:113, in degree_of_rational_fctn(f, F)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_ring_constructor.py:554, in PolynomialRing(base_ring, *args, **kwds)
+     52 r"""
+     53 Return the globally unique univariate or multivariate polynomial
+     54 ring with given properties and variable name or names.
+   (...)
+    551     TypeError: unable to convert 'x' to an integer
+    552 """
+    553 if not ring.is_Ring(base_ring):
+--> 554     raise TypeError("base_ring {!r} must be a ring".format(base_ring))
+    556 n = -1  # Unknown number of variables
+    557 names = None  # Unknown variable names
+
+TypeError: base_ring 3 must be a ring
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx, y = C_super.x, C_super.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.x

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [2], in <cell line: 1>()
+----> 1 C.x
+
+NameError: name 'C' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l_super.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C_super.x

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltC_super.x[?7h[?12l[?25h[?25l[?7lyC_super.x[?7h[?12l[?25h[?25l[?7lpC_super.x[?7h[?12l[?25h[?25l[?7leC_super.x[?7h[?12l[?25h[?25l[?7ltype(C_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: type(C_super.x)

+[?7h[?12l[?25h[?2004l[?7h<class '__main__.superelliptic_function'>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(C_super.x)[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C_super.x.diffn()

+[?7h[?12l[?25h[?2004l[?7h1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [6], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:13, in <module>
+
+File <string>:46, in __mul__(self, other)
+
+AttributeError: 'superelliptic_form' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x.diffn()[?7h[?12l[?25h[?25l[?7l_super.x.diffn()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7liC_super.x[?7h[?12l[?25h[?25l[?7lsC_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_C_super.x[?7h[?12l[?25h[?25l[?7liC_super.x[?7h[?12l[?25h[?25l[?7lsC_super.x[?7h[?12l[?25h[?25l[?7lC_super.x[?7h[?12l[?25h[?25l[?7lnC_super.x[?7h[?12l[?25h[?25l[?7lsC_super.x[?7h[?12l[?25h[?25l[?7ltC_super.x[?7h[?12l[?25h[?25l[?7laC_super.x[?7h[?12l[?25h[?25l[?7lnC_super.x[?7h[?12l[?25h[?25l[?7lcC_super.x[?7h[?12l[?25h[?25l[?7leC_super.x[?7h[?12l[?25h[?25l[?7l(C_super.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7ls)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lsuper)[?7h[?12l[?25h[?25l[?7lsupere)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l_)[?7h[?12l[?25h[?25l[?7lf)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lt)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lo)[?7h[?12l[?25h[?25l[?7ln)[?7h[?12l[?25h[?25l[?7lsage: is_instance(C_super.x, superelliptic_function)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [7], in <cell line: 1>()
+----> 1 is_instance(C_super.x, superelliptic_function)
+
+NameError: name 'is_instance' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lis_instance(C_super.x, superelliptic_function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lisinstance(C_super.x, supereliptic_function)[?7h[?12l[?25h[?25l[?7lsage: isinstance(C_super.x, superelliptic_function)

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lisinstance(C_super.x, superelliptic_function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: isinstance(C_super.x, superelliptic_function)

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x.diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(C_super.x)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7ltype[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l(C_super.x)[?7h[?12l[?25h[?25l[?7lsage: type(C_super.x)

+[?7h[?12l[?25h[?2004l[?7h<class '__main__.superelliptic_function'>
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ltype(C_super.x)[?7h[?12l[?25h[?25l[?7lisinstance(C_super.x, superelliptic_function)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsuper)[?7h[?12l[?25h[?25l[?7lsupe)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsuperelliptic_function)[?7h[?12l[?25h[?25l[?7lsage: isinstance(C_super.x, superelliptic_function)

+[?7h[?12l[?25h[?2004l[?7hFalse
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+!
+!
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [12], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:13, in <module>
+
+File <string>:47, in __mul__(self, other)
+
+AttributeError: 'superelliptic_form' object has no attribute 'function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [13], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:13, in <module>
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__()
+    492         AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah'
+    493     """
+--> 494     return self.getattr_from_category(name)
+    495 
+    496 cdef getattr_from_category(self, name):
+
+File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category()
+    505     else:
+    506         cls = P._abstract_element_class
+--> 507     return getattr_from_other_class(self, cls, name)
+    508 
+    509 def __dir__(self):
+
+File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class()
+    359     dummy_error_message.cls = type(self)
+    360     dummy_error_message.name = name
+--> 361     raise AttributeError(dummy_error_message)
+    362 attribute = <object>attr
+    363 # Check for a descriptor (__get__ in Python)
+
+AttributeError: 'sage.rings.fraction_field_element.FractionFieldElement' object has no attribute 'diffn'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC_super.x.diffn()[?7h[?12l[?25h[?25l[?7l.x[?7h[?12l[?25h[?25l[?7lde_rham_basis()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.dx

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [14], in <cell line: 1>()
+----> 1 C.dx
+
+AttributeError: 'superelliptic' object has no attribute 'dx'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [15], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:21, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:13, in <module>
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:2037, in sage.rings.integer.Integer.__truediv__()
+   2035         return y
+   2036 
+-> 2037     return coercion_model.bin_op(left, right, operator.truediv)
+   2038 
+   2039 cpdef _div_(self, right):
+
+File /ext/sage/9.7/src/sage/structure/coerce.pyx:1248, in sage.structure.coerce.CoercionModel.bin_op()
+   1246     # We should really include the underlying error.
+   1247     # This causes so much headache.
+-> 1248     raise bin_op_exception(op, x, y)
+   1249 
+   1250 cpdef canonical_coercion(self, x, y):
+
+TypeError: unsupported operand parent(s) for /: 'Integer Ring' and '<class '__main__.superelliptic_function'>'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [16] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:1 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:21
+    self.gen(1) = superelliptic_function(self, Rxy(_sage_const_1 ))
+    ^
+SyntaxError: cannot assign to function call here. Maybe you meant '==' instead of '='?
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[((1/y) dx, 0, (1/y) dx), ((x/y) dx, 2/x*y, ((-1)/(x*y)) dx)]
+((x^11 - x^9 + x^7 - x^3 + y)/(x^5*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l((x^12 - x^10 + x^8 - x^4 - x^2 + 1)/(x^6*y)) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lIfactors = I.factor()[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()([?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: Integers(9)(5/2)

+[?7h[?12l[?25h[?2004l[?7h7
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+ [?7h[?12l[?25h[?25l[?7lIntegers(9)(5/2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/2)[?7h[?12l[?25h[?25l[?7l-/2)[?7h[?12l[?25h[?25l[?7l7/2)[?7h[?12l[?25h[?25l[?7lsage: Integers(9)(-7/2)

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2-1)^4[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^2/y^3).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^5 + O(t^15)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l4/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lsage: (x^4/y^3).expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht + 2*t^5 + 2*t^9 + O(t^11)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^4/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^4/y^3).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (x^2+x^4)*y^2*y.diffn()

+[?7h[?12l[?25h[?2004l[?7h((x^7 - x^3)/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = A[0][?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2+x^4)*y^2*y.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lo(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7lm(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l (x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l=(x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7l (x^2+x^4)*y^2*y.difn()[?7h[?12l[?25h[?25l[?7lsage: om = (x^2+x^4)*y^2*y.diffn()

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lom = (x^2+x^4)*y^2*y.diffn()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.form[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: om.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-14 + O(t^-4)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: 

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lP[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: P1

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equation:
+ z^3 - z = x^2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le_rham_basis()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lgical_element[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.

