From 1f66cae85d0eccb51b2c0fc1a09239f96e8b5187 Mon Sep 17 00:00:00 2001 From: jgarnek Date: Wed, 5 Apr 2023 09:03:19 +0000 Subject: [PATCH] naprawiony brak (1/p)-liniowosci cartiera --- sage/.run.term-0.term | 2392 ++++++++++++++++- sage/drafty/draft.sage | 24 +- .../superelliptic_cech_class.sage | 4 +- .../superelliptic_form_class.sage | 6 +- sage/superelliptic_drw/regular_form.sage | 10 + .../superelliptic_drw_cech.sage | 5 +- 6 files changed, 2428 insertions(+), 13 deletions(-) diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term index 0baea02..1510ec7 100644 --- a/sage/.run.term-0.term +++ b/sage/.run.term-0.term @@ -31875,4 +31875,2394 @@ Computing 1. basis element [?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lq[?7h[?12l[?25h[?25l[?7lu[?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;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u \ No newline at end of file +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git commit -m ""n"a"p"r"a"w"i"o"n"e" "C"."c"o"h"o"m"o"l"o"g"y"_"o"f"_"s"t"r"_"s"h"_""."c"o"o"r"d"i"n"a"t"e"s"." "A"l"e" "d"r"w"_"c"e"c"h"."r"e"d"u"c"e" "n"a"d"a"l" "z"m"i"e"n"i"a" "a"r"g"u"m"e"n"t" +[master a5c2ce2] naprawione C.cohomology_of_str_sh.coordinates. Ale drw_cech.reduce nadal zmienia argument + 3 files changed, 1586 insertions(+), 6 deletions(-) +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git push +Username for 'https://git.wmi.amu.edu.pl': jgarnek +Password for 'https://jgarnek@git.wmi.amu.edu.pl': +Enumerating objects: 15, done. +Counting objects: 6% (1/15) Counting objects: 13% (2/15) Counting objects: 20% (3/15) Counting objects: 26% (4/15) Counting objects: 33% (5/15) Counting objects: 40% (6/15) Counting objects: 46% (7/15) Counting objects: 53% (8/15) Counting objects: 60% (9/15) Counting objects: 66% (10/15) Counting objects: 73% (11/15) Counting objects: 80% (12/15) Counting objects: 86% (13/15) Counting objects: 93% (14/15) Counting objects: 100% (15/15) Counting objects: 100% (15/15), done. +Delta compression using up to 8 threads +Compressing objects: 12% (1/8) Compressing objects: 25% (2/8) Compressing objects: 37% (3/8) Compressing objects: 50% (4/8) Compressing objects: 62% (5/8) Compressing objects: 75% (6/8) Compressing objects: 87% (7/8) Compressing objects: 100% (8/8) Compressing objects: 100% (8/8), done. +Writing objects: 12% (1/8) Writing objects: 25% (2/8) Writing objects: 37% (3/8) Writing objects: 50% (4/8) Writing objects: 62% (5/8) Writing objects: 75% (6/8) Writing objects: 87% (7/8) Writing objects: 100% (8/8) Writing objects: 100% (8/8), 19.86 KiB | 207.00 KiB/s, done. +Total 8 (delta 7), reused 0 (delta 0) +remote: . Processing 1 references +remote: Processed 1 references in total +To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git + 64fe2ee..a5c2ce2 master -> master +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ ]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 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. 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[?7la[?7h[?12l[?25h[?25l[?7ld('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: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +   +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +   +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +   +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2   +....: + C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +.diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +  +2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 + + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +  +2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +  +3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2  ++ C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lsage: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 + +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 + +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 + +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2 +....: + C1.one)*C1.y.diffn()).verschiebung() +[?7h[?12l[?25h[?2004lf[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lfor b in C2.holomorphic_differentials_basis():[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfor b in C2.holomorphic_differentials_basis():[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34   +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7l = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +*C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34  ++ 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +ne)/C1.x^2)*C1.y).verschiebung()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l( + + +)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l( + + +)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l( + + +)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l( + + +)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l( + + +)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l( + + +)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l +()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()sd[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung()sdffds +[?7h[?12l[?25h[?2004l Cell In [3], line 1 + ff = (((Integer(2)*C1.x**Integer(98) + Integer(4)*C1.x**Integer(94) + C1.x**Integer(92) + Integer(3)*C1.x**Integer(90) + Integer(4)*C1.x**Integer(86) + Integer(2)*C1.x**Integer(84) + Integer(4)*C1.x**Integer(82) + Integer(2)*C1.x**Integer(78) + C1.x**Integer(76) + Integer(3)*C1.x**Integer(74) + C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(68) + Integer(3)*C1.x**Integer(66) + Integer(2)*C1.x**Integer(64) + Integer(3)*C1.x**Integer(62) + C1.x**Integer(60) + Integer(4)*C1.x**Integer(56) + Integer(3)*C1.x**Integer(54) + C1.x**Integer(52) + Integer(2)*C1.x**Integer(50) + C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(2)*C1.x**Integer(44) + Integer(4)*C1.x**Integer(38) + C1.x**Integer(36) + Integer(2)*C1.x**Integer(34) + Integer(4)*C1.x**Integer(32) + C1.x**Integer(30) + C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(2)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(3)*C1.x**Integer(18) + Integer(3)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(12) + Integer(3)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(6) + Integer(2)*C1.x**Integer(4) + Integer(3)*C1.x**Integer(2) + Integer(4)*C1.one)/C1.x**Integer(2))*C1.y).verschiebung()sdffds + ^ +SyntaxError: invalid syntax + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34   +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung()sdffds[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l= (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +*C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34  ++ 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +ne)/C1.x^2)*C1.y).verschiebung()sdffds[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung()sdffds +[?7h[?12l[?25h[?2004l Cell In [4], line 1 + ff = (((Integer(2)*C1.x**Integer(98) + Integer(4)*C1.x**Integer(94) + C1.x**Integer(92) + Integer(3)*C1.x**Integer(90) + Integer(4)*C1.x**Integer(86) + Integer(2)*C1.x**Integer(84) + Integer(4)*C1.x**Integer(82) + Integer(2)*C1.x**Integer(78) + C1.x**Integer(76) + Integer(3)*C1.x**Integer(74) + C1.x**Integer(72) + Integer(3)*C1.x**Integer(70) + C1.x**Integer(68) + Integer(3)*C1.x**Integer(66) + Integer(2)*C1.x**Integer(64) + Integer(3)*C1.x**Integer(62) + C1.x**Integer(60) + Integer(4)*C1.x**Integer(56) + Integer(3)*C1.x**Integer(54) + C1.x**Integer(52) + Integer(2)*C1.x**Integer(50) + C1.x**Integer(48) + Integer(3)*C1.x**Integer(46) + Integer(2)*C1.x**Integer(44) + Integer(4)*C1.x**Integer(38) + C1.x**Integer(36) + Integer(2)*C1.x**Integer(34) + Integer(4)*C1.x**Integer(32) + C1.x**Integer(30) + C1.x**Integer(28) + Integer(4)*C1.x**Integer(26) + Integer(2)*C1.x**Integer(24) + Integer(4)*C1.x**Integer(22) + Integer(3)*C1.x**Integer(18) + Integer(3)*C1.x**Integer(14) + Integer(4)*C1.x**Integer(12) + Integer(3)*C1.x**Integer(10) + Integer(3)*C1.x**Integer(6) + Integer(2)*C1.x**Integer(4) + Integer(3)*C1.x**Integer(2) + Integer(4)*C1.one)/C1.x**Integer(2))*C1.y).verschiebung()sdffds + ^ +SyntaxError: invalid syntax + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung()sdffds[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: ff = (((2*C1.x^98 + 4*C1.x^94 + C1.x^92 + 3*C1.x^90 + 4*C1.x^86 + 2*C1.x^84 + 4*C1.x^82 + 2*C1.x^78 + C1.x^76 + 3*C1.x^74 + C1.x^72 + 3*C1.x^70 + C1.x^68 + 3 +....: *C1.x^66 + 2*C1.x^64 + 3*C1.x^62 + C1.x^60 + 4*C1.x^56 + 3*C1.x^54 + C1.x^52 + 2*C1.x^50 + C1.x^48 + 3*C1.x^46 + 2*C1.x^44 + 4*C1.x^38 + C1.x^36 + 2*C1.x^34 +....: + 4*C1.x^32 + C1.x^30 + C1.x^28 + 4*C1.x^26 + 2*C1.x^24 + 4*C1.x^22 + 3*C1.x^18 + 3*C1.x^14 + 4*C1.x^12 + 3*C1.x^10 + 3*C1.x^6 + 2*C1.x^4 + 3*C1.x^2 + 4*C1. o +....: ne)/C1.x^2)*C1.y).verschiebung() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l = sprelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7l= superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7lsage: xi = superelliptic_drw_cech(om, ff) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi = superelliptic_drw_cech(om, ff)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.redc()[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lduce()[?7h[?12l[?25h[?25l[?7lsage: xi.reduce() +[?7h[?12l[?25h[?2004l[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lreduce()[?7h[?12l[?25h[?25l[?7lsage: xi.reduce() +[?7h[?12l[?25h[?2004l[?7h([(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((4*x^36 + 3*x^32 + 3*x^30 + 3*x^26 + x^24 + 3*x^18 + 2*x^16 + 2*x^14 + 3*x^12 + 4*x^10 + 2*x^8 + 2*x^6 + 3*x^4 + 4*x^2 + 2)/(x^38 + 2*x^34 + 3*x^30 + 3*x^28 + 4*x^26 + 2*x^24 + 2*x^18 + x^14 + 3*x^8 + 4*x^6 + x^4 + 3*x^2 + 1))*y]), V(4/x^2*y), [(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y] d[x] + V(((-x^36 + x^32 - x^28 + x^26 - x^24 - 2*x^22 + 2*x^20 + 2*x^18 + 2*x^16 + 2*x^14 + x^12 + 2*x^8 + x^2 + 2)/(x^38*y + 2*x^34*y - 2*x^30*y - 2*x^28*y - x^26*y + 2*x^24*y + 2*x^18*y + x^14*y - 2*x^8*y - x^6*y + x^4*y - 2*x^2*y + y)) dx) + dV([((3*x^32 + 3*x^30 + x^28 + 2*x^24 + 3*x^20 + 4*x^18 + 2*x^16 + 4*x^14 + 4*x^12 + 2*x^10 + 2*x^6 + 1)/(x^40 + 2*x^36 + 3*x^32 + 3*x^30 + 4*x^28 + 2*x^26 + 2*x^20 + x^16 + 3*x^10 + 4*x^8 + x^6 + 3*x^4 + x^2))*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.reduce()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lomega8.is_regular_on_Uinfty()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l00()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: xi.omega0.h1 +[?7h[?12l[?25h[?2004l[?7h(x^3/(x^14 + 2*x^10 + 3*x^6 + x^4 + 4*x^2 + 4))*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lxi.omega0.h1[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lomega0.h1[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: xi.omega0.r() +[?7h[?12l[?25h[?2004l[?7h(x^4/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 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. 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[?2004lComputing 0. basis element +Computing 1. basis element +Computing 0. basis element +Computing 1. basis element +Computing 2. basis element +Computing 3. basis element +Computing 4. basis element +Computing 5. basis element +Computing 6. basis element +Computing 7. basis element +( [0] d[x] + [2] d[y] + V((x^5 + 2*x^3 + 2*x^2 + 1) dy) + dV(0), V(((x^2 + x + 2)/x)*y) ) +( [0] d[x] + [2*x] d[y] + V((x^8 + x^6 + x^5 + x^3 + x^2 + x + 1) dy) + dV(0), [2/x*y] + V(((x^5 + x^4 + 2*x^3 + x^2 + 1)/x)*y) ) +( [0] d[x] + [1] d[y] + V((2*x + 1) dy) + dV(0), V((x + 2)*y) ) +( [0] d[x] + [x] d[y] + V((x^12 + 2*x^11 + 2*x^4 + x^3) dy) + dV(0), V(((x^8 + 2*x^7 + 1)/x^4)*y) ) +( [0] d[x] + [x^2] d[y] + V((2*x^15 + x^14 + 2*x^7 + x^6) dy) + dV(0), V(((x^10 + 2*x^9 + x^2 + x + 1)/x^3)*y) ) +( [0] d[x] + [x^3] d[y] + V((2*x^10 + x^9 + 2*x^2 + x) dy) + dV(0), V((x^10 + 2*x^9 + x^2 + x + 1)*y) ) +( [0] d[x] + [x^7] d[y] + V((x^30 + 2*x^29 + 2*x^22 + x^21 + x^14 + x^13 + 2*x^6 + x^4) dy) + dV(0), [2/x*y] + V(((x^26 + 2*x^25 + x^18 + x^17 + x^16 + x^10 + 2*x^9 + x^8 + 2*x^7 + 2*x^2 + 2*x + 1)/x^4)*y) ) +( [0] d[x] + [2*x^6] d[y] + V((x^19 + 2*x^18 + x^10 + x^9 + 2*x^3 + x^2 + x + 2) dy) + dV(0), [2/x^2*y] + V((2*x^19 + x^18 + 2*x^11 + 2*x^10 + 2*x^9 + 2*x^3 + x^2 + 2*x + 1)*y) ) +( [0] d[x] + [0] d[y] + V((x^8 + 1) dy) + dV(0), [2/x^3*y] ) +( [0] d[x] + [x^4] d[y] + V((x^21 + 2*x^20 + 2*x^13 + x^12 + 2*x^5 + x^4) dy) + dV(0), [2/x^4*y] + V(((x^17 + 2*x^16 + x^9 + x^8 + x^7 + x + 2)/x^4)*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7laa.coordinates()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8 3 +....:  + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +   +....