+  C.at_most_poles                       C.cohomology_of_structure_sheaf_basis C.exponent_of_different               C.genus                               
 

+  C.at_most_poles_forms                 C.de_rham_basis                       C.exponent_of_different_prim          C.group                               
 

+  C.base_ring                           C.dx                                  C.fct_field                           C.height                              
>

+  C.characteristic                      C.dx_series                           C.functions                           C.holomorphic_differentials_basis     
 

+ [?7h[?12l[?25h[?25l[?7lat_most_poles

+ C.at_most_poles                      

+

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis

+ C.at_most_poles                       C.cohomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7lexpnent_of_different

+ C.cohomology_of_structure_sheaf_basis C.exponent_of_different              [?7h[?12l[?25h[?25l[?7lgenus

+ C.exponent_of_different               C.genus                              [?7h[?12l[?25h[?25l[?7lith_ramification_gp

+ cohomology_of_structure_sheaf_basisexpnent_of_different              genus                ith_ramification_gp

+ derhambasi      exponent_of_different_primgroup                     jumps

+<dx       fct_fieldheight   lift_o_de_rham

+ dx_seris     functionholomorphic_differentials_basismagical_element                [?7h[?12l[?25h[?25l[?7lnb_of_pts_at_nfty

+expnent_of_different              genus                ith_ramification_gpnb_of_pts_at_nfty 

+exponent_of_different_primgroup                     jumpsprec 

+fct_fieldheight   lift_o_de_rhampseudo_magical_element

+functionholomorphic_differentials_basismagical_element                quotient       [?7h[?12l[?25h[?25l[?7lramiicationjumps

+genus                ith_ramification_gpnb_of_pts_at_nfty ramiicationjumps

+group                     jumpsprec uniformizer

+height   lift_o_de_rhampseudo_magical_elementx                     

+holomorphic_differentials_basismagical_element                quotient       x_series[?7h[?12l[?25h[?25l[?7ly

+ith_ramification_gpnb_of_pts_at_nfty ramiicationjumpsy                  

+jumpsprec uniformizery_series    

+lift_o_de_rhampseudo_magical_elementx                     z 

+magical_element                quotient       x_seriesz 
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_series

+ C.y                                  

+ C.y_series                           [?7h[?12l[?25h[?25l[?7lz

+

+ C.y_series                           

+ C.z                                  [?7h[?12l[?25h[?25l[?7l_series

+

+

+ C.z                                  

+ C.z_series                           [?7h[?12l[?25h[?25l[?7l

+ a_most_poles      cohmology_of_structure_sheaf_basisexponent_of_differentgenus 

+ at_most_poles_formsde_rham_basisexponent_of_different_primgroup    

+ basering      dx                    fct_fieldheight>

+ characteristic dx_seriesfunctons C.holomorphic_differentials_basis     

+[?7h[?12l[?25h[?25l[?7l

+

+

+

+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+  C                                  CFiniteSequence                    CPRFanoToricVariety                CRT_vectors                         

+  CBF                                CFiniteSequences                   CRT                                C_super                             

+  CC                                 CIF                                CRT_basis                          CachedFunction                     >

+  CDF                                CLF                                CRT_list                           CallableSymbolicExpressionRing      [?7h[?12l[?25h[?25l[?7l

+ C                                 

+

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7lFiniteSequence.

+ C                                  CFiniteSequence                   [?7h[?12l[?25h[?25l[?7lPRFanoToricVariety.

+ CFiniteSequence                    CPRFanoToricVariety               [?7h[?12l[?25h[?25l[?7l.

+

+

+

+

+[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7l

+  C.at_most_poles                       C.cohomology_of_structure_sheaf_basis C.exponent_of_different               C.genus                               
 

+  C.at_most_poles_forms                 C.de_rham_basis                       C.exponent_of_different_prim          C.group                               
 

+  C.base_ring                           C.dx                                  C.fct_field                           C.height                              
>

+  C.characteristic                      C.dx_series                           C.functions                           C.holomorphic_differentials_basis     
 
[?7h[?12l[?25h[?25l[?7lat_most_poles

+ C.at_most_poles                      

+

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_forms

+ C.at_most_poles                      

+ C.at_most_poles_forms                [?7h[?12l[?25h[?25l[?7lbase_ring

+

+ C.at_most_poles_forms                

+ C.base_ring                          [?7h[?12l[?25h[?25l[?7lcharacteristic

+

+

+ C.base_ring                          

+ C.characteristic                     [?7h[?12l[?25h[?25l[?7lohomology_of_structure_sheaf_basis

+ C.cohomology_of_structure_sheaf_basis

+

+

+ C.characteristic                     [?7h[?12l[?25h[?25l[?7lde_rham_basis

+ C.cohomology_of_structure_sheaf_basis

+ C.de_rham_basis                      [?7h[?12l[?25h[?25l[?7lx

+

+ C.de_rham_basis                      

+ C.dx                                 [?7h[?12l[?25h[?25l[?7l_series

+

+

+ C.dx                                 

+ C.dx_series                          [?7h[?12l[?25h[?25l[?7leponent_of_different

+ C.exponent_of_different              

+

+

+ C.dx_series                          [?7h[?12l[?25h[?25l[?7l_prim

+ C.exponent_of_different              

+ C.exponent_of_different_prim         [?7h[?12l[?25h[?25l[?7lfct_field

+

+ C.exponent_of_different_prim         

+ C.fct_field                          [?7h[?12l[?25h[?25l[?7lunctons

+

+

+ C.fct_field                          

+ C.functions                          [?7h[?12l[?25h[?25l[?7lgeus

+ C.genus                              

+

+

+ C.functions                          [?7h[?12l[?25h[?25l[?7lrop

+ C.genus                              

+ C.group                              [?7h[?12l[?25h[?25l[?7lheight

+

+ C.group                              

+ C.height                             [?7h[?12l[?25h[?25l[?7lolomorphic_differentials_basis

+

+

+ C.height                             

+ C.holomorphic_differentials_basis    [?7h[?12l[?25h[?25l[?7lith_ramifaton_gp

+ cohomology_of_structure_sheaf_basisexpnent_of_different              genus                 C.ith_ramification_gp                

+ derhambasi      exponent_of_different_primgroup                     jumps

+<dx       fct_fieldheight   lift_o_de_rham

+ dx_seris     functionholomorphic_differentials_basis C.magical_element                    [?7h[?12l[?25h[?25l[?7ljumps

+ C.ith_ramification_gp                

+ C.jumps                              [?7h[?12l[?25h[?25l[?7llift_to_de_rham

+

+ C.jumps                              

+ C.lift_to_de_rham                    [?7h[?12l[?25h[?25l[?7lmagicalelement

+

+

+ C.lift_to_de_rham                    

+ C.magical_element                    [?7h[?12l[?25h[?25l[?7lnb_of_pts_at_infty

+expnent_of_different              genus                ith_ramification_gp C.nb_of_pts_at_infty                 

+exponent_of_different_primgroup                     jumpsprec 

+fct_fieldheight   lift_o_de_rhampseudo_magical_element

+functionholomorphic_differentials_basismagical_element                 C.quotient                           [?7h[?12l[?25h[?25l[?7lprec

+ C.nb_of_pts_at_infty                 

+ C.prec                               [?7h[?12l[?25h[?25l[?7lsudo_magical_element

+

+ C.prec                               

+ C.pseudo_magical_element             [?7h[?12l[?25h[?25l[?7lquotient

+

+

+ C.pseudo_magical_element             

+ C.quotient                           [?7h[?12l[?25h[?25l[?7lramification_jumps

+genus                ith_ramification_gpnb_of_pts_at_nfty  C.ramification_jumps                 

+group                     jumpsprec uniformizer

+height   lift_o_de_rhampseudo_magical_elementx                     

+holomorphic_differentials_basismagical_element                quotient        C.x_series                           [?7h[?12l[?25h[?25l[?7luniformizer

+ C.ramification_jumps                 

+ C.uniformizer                        [?7h[?12l[?25h[?25l[?7lx

+

+ C.uniformizer                        

+ C.x                                  [?7h[?12l[?25h[?25l[?7l_series

+

+

+ C.x                                  

+ C.x_series                           [?7h[?12l[?25h[?25l[?7ly

+ith_ramification_gpnb_of_pts_at_nfty ramiicationjumps C.y                                   

+jumpsprec uniformizery_series    

+lift_o_de_rhampseudo_magical_elementx                     z 

+magical_element                quotient       x_series C.z_series                            
[?7h[?12l[?25h[?25l[?7l_series

+ C.y                                  

+ C.y_series                           [?7h[?12l[?25h[?25l[?7lz

+

+ C.y_series                           

+ C.z                                  [?7h[?12l[?25h[?25l[?7l_series

+

+

+ C.z                                  

+ C.z_series                           [?7h[?12l[?25h[?25l[?7l

+ a_most_poles      cohmology_of_structure_sheaf_basisexponent_of_differentgenus 

+ at_most_poles_formsde_rham_basisexponent_of_different_primgroup    

+ basering      dx                    fct_fieldheight>

+ characteristic dx_seriesfunctons C.holomorphic_differentials_basis     

+[?7h[?12l[?25h[?25l[?7lat_most_poles

+ C.at_most_poles                      

+

+

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lcohomology_of_structure_sheaf_basis

+ C.at_most_poles                       C.cohomology_of_structure_sheaf_basis[?7h[?12l[?25h[?25l[?7lexpnent_of_different

+ C.cohomology_of_structure_sheaf_basis C.exponent_of_different              [?7h[?12l[?25h[?25l[?7lgenus

+ C.exponent_of_different               C.genus                              [?7h[?12l[?25h[?25l[?7lith_ramification_gp

+ cohomology_of_structure_sheaf_basisexpnent_of_different              genus                ith_ramification_gp

+ derhambasi      exponent_of_different_primgroup                     jumps

+<dx       fct_fieldheight   lift_o_de_rham

+ dx_seris     functionholomorphic_differentials_basismagical_element                [?7h[?12l[?25h[?25l[?7lnb_of_pts_at_nfty

+expnent_of_different              genus                ith_ramification_gpnb_of_pts_at_nfty 

+exponent_of_different_primgroup                     jumpsprec 

+fct_fieldheight   lift_o_de_rhampseudo_magical_element

+functionholomorphic_differentials_basismagical_element                quotient       [?7h[?12l[?25h[?25l[?7lramiicationjumps

+genus                ith_ramification_gpnb_of_pts_at_nfty ramiicationjumps

+group                     jumpsprec uniformizer

+height   lift_o_de_rhampseudo_magical_elementx                     

+holomorphic_differentials_basismagical_element                quotient       x_series[?7h[?12l[?25h[?25l[?7ly

+ith_ramification_gpnb_of_pts_at_nfty ramiicationjumpsy                  

+jumpsprec uniformizery_series    

+lift_o_de_rhampseudo_magical_elementx                     z 

+magical_element                quotient       x_seriesz 
[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lramification_jumps

+ C.ramification_jumps                  C.y                                  [?7h[?12l[?25h[?25l[?7luniformizer

+ C.ramification_jumps                 

+ C.uniformizer                        [?7h[?12l[?25h[?25l[?7lx

+

+ C.uniformizer                        

+ C.x                                  [?7h[?12l[?25h[?25l[?7lpseudo_magical_element

+

+

+ C.pseudo_magical_element              C.x                                  [?7h[?12l[?25h[?25l[?7lquotient

+

+

+ C.pseudo_magical_element             

+ C.quotient                           [?7h[?12l[?25h[?25l[?7lpseudo_magical_element

+

+

+ C.pseudo_magical_element             

+ C.quotient                           [?7h[?12l[?25h[?25l[?7lrc

+

+ C.prec                               

+ C.pseudo_magical_element             [?7h[?12l[?25h[?25l[?7lnb_of_pts_at_infty

+ C.nb_of_pts_at_infty                 

+ C.prec                               [?7h[?12l[?25h[?25l[?7lith_ramificaton_gp

+ C.ith_ramification_gp                 C.nb_of_pts_at_infty                 [?7h[?12l[?25h[?25l[?7ljumps

+ C.ith_ramification_gp                

+ C.jumps                              [?7h[?12l[?25h[?25l[?7llift_to_de_rham

+

+ C.jumps                              

+ C.lift_to_de_rham                    [?7h[?12l[?25h[?25l[?7lmagicalelement

+

+

+ C.lift_to_de_rham                    

+ C.magical_element                    [?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis

+genus              ith_ramificaton_gpnb_o_pts_atinftyramification_jumps 

+groupjumpsprec       uniformizer 

+heigh         lift_to_de_rham       pseudo_magical_elementx>

+holomorphic_differentials_basismagical_elementquotientx 
[?7h[?12l[?25h[?25l[?7leight

+

+

+ C.height                             

+ C.holomorphic_differentials_basis    [?7h[?12l[?25h[?25l[?7lgroup

+

+ C.group                              

+ C.height                             [?7h[?12l[?25h[?25l[?7lens

+ C.genus                              

+ C.group                              [?7h[?12l[?25h[?25l[?7lexponent_of_different

+exponent_of_differentgenus              ith_ramificaton_gpnb_o_pts_atinfty

+exponent_of_different_primgroupjumpsprec       

+fct_fieldheigh         lift_to_de_rham       pseudo_magical_element

+functions                      holomorphic_differentials_basismagical_elementquotient[?7h[?12l[?25h[?25l[?7l_prim

+ C.exponent_of_different              

+ C.exponent_of_different_prim         [?7h[?12l[?25h[?25l[?7lfct_field

+

+ C.exponent_of_different_prim         

+ C.fct_field                          [?7h[?12l[?25h[?25l[?7lunctons

+

+

+ C.fct_field                          

+ C.functions                          [?7h[?12l[?25h[?25l[?7ldx_serie

+cohmology_of_structure_sheaf_basisexponent_of_differentgenus              ith_ramificaton_gp

+de_rham_basis             exponent_of_different_primgroupjumps

+dx       fct_fieldheigh         lift_to_de_rham       

+dx_seriefunctions                      holomorphic_differentials_basismagical_element[?7h[?12l[?25h[?25l[?7lcharactristic

+ at_most_poles                      cohmology_of_structure_sheaf_basisexponent_of_differentgenus              

+ atmostpole_formsde_rham_basis             exponent_of_different_primgroup

+ base_ringdx       fct_fieldheigh         

+ charactristicdx_seriefunctions                      holomorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+

+

+

+

+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[[1 2]
+[0 1]]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+ [?7h[?12l[?25h[?25l[?7lIntegers(9)(-7/2)[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l9)(-7/2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/2)[?7h[?12l[?25h[?25l[?7l/2)[?7h[?12l[?25h[?25l[?7l5/2)[?7h[?12l[?25h[?25l[?7lsage: Integers(9)(5/2)

+[?7h[?12l[?25h[?2004l[?7h7
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l%[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7lsage: 7%3

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sa
+bash: sa: command not found
+]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ gesage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista2 = [][?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[[1 2]
+[0 1]]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equation:
+ z^3 - z = x^2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.x

+[?7h[?12l[?25h[?2004l[?7hx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lnsion_at_infty[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()

+[?7h[?12l[?25h[?2004l[?7ht^-3 + t + t^5 + O(t^7)
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()[-3]

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[-3][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l2][?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()[-2]

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[-2][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()[-1]

+[?7h[?12l[?25h[?2004l[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[-1][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7lsage: C.x.expansion_at_infty()[1]

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [9] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:21 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:32
+    basis += [superelliptic_cohomology(C, Fxy(m*y**(m-j)/x**i)))]
+                                                               ^
+SyntaxError: closing parenthesis ')' does not match opening parenthesis '['
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[[1 2]
+[0 1]]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: basis

+ basis              

+ basis_of_cohomology

+

+

+ [?7h[?12l[?25h[?25l[?7l

+ basis              

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l_of_cohomology

+ basis              

+ basis_of_cohomology[?7h[?12l[?25h[?25l[?7l

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: basis_of_cohomology(C)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [11], in <cell line: 1>()
+----> 1 basis_of_cohomology(C)
+
+File <string>:18, in basis_of_cohomology(C)
+
+AttributeError: 'as_cover' object has no attribute 'exponent'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7h(Z/p)-cover of Superelliptic curve with the equation y^1 = x over Finite Field of size 3 with the equation:
+ z^3 - z = x^2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lsage: basis_of_cohomology(C)

+[?7h[?12l[?25h[?2004l[?7h[<__main__.superelliptic_cohomology object at 0x7f4110fc8a60>]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lsage: basis_of_cohomology(C)

+[?7h[?12l[?25h[?2004l[?7h[[(-y)/x]]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: C.bas

+ C.base_ring                             

+ C.basis_de_rham_degrees                 

+ C.basis_holomorphic_differentials_degree

+

+ [?7h[?12l[?25h[?25l[?7l

+

+

+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?7h[(1/y) dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage: 

+

+

+ [?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004lTraceback (most recent call last):
+
+  File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code
+    exec(code_obj, self.user_global_ns, self.user_ns)
+
+  Input In [18] in <cell line: 1>
+    load('init.sage')
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:22 in <module>
+
+  File sage/misc/persist.pyx:175 in sage.misc.persist.load
+    sage.repl.load.load(filename, globals())
+
+  File /ext/sage/9.7/src/sage/repl/load.py:272 in load
+    exec(preparse_file(f.read()) + "\n", globals)
+
+  File <string>:10
+    print f.prod(omega)
+    ^
+SyntaxError: Missing parentheses in call to 'print'. Did you mean print(...)?
+
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [19], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:9, in <module>
+
+NameError: name 'basis_cohomology' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [20], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:10, in <module>
+
+File <string>:13, in prod(self, form)
+
+TypeError: unsupported operand type(s) for *: 'superelliptic_form' and 'superelliptic_cohomology'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [21], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:10, in <module>
+
+File <string>:14, in prod(self, form)
+
+File <string>:59, in __rmul__(self, constant)
+
+TypeError: unsupported operand type(s) for *: 'superelliptic_form' and 'PolynomialRing_field_with_category.element_class'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [22], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:10, in <module>
+
+File <string>:14, in prod(self, form)
+
+TypeError: superelliptic_form.expansion_at_infty() got an unexpected keyword argument 'place'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [24], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:10, in <module>
+
+File <string>:14, in prod(self, form)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
+    542         return type(self)(self._parent, f, self.__n)
+    543 
+--> 544     return self.__u[i - self.__n]
+    545 
+    546 def __iter__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
+    451         return self.base_ring().zero()
+    452     else:
+--> 453         raise IndexError("coefficient not known")
+    454 return self.__f[n]
+    455 
+
+IndexError: coefficient not known
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l2*t^-11 + O(t^-1)
+---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [25], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:10, in <module>
+
+File <string>:15, in prod(self, form)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
+    542         return type(self)(self._parent, f, self.__n)
+    543 
+--> 544     return self.__u[i - self.__n]
+    545 
+    546 def __iter__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
+    451         return self.base_ring().zero()
+    452     else:
+--> 453         raise IndexError("coefficient not known")
+    454 return self.__f[n]
+    455 
+
+IndexError: coefficient not known
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l2*t^-11 + 2*t^5 + O(t^9)
+0
+2*t^-7 + 2*t^9 + O(t^13)
+0
+2*t^-3 + 2*t^13 + O(t^17)
+0
+2*t^-6 + t^10 + O(t^14)
+0
+2*t^-2 + t^14 + O(t^18)
+0
+2*t^-1 + O(t^19)
+2
+2*t^-6 + t^10 + O(t^14)
+0
+2*t^-2 + t^14 + O(t^18)
+0
+2*t^2 + t^18 + O(t^22)
+0
+2*t^-1 + O(t^19)
+2
+2*t^3 + O(t^23)
+0
+2*t^4 + t^20 + O(t^24)
+0
+2*t^-10 + t^6 + O(t^10)
+0
+2*t^-6 + t^10 + O(t^14)
+0
+2*t^-2 + t^14 + O(t^18)
+0
+2*t^-5 + O(t^15)
+0
+2*t^-1 + O(t^19)
+2
+2 + t^16 + O(t^20)
+0
+2*t^-1 + O(t^19)
+2
+2*t^3 + O(t^23)
+0
+2*t^7 + O(t^27)
+0
+2*t^4 + t^20 + O(t^24)
+0
+2*t^8 + t^24 + O(t^28)
+0
+2*t^9 + O(t^29)
+0
+2*t^-5 + O(t^15)
+0
+2*t^-1 + O(t^19)
+2
+2*t^3 + O(t^23)
+0
+2 + t^16 + O(t^20)
+0
+2*t^4 + t^20 + O(t^24)
+0
+2*t^5 + O(t^25)
+0
+2*t^-9 + O(t^11)
+0
+2*t^-5 + O(t^15)
+0
+2*t^-1 + O(t^19)
+2
+2*t^-4 + t^12 + O(t^16)
+0
+2 + t^16 + O(t^20)
+0
+2*t + O(t^21)
+0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lholomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7lsage: C.holomorphic_differentials_basis()

+[?7h[?12l[?25h[?2004l[?7h[(1/y) dx, (1/y^2) dx, (x/y^2) dx, (1/y^3) dx, (x/y^3) dx, (x^2/y^3) dx]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l_of_pts_at_infty[?7h[?12l[?25h[?25l[?7lsage: C.nb_of_pts_at_infty

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.nb_of_pts_at_infty[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls_of_cohomology(C)[?7h[?12l[?25h[?25l[?7lsage: basis_of_cohomology(C)

+[?7h[?12l[?25h[?2004l[?7h[[y^3/x], [y^3/x^2], [y^3/x^3], [y^2/x], [y^2/x^2], [y/x]]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbasis_of_cohomology(C)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7labasis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l=basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7lsage: a = basis_of_cohomology(C)[0]

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = basis_of_cohomology(C)[0][?7h[?12l[?25h[?25l[?7l.squre_rot()[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC.holomorphic_differentials_basis()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7lsage: a.prod(C.holomorphic_differentials_basis()[0])

+[?7h[?12l[?25h[?2004l2*t^-11 + 2*t^5 + O(t^9)
+[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.prod(C.holomorphic_differentials_basis()[0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7lsage: a.prod(C.holomorphic_differentials_basis()[1])

+[?7h[?12l[?25h[?2004l2*t^-6 + t^10 + O(t^14)
+[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.prod(C.holomorphic_differentials_basis()[1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7lsage: a.prod(C.holomorphic_differentials_basis()[2])

+[?7h[?12l[?25h[?2004l2*t^-10 + t^6 + O(t^10)
+[?7h0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.prod(C.holomorphic_differentials_basis()[2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l3])[?7h[?12l[?25h[?25l[?7lsage: a.prod(C.holomorphic_differentials_basis()[3])

+[?7h[?12l[?25h[?2004l2*t^-1 + O(t^19)
+[?7h2
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.genus()

+[?7h[?12l[?25h[?2004l[?7h6
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+0
+0
+0
+0
+2
+0
+0
+0
+2
+0
+0
+0
+0
+0
+0
+2
+0
+2
+0
+0
+0
+0
+0
+0
+2
+0
+0
+0
+0
+0
+0
+2
+0
+0
+0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l0
+0
+0
+0
+0
+1
+0
+0
+0
+1
+0
+0
+0
+0
+0
+0
+1
+0
+1
+0
+0
+0
+0
+0
+0
+1
+0
+0
+0
+0
+0
+0
+1
+0
+0
+0
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lista2 = [][?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7l = [][?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: lista = ['a', 'b', 'c']

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor a in lista2:[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lirange(0, p):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, f in enumerate(AS.cohomology_of_structure_sheaf_basis()):[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lsage: for i, x in enum

+ enum_affine_finite_field          enumerate_totallyreal_fields_all 

+ enum_affine_rational_field        enumerate_totallyreal_fields_prim

+ enumerate                         enumerate_totallyreal_fields_rel 

+

+ [?7h[?12l[?25h[?25l[?7le

+

+

+[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lenumerate[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7llist[?7h[?12l[?25h[?25l[?7llista[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l

+....: [?7h[?12l[?25h[?25l[?7lprint(a, lista.count(a))[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()

+....: [?7h[?12l[?25h[?25l[?7lsage: for i, x in enumerate(lista):

+....:     print(i, x)

+....: 

+[?7h[?12l[?25h[?2004l0 a
+1 b
+2 c
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7llista = ['a', 'b', 'c'][?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[0, 0, 0, 1, 0, 0]
+[0, 0, 0, 0, 1, 0]
+[0, 0, 0, 0, 0, 1]
+[0, 1, 0, 0, 0, 0]
+[0, 0, 1, 0, 0, 0]
+[1, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[1, 0, 0, 0, 0, 0]
+[0, 1, 0, 0, 0, 0]
+[0, 0, 1, 0, 0, 0]
+[0, 0, 0, 1, 0, 0]
+[0, 0, 0, 0, 1, 0]
+[0, 0, 0, 0, 0, 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[1, 0, 0, 0, 0, 0]
+[0, 1, 0, 0, 0, 0]
+[0, 0, 1, 0, 0, 0]
+[0, 0, 0, 1, 0, 0]
+[0, 0, 0, 0, 1, 0]
+[0, 0, 0, 0, 0, 1]
+---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [44], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:10, in <module>
+
+File <string>:59, in frobenius_matrix(C)
+
+File <string>:35, in frobenius(self)
+
+AttributeError: 'superelliptic_cohomology' object has no attribute 'base_ring'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[1, 0, 0, 0, 0, 0]
+[0, 1, 0, 0, 0, 0]
+[0, 0, 1, 0, 0, 0]
+[0, 0, 0, 1, 0, 0]
+[0, 0, 0, 0, 1, 0]
+[0, 0, 0, 0, 0, 1]
+---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [45], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:10, in <module>
+
+File <string>:59, in frobenius_matrix(C)
+
+File /ext/sage/9.7/src/sage/matrix/matrix0.pyx:1509, in sage.matrix.matrix0.Matrix.__setitem__()
+   1507     raise IndexError("value does not have the right number of rows")
+   1508 for value_row in value_list:
+-> 1509     if col_list_len != len(value_row):
+   1510         raise IndexError("value does not have the right number of columns")
+   1511 
+
+TypeError: object of type 'sage.rings.finite_rings.integer_mod.IntegerMod_int' has no len()
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[1, 0, 0, 0, 0, 0]
+[0, 1, 0, 0, 0, 0]
+[0, 0, 1, 0, 0, 0]
+[0, 0, 0, 1, 0, 0]
+[0, 0, 0, 0, 1, 0]
+[0, 0, 0, 0, 0, 1]
+---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [46], in <cell line: 1>()
+----> 1 load('init.sage')
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:22, in <module>
+
+File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load()
+    173 
+    174     if sage.repl.load.is_loadable_filename(filename):
+--> 175         sage.repl.load.load(filename, globals())
+    176         return
+    177 
+
+File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach)
+    270             add_attached_file(fpath)
+    271         with open(fpath) as f:
+--> 272             exec(preparse_file(f.read()) + "\n", globals)
+    273 elif ext == '.spyx' or ext == '.pyx':
+    274     if attach:
+
+File <string>:10, in <module>
+
+File <string>:59, in frobenius_matrix(C)
+
+File <string>:29, in coordinates(self, basis, basis_holo)
+
+File <string>:14, in prod(self, form, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
+    542         return type(self)(self._parent, f, self.__n)
+    543 
+--> 544     return self.__u[i - self.__n]
+    545 
+    546 def __iter__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
+    451         return self.base_ring().zero()
+    452     else:
+--> 453         raise IndexError("coefficient not known")
+    454 return self.__f[n]
+    455 
+
+IndexError: coefficient not known
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[1, 0, 0, 0, 0, 0]
+[0, 1, 0, 0, 0, 0]
+[0, 0, 1, 0, 0, 0]
+[0, 0, 0, 1, 0, 0]
+[0, 0, 0, 0, 1, 0]
+[0, 0, 0, 0, 0, 1]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM.jordan_form()[?7h[?12l[?25h[?25l[?7lsage: M

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [48], in <cell line: 1>()
+----> 1 M
+
+NameError: name 'M' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor i, x in enumerate(lista):[?7h[?12l[?25h[?25l[?7lrom itertools import product[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [49], in <cell line: 1>()
+----> 1 frobenius_matrix(C)
+
+File <string>:59, in frobenius_matrix(C, prec)
+
+File <string>:29, in coordinates(self, basis, basis_holo, prec)
+
+File <string>:14, in prod(self, form, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
+    542         return type(self)(self._parent, f, self.__n)
+    543 
+--> 544     return self.__u[i - self.__n]
+    545 
+    546 def __iter__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
+    451         return self.base_ring().zero()
+    452     else:
+--> 453         raise IndexError("coefficient not known")
+    454 return self.__f[n]
+    455 
+
+IndexError: coefficient not known
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l-)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C, prec=50)

+[?7h[?12l[?25h[?2004l[?7h[0 0 0 1 0 0]
+[0 0 1 0 0 0]
+[0 1 0 0 0 0]
+[0 0 0 0 0 0]
+[0 0 0 0 0 0]
+[1 0 0 0 0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7l(),[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic_curve(2, x^3 - x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [51], in <cell line: 1>()
+----> 1 C = superelliptic_curve(Integer(2), x**Integer(3) - x)
+
+NameError: name 'superelliptic_curve' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic_curve(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l(2, x^3 - x)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(2, x^3 - x)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2441, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__()
+   2440 try:
+-> 2441     right = Integer(right)
+   2442 except TypeError:
+
+File /ext/sage/9.7/src/sage/rings/integer.pyx:658, in sage.rings.integer.Integer.__init__()
+    657 if otmp is not None:
+--> 658     set_from_Integer(self, otmp(the_integer_ring))
+    659     return
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:1390, in sage.rings.polynomial.polynomial_element.Polynomial._scalar_conversion()
+   1389 if self.degree() > 0:
+-> 1390     raise TypeError("cannot convert nonconstant polynomial")
+   1391 return R(self.get_coeff_c(0))
+
+TypeError: cannot convert nonconstant polynomial
+
+During handling of the above exception, another exception occurred:
+
+TypeError                                 Traceback (most recent call last)
+Input In [52], in <cell line: 1>()
+----> 1 C = superelliptic(Integer(2), x**Integer(3) - x)
+
+File <string>:19, in __init__(self, f, m)
+
+File <string>:13, in __init__(self, C, g)
+
+File <string>:188, in reduction(C, g)
+
+File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2443, in sage.rings.polynomial.polynomial_element.Polynomial.__pow__()
+   2441         right = Integer(right)
+   2442     except TypeError:
+-> 2443         raise TypeError("non-integral exponents not supported")
+   2444 
+   2445 d = self.degree()
+
+TypeError: non-integral exponents not supported
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(2, x^3 - x)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx^3 - x)[?7h[?12l[?25h[?25l[?7lx^3 - x)[?7h[?12l[?25h[?25l[?7lx^3 - x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l,)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 - x, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l.gens()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lus_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C, prec=50)

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 - x, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + 1, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C, prec=50)

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + 1, 2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 2)[?7h[?12l[?25h[?25l[?7lx, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l+, 2)[?7h[?12l[?25h[?25l[?7l , 2)[?7h[?12l[?25h[?25l[?7l1, 2)[?7h[?12l[?25h[?25l[?7lsage: C = superelliptic(x^3 + x + 1, 2)

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_matrix(C, prec=50)

+[?7h[?12l[?25h[?2004l[?7h[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.local_data(2)[?7h[?12l[?25h[?25l[?7l = ElipticCurve([0, 16])[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lEllipticCurve([0, 16])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lG[0, 16])[?7h[?12l[?25h[?25l[?7lF[0, 16])[?7h[?12l[?25h[?25l[?7l([0, 16])[?7h[?12l[?25h[?25l[?7l)[0, 16])[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l3)[0, 16])[?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l,[0, 16])[?7h[?12l[?25h[?25l[?7l [0, 16])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l,])[?7h[?12l[?25h[?25l[?7l ])[?7h[?12l[?25h[?25l[?7l1])[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [1, 1])

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [1, 1])[?7h[?12l[?25h[?25l[?7l.loca_data(2)[?7h[?12l[?25h[?25l[?7lis_goo(3)[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_[?7h[?12l[?25h[?25l[?7lsingular(2)[?7h[?12l[?25h[?25l[?7lupersingular(2)[?7h[?12l[?25h[?25l[?7lpersingular(2)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.is_supersingular()[?7h[?12l[?25h[?25l[?7l = EllipticCurve(GF(3), [1, 1])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [1, 2])

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [1, 2])[?7h[?12l[?25h[?25l[?7l.is_supersingular()[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.is_supersingular()[?7h[?12l[?25h[?25l[?7l = EllipticCurve(GF(3), [1, 2])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l0])[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [1, 0])

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [1, 0])[?7h[?12l[?25h[?25l[?7l.is_supersingular()[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.is_supersingular()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l = EllipticCurve(GF(3), [1, 0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, 0])[?7h[?12l[?25h[?25l[?7l2, 0])[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [2, 0])

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [2, 0])[?7h[?12l[?25h[?25l[?7l.is_supersingular()[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE.is_supersingular()[?7h[?12l[?25h[?25l[?7l = EllipticCurve(GF(3), [2, 0])[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l([])[?7h[?12l[?25h[?25l[?7l])[?7h[?12l[?25h[?25l[?7l2])[?7h[?12l[?25h[?25l[?7lsage: E = EllipticCurve(GF(3), [2, 2])

+[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lE = EllipticCurve(GF(3), [2, 2])[?7h[?12l[?25h[?25l[?7l.is_supersingular()[?7h[?12l[?25h[?25l[?7lsage: E.is_supersingular()

+[?7h[?12l[?25h[?2004l[?7hTrue
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[1, 0, 0, 0, 0, 0]
+[0, 1, 0, 0, 0, 0]
+[0, 0, 1, 0, 0, 0]
+[0, 0, 0, 1, 0, 0]
+[0, 0, 0, 0, 1, 0]
+[0, 0, 0, 0, 0, 1]
+[0 0 0 1 0 0]
+[0 0 1 0 0 0]
+[0 1 0 0 0 0]
+[0 0 0 0 0 0]
+[0 0 0 0 0 0]
+[1 0 0 0 0 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7load('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[5]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?7h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[5]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lkronecker_symbol(7, 8)[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lel[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_matrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsage: frobenius_

+ frobenius_kernel

+ frobenius_matrix

+

+

+ [?7h[?12l[?25h[?25l[?7lmatrix(C, prec=50)[?7h[?12l[?25h[?25l[?7lkernel

+ frobenius_kernel

+

+ <unknown> [?7h[?12l[?25h[?25l[?7l

+

+

+[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+TypeError                                 Traceback (most recent call last)
+Input In [73], in <cell line: 1>()
+----> 1 frobenius_kernel(C, prec=Integer(50))
+
+File <string>:89, in frobenius_kernel(C, prec)
+
+File /ext/sage/9.7/src/sage/misc/functional.py:585, in symbolic_sum(expression, *args, **kwds)
+    583     return expression.sum(*args, **kwds)
+    584 elif max(len(args),len(kwds)) <= 1:
+--> 585     return sum(expression, *args, **kwds)
+    586 else:
+    587     from sage.symbolic.ring import SR
+
+TypeError: unsupported operand type(s) for +: 'int' and 'superelliptic_function'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[5]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)

+[?7h[?12l[?25h[?2004l[?7h[1/x*y^3, 1/x^2*y^3]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[].[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+AttributeError                            Traceback (most recent call last)
+Input In [76], in <cell line: 1>()
+----> 1 frobenius_kernel(C, prec=Integer(50))[Integer(0)].frobenius().coordinates()
+
+AttributeError: 'superelliptic_function' object has no attribute 'frobenius'
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[5]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates()

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+IndexError                                Traceback (most recent call last)
+Input In [78], in <cell line: 1>()
+----> 1 frobenius_kernel(C, prec=Integer(50))[Integer(0)].frobenius().coordinates()
+
+File <string>:48, in coordinates(self, basis, basis_holo, prec)
+
+File <string>:14, in prod(self, form, prec)
+
+File /ext/sage/9.7/src/sage/rings/laurent_series_ring_element.pyx:544, in sage.rings.laurent_series_ring_element.LaurentSeries.__getitem__()
+    542         return type(self)(self._parent, f, self.__n)
+    543 
+--> 544     return self.__u[i - self.__n]
+    545 
+    546 def __iter__(self):
+
+File /ext/sage/9.7/src/sage/rings/power_series_poly.pyx:453, in sage.rings.power_series_poly.PowerSeries_poly.__getitem__()
+    451         return self.base_ring().zero()
+    452     else:
+--> 453         raise IndexError("coefficient not known")
+    454 return self.__f[n]
+    455 
+
+IndexError: coefficient not known
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lp)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7l=)[?7h[?12l[?25h[?25l[?7l5)[?7h[?12l[?25h[?25l[?7l0)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)

+[?7h[?12l[?25h[?2004l[?7h[1, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius()

+[?7h[?12l[?25h[?2004l[?7h[1/x^3*y^9]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lsage: M

+[?7h[?12l[?25h[?2004l---------------------------------------------------------------------------
+NameError                                 Traceback (most recent call last)
+Input In [81], in <cell line: 1>()
+----> 1 M
+
+NameError: name 'M' is not defined
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[5]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius()[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius()

+[?7h[?12l[?25h[?2004l[?7h[1/x^6*y^9]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius()[?7h[?12l[?25h[?25l[?7l().coordinates(prec=50)[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ltes(prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

+[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ 
]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage
+┌────────────────────────────────────────────────────────────────────┐
+│ SageMath version 9.7, Release Date: 2022-09-19                     │
+│ Using Python 3.10.5. Type "help()" for help.                       │
+└────────────────────────────────────────────────────────────────────┘
+]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage')

+[?7h[?12l[?25h[?2004l[5]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)[?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)

+[?7h[?12l[?25h[?2004l[?7h[0, 0, 0, 0, 0, 0]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0].frobenius().coordinates(prec=50)[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: frobenius_kernel(C, prec=50)[0]

+[?7h[?12l[?25h[?2004l[?7h[1/x^2*y^3]
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC = superelliptic(x^3 + x + 1, 2)[?7h[?12l[?25h[?25l[?7l.gens()[?7h[?12l[?25h[?25l[?7ldx[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.dx

+[?7h[?12l[?25h[?2004l[?7h1 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.cartier()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(x^2+x^4)*y^2*y.diffn()[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.cartier()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lD[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.dx).cartier()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.dx).cartier()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.C.dx).cartier()[?7h[?12l[?25h[?25l[?7loC.dx).cartier()[?7h[?12l[?25h[?25l[?7lnC.dx).cartier()[?7h[?12l[?25h[?25l[?7leC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7leC.dx).cartier()[?7h[?12l[?25h[?25l[?7l/C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.dx).cartier()[?7h[?12l[?25h[?25l[?7l.C.dx).cartier()[?7h[?12l[?25h[?25l[?7lxC.dx).cartier()[?7h[?12l[?25h[?25l[?7l*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: (C.one/C.x*C.dx).cartier()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrun.term-0.term[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfrobenius_kernel(C, prec=50)[0][?7h[?12l[?25h[?25l[?7lor i, x in eumerate(lista:[?7h[?12l[?25h[?25l[?7lfor[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l i, x in enumerate(lista):[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: for om in C.basis_

+ C.basis_de_rham_degrees                 

+ C.basis_holomorphic_differentials_degree

+

+

+ [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l

+

+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lmorphic_differentials_basis[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l():[?7h[?12l[?25h[?25l[?7l

+....: [?7h[?12l[?25h[?25l[?7lprint(i, x)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lom.serre_duality_pairing(f))[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()

+....: [?7h[?12l[?25h[?25l[?7lsage: for om in C.holomorphic_differentials_basis():

+....:     print(om.cartier())

+....: 

+[?7h[?12l[?25h[?2004l(1/y^3) dx
+(x/y^2) dx
+(1/y^2) dx
+0 dx
+0 dx
+(1/y) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: for om in C.holomorphic_differentials_basis():

+....:     print(om.cartier())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx).carter()

+ [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.one/C.x*C.dx)

+[?7h[?12l[?25h[?2004l[?7h(1/x) dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx)[?7h[?12l[?25h[?25l[?7l().cartier()[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrtier()[?7h[?12l[?25h[?25l[?7lsage: (C.one/C.x*C.dx).cartier()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.cartier()[?7h[?12l[?25h[?25l[?7lsage: C

+[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.dx.cartier()[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lis[?7h[?12l[?25h[?25l[?7lis_smooth()[?7h[?12l[?25h[?25l[?7lsage: C.is_smooth()

+[?7h[?12l[?25h[?2004l[?7h1
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.is_smooth()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.one/C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l(C.x*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()^*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l2*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)^2*C.dx).cartier()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l((C.x)^2*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l()*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lC*C.dx).cartier()[?7h[?12l[?25h[?25l[?7l.*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lx*C.dx).cartier()[?7h[?12l[?25h[?25l[?7lsage: ((C.x)*C.x*C.dx).cartier()

+[?7h[?12l[?25h[?2004l[?7h0 dx
+[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq = 5[?7h[?12l[?25h[?25l[?7luadratic_form(parity_quadratic_form(v0, q))[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: quit()

+[?7h[?12l[?25h[?2004l]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ cd
+]0;~~$ cd Research/2021\ De\ Rham/DEReRhamComputation/
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add draft/supsage/drafty/superelliptic_cohomology_class.sage 
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ gid add -u
+bash: gid: command not found
+]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ gid add -u
\ No newline at end of file
diff --git a/sage/as_covers/as_auxilliary.sage b/sage/as_covers/as_auxilliary.sage
index df736ae..1539a79 100644
--- a/sage/as_covers/as_auxilliary.sage
+++ b/sage/as_covers/as_auxilliary.sage
@@ -1,7 +1,8 @@
-def magmathis(A, B, text = False):
+def magmathis(A, B, text = False, prefix="", sufix=""):
     """Find decomposition of Z/p^2-module given by matrices A, B into indecomposables using magma.
     If text = True, print the command for Magma. Else - return the output of Magma free."""
     q = parent(A).base_ring().order()
+    p = q.factor()[0][0]
     n = A.dimensions()[0]
     A = str(list(A))
     B = str(list(B))
@@ -9,11 +10,16 @@ def magmathis(A, B, text = False):
     A = A.replace(")", "")
     B = B.replace("(", "")
     B = B.replace(")", "")
-    result = "A := MatrixAlgebra<GF("+str(q) + "),"+ str(n) + "|"
+    result = prefix
+    if q != p:
+        result += "F<a> := GF(" + str(q) + ");"
+    result += "A := MatrixAlgebra<GF("+str(q) + "),"+ str(n) + "|"
     result += A + "," + B
     result += ">;"
     result += "M := RModule(RSpace(GF("+str(q)+")," + str(n) + "), A);"
-    result += "IndecomposableSummands(M);"
+    result += "L := IndecomposableSummands(M); L;"
+    result += "for i in [1 .. #L] do print(Generators(Action(L[i]))); end for;"
+    result += sufix
     if text:
         return result
-    print(magma_free(result))
+    return(magma_free(result))
diff --git a/sage/as_covers/as_cover/uniformizer.sage b/sage/as_covers/as_cover/uniformizer.sage
deleted file mode 100644
index e69de29..0000000
diff --git a/sage/as_covers/as_form_class.sage b/sage/as_covers/as_form_class.sage
index 303d5ed..715ff84 100644
--- a/sage/as_covers/as_form_class.sage
+++ b/sage/as_covers/as_form_class.sage
@@ -73,7 +73,6 @@ class as_form:
         denom = LCM([denominator(omega.form) for omega in basis])
         basis = [denom*omega for omega in basis]
         self_with_no_denominator = denom*self
-        print(self_with_no_denominator, basis)
         return linear_representation_polynomials(Rxyz(self_with_no_denominator.form), [Rxyz(omega.form) for omega in basis])
 
     def trace(self):
diff --git a/sage/drafty/draft2.sage b/sage/drafty/draft2.sage
index 3164710..36474e2 100644
--- a/sage/drafty/draft2.sage
+++ b/sage/drafty/draft2.sage
@@ -1,14 +1,13 @@
 p = 3
-m = 1
-F = GF(p^2, 'a')
-a = F.gens()[0]
+m = 2
+F = GF(p)
 Rx.<x> = PolynomialRing(F)
-f = x
-C_super = superelliptic(f, m)
-
-Rxy.<x, y> = PolynomialRing(F, 2)
-f1 = superelliptic_function(C_super, x^7)
-f2 = superelliptic_function(C_super, a*x^7)
-AS = as_cover(C_super, [f1, f2], prec=1000)
-#print(AS.uniformizer())
-print(AS.ramification_jumps())
+f = x^3 - x
+C = superelliptic(f, m)
+x = C.x
+y = C.y
+dx = C.dx
+om1 = x^3*y*dx
+u = (C.one)/x
+v = y/x^2
+print(om1 + u^3*v*u.diffn() - (y/x)^2*(y/x).diffn())
\ No newline at end of file
diff --git a/sage/drafty/draft3.sage b/sage/drafty/draft3.sage
index fd8aeb7..dd98424 100644
--- a/sage/drafty/draft3.sage
+++ b/sage/drafty/draft3.sage
@@ -1,13 +1,46 @@
-p = 2
-m = 1
-F = GF(p^(2), 'a')
-a = F.gens()[0]
+p = 3
+m = 2
+#F = GF(p)
+F = GF(p)
 Rx.<x> = PolynomialRing(F)
-f = x
-C_super = superelliptic(f, m)
+f = x^5 + 1
+g = f(x^p - x)
+Cf = superelliptic(f, m)
+C = superelliptic(g, m)
 
-Rxy.<x, y> = PolynomialRing(F, 2)
-f1 = superelliptic_function(C_super, x^3)
-f2 = superelliptic_function(C_super, a*x^3)
-AS = as_cover(C_super, [f1, f2], prec=1000)
-#print(AS.at_most_poles(7))
\ No newline at end of file
+#class superelliptic_automorphism:
+#    def __init__
+
+def autom(omega):
+    C1 = omega.curve
+    f = omega.form
+    F = C1.base_ring
+    Rxy.<x, y> = PolynomialRing(F, 2)
+    RxyQ = FractionField(Rxy)
+    f = RxyQ(f)
+    return superelliptic_form(C1, f(x=x+1, y=y))
+
+def automdR(omega):
+    C1 = omega.curve
+    om0 = omega.omega0.form
+    f = omega.f.function
+    F = C1.base_ring
+    Rxy.<x, y> = PolynomialRing(F, 2)
+    RxyQ = FractionField(Rxy)
+    f = RxyQ(f)
+    om0 = RxyQ(om0)
+    f = f(x=x+1, y=y)
+    om0 = om0(x=x+1, y=y)
+    f = superelliptic_function(C1, f)
+    om0 = superelliptic_form(C1, om0)
+    return superelliptic_cech(C1, om0, f)
+
+A = C.de_rham_basis()
+gC = C.genus()
+M = matrix(C.base_ring, 2*gC, 2*gC)
+for i in range(2*gC):
+    M[:, i] = vector(automdR(A[i]).coordinates())
+print(M, M^p == identity_matrix(2*gC))
+
+N = C.verschiebung_matrix().transpose()
+print(magmathis(M, N))
\ No newline at end of file
diff --git a/sage/drafty/superelliptic_cohomology_class.sage b/sage/drafty/superelliptic_cohomology_class.sage
new file mode 100644
index 0000000..78ecaf9
--- /dev/null
+++ b/sage/drafty/superelliptic_cohomology_class.sage
@@ -0,0 +1,92 @@
+class superelliptic_cohomology:
+    '''Cohomology of structure sheaf.'''
+    def __init__(self, C, f):
+        self.curve = C
+        self.function = f
+        
+    def prod(self, form, prec=20):
+        result = 0
+        C = self.curve
+        delta = C.nb_of_pts_at_infty
+        fct = superelliptic_function(C, self.function)
+        for i in range(delta):
+            result += (fct*form).expansion_at_infty(place=i, prec=prec)[-1]
+        return -result
+    
+    def __repr__(self):
+        return "[" + str(self.function) + "]"
+    
+    def __add__(self, other):
+        C = self.curve
+        g1 = self.function
+        g2 = other.function
+        g = reduction(C, g1 + g2)
+        return superelliptic_cohomology(C, g)
+    
+    def __sub__(self, other):
+        C = self.curve
+        g1 = self.function
+        g2 = other.function
+        g = reduction(C, g1 - g2)
+        return superelliptic_cohomology(C, g)
+    
+    def __rmul__(self, constant):
+        C = self.curve
+        g = self.function
+        return superelliptic_cohomology(C, constant*g)
+
+    def coordinates(self, basis = 0, basis_holo = 0, prec=20):
+        C = self.curve
+        if basis == 0:
+            basis = basis_of_cohomology(C)
+        if basis_holo == 0:
+            basis_holo = C.holomorphic_differentials_basis()
+        g = C.genus()
+        coordinates = g*[0]
+        for i, omega in enumerate(basis_holo):
+            coordinates[i] = self.prod(omega, prec=prec)
+        return coordinates
+    
+    def frobenius(self):
+        C = self.curve
+        f = self.function
+        p = C.base_ring.characteristic()
+        return superelliptic_cohomology(C, f^p)
+    
+def basis_of_cohomology(C):
+    m = C.exponent
+    f = C.polynomial
+    r = f.degree()
+    F = C.base_ring
+    delta = C.nb_of_pts_at_infty
+    Rx.<x> = PolynomialRing(F)
+    Rxy.<x, y> = PolynomialRing(F, 2)
+    Fxy = FractionField(Rxy)
+    basis = []
+    for j in range(1, m):
+            for i in range(1, r):
+                if (r*j - m*i >= delta):
+                    basis += [superelliptic_cohomology(C, Fxy(m*y^(j)/x^i))]
+    return basis
+
+def frobenius_matrix(C, prec=20):
+    g = C.genus()
+    F = C.base_ring
+    M = matrix(F, g, g)
+    for i, f in enumerate(basis_of_cohomology(C)):
+        M[i, :] = vector(f.frobenius().coordinates(prec=prec))
+    return M
+
+
+def frobenius_kernel(C, prec=20):
+    M = frobenius_matrix(C, prec=prec)
+    K = M.kernel().basis()
+    g = C.genus()
+    result = []
+    basis = basis_of_cohomology(C)
+    for v in K:
+        coh = superelliptic_cohomology(C, 0)
+        for i in range(g):
+            coh += v[i] * basis[i]
+        result += [coh]
+    return result
\ No newline at end of file
diff --git a/sage/init.sage b/sage/init.sage
index 476f450..d56179a 100644
--- a/sage/init.sage
+++ b/sage/init.sage
@@ -18,6 +18,7 @@ load('auxilliaries/linear_combination_polynomials.sage')
 ##############
 ##############
 load('drafty/lift_to_de_rham.sage')
+load('drafty/superelliptic_cohomology_class.sage')
 load('drafty/draft5.sage')
 load('drafty/pole_numbers.sage')
 #load('drafty/draft4.sage')
\ No newline at end of file
diff --git a/sage/superelliptic/superelliptic_class.sage b/sage/superelliptic/superelliptic_class.sage
index ee1434a..7c6fe71 100644
--- a/sage/superelliptic/superelliptic_class.sage
+++ b/sage/superelliptic/superelliptic_class.sage
@@ -14,6 +14,11 @@ class superelliptic:
         self.characteristic = F.characteristic()
         r = Rx(f).degree()
         delta = GCD(r, m)
+        self.nb_of_pts_at_infty = delta
+        self.x = superelliptic_function(self, Rxy(x))
+        self.y = superelliptic_function(self, Rxy(y))
+        self.dx = superelliptic_form(self, Rxy(1))
+        self.one = superelliptic_function(self, Rxy(1))
         
     def __repr__(self):
         f = self.polynomial
diff --git a/sage/superelliptic/superelliptic_form_class.sage b/sage/superelliptic/superelliptic_form_class.sage
index 8197a09..e5de107 100644
--- a/sage/superelliptic/superelliptic_form_class.sage
+++ b/sage/superelliptic/superelliptic_form_class.sage
@@ -30,7 +30,7 @@ class superelliptic_form:
     def __rmul__(self, constant):
         C = self.curve
         omega = self.form
-        return superelliptic_form(C, constant*omega)        
+        return superelliptic_form(C, constant*omega)
     
     def cartier(self):
         C = self.curve
@@ -119,11 +119,11 @@ class superelliptic_form:
                 return 0
         return 1
 
-    def expansion_at_infty(self, i = 0, prec=10):
+    def expansion_at_infty(self, place = 0, prec=10):
         g = self.form
         C = self.curve
         g = superelliptic_function(C, g)
-        g = g.expansion_at_infty(i = i, prec=prec)
-        x_series = superelliptic_function(C, x).expansion_at_infty(i = i, prec=prec)
+        g = g.expansion_at_infty(place = place, prec=prec)
+        x_series = superelliptic_function(C, x).expansion_at_infty(place = place, prec=prec)
         dx_series = x_series.derivative()
         return g*dx_series
diff --git a/sage/superelliptic/superelliptic_function_class.sage b/sage/superelliptic/superelliptic_function_class.sage
index 003c475..4cb651e 100644
--- a/sage/superelliptic/superelliptic_function_class.sage
+++ b/sage/superelliptic/superelliptic_function_class.sage
@@ -42,10 +42,21 @@ class superelliptic_function:
     
     def __mul__(self, other):
         C = self.curve
-        g1 = self.function
-        g2 = other.function
-        g = reduction(C, g1 * g2)
-        return superelliptic_function(C, g)
+        try:
+            g1 = self.function
+            g2 = other.function
+            g = reduction(C, g1 * g2)
+            return superelliptic_function(C, g)
+        except:
+            g1 = self.function
+            g2 = other.form
+            g = reduction(C, g1 * g2)
+            return superelliptic_form(C, g)
+        
+    def __rmul__(self, constant):
+        C = self.curve
+        g = self.function
+        return superelliptic_function(C, constant*g)
     
     def __truediv__(self, other):
         C = self.curve
@@ -73,7 +84,7 @@ class superelliptic_function:
         return superelliptic_form(C, A+B)
 
     
-    def expansion_at_infty(self, i = 0, prec=10):
+    def expansion_at_infty(self, place = 0, prec=10):
         C = self.curve
         f = C.polynomial
         m = C.exponent
@@ -98,7 +109,7 @@ class superelliptic_function:
         
         g = (x^r*f(x = 1/x))
         gW = RptWQ(g(x = t^M * W^b)) - W^(delta)
-        ww = naive_hensel(gW, F, start = root_of_unity(F, delta)^i, prec = prec)
+        ww = naive_hensel(gW, F, start = root_of_unity(F, delta)^place, prec = prec)
         xx = Rt(1/(t^M*ww^b))
         yy = 1/(t^R*ww^a)
         return Rt(fct(x = Rt(xx), y = Rt(yy)))