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x)[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lc +  + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_expansion_polynomial(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8 3 +....:  + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +   +....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x)[?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[?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[?7lion + adic_expansion  +  adic_expansion_polynomial + + + [?7h[?12l[?25h[?25l[?7l_polynomial(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8 3 +....:  + 4*x^81 + x^3 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +   +....: 2*x^31 + 3*x^2 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x)[?7h[?12l[?25h[?25l[?7l + adic_expansion  + + [?7h[?12l[?25h[?25l[?7l_polynomial +  adic_expansion  +  adic_expansion_polynomial[?7h[?12l[?25h[?25l[?7l(x^119 + 4*x^115 + 4*x^111 + x^107 + 3*x^105 + 3*x^103 + x^101 + 3*x^99 + x^97 + 4*x^95 + 3*x^93 + 3*x^89 + 2*x^87 + 4*x^85 + 2*x^8 3 +....:  + 4*x^81 + x^79 + 4*x^69 + x^65 + 4*x^63 + 4*x^59 + 3*x^57 + 3*x^55 + x^53 + x^51 + 4*x^47 + 3*x^45 + 4*x^43 + 2*x^41 + 2*x^39 + 3*x^37 + 4*x^35 + 3*x^33 +   +....: 2*x^31 + 3*x^29 + 4*x^25 + x^23 + 3*x^21 + 4*x^19 + 2*x^17 + x^15 + x^13 + 2*x^9 + x^7 + 2*x^5 + 4*x, x^5 - x) +[?7h[?12l[?25h[?25l[?7l2*x^15 + x^14 + 2*x^7 + x^6 +  + [?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[?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[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(2*x^15 + x^14 + 2*x^7 + x^6, f) +[?7h[?12l[?25h[?2004l[?7h2*t^5 + (x^2 + 2*x + 1)*t^4 + (x^2 + 2*x + 1)*t^3 + (2*x^2 + 2*x + 1)*t^2 + x*t + x^2 + x + 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lfor N in range(1, 7):[?7h[?12l[?25h[?25l[?7lsage: f +[?7h[?12l[?25h[?2004l[?7hx^3 + x + 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lC2 = superelliptic(x^7 + x + 1, 2)[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x + 1 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[?7l1 = superelliptic(f1, m, prec = 500)[?7h[?12l[?25h[?25l[?7lsage: C1 +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^9 + 2*x + 1 over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1 = f(x = x^5 - x)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l(x^5 + 2*x^3 + 2*x^2 + 1)[?7h[?12l[?25h[?25l[?7lsage: f1 = (x^5 + 2*x^3 + 2*x^2 + 1) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = (x^5 + 2*x^3 + 2*x^2 + 1)[?7h[?12l[?25h[?25l[?7l2.diffn().int()[?7h[?12l[?25h[?25l[?7l = 1.pth_root()[?7h[?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^15 + x^14 + 2*x^7 + x^6)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7lsage: f2 = -((2*x^15 + x^14 + 2*x^7 + x^6) +....: [?7h[?12l[?25h[?25l[?7l( +)[?7h[?12l[?25h[?25l[?7lsage: f2 = -((2*x^15 + x^14 + 2*x^7 + x^6) +....: ) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2 = -((2*x^15 + x^14 + 2*x^7 + x^6)[?7h[?12l[?25h[?25l[?7l1(x^5 + 2*x^3 + 2*x^ + 1)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lf(x = x^5 - x)[?7h[?12l[?25h[?25l[?7l1[?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[?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: f1 = f1(x = x^3 - x) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1 = f1(x = x^3 - x)[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f1 +[?7h[?12l[?25h[?2004l[?7hx^15 + x^13 + x^11 + x^9 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + x^3 + 2*x^2 + 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf1[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l = f1(x = 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[?7lf1[?7h[?12l[?25h[?25l[?7l2 = -((2*x^15 + x^14 + 2*x^7 + x^6)[?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[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7lsage: f2 - x^2*f1 +[?7h[?12l[?25h[?2004l[?7h2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^15 + x^14 + 2*x^7 + x^6, f)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lsage: adic_expansion + adic_expansion  + adic_expansion_polynomial + + + [?7h[?12l[?25h[?25l[?7l_polynomial(2*x^15 + x^14 + 2*x^7 + x^6, f)[?7h[?12l[?25h[?25l[?7l + adic_expansion  + + [?7h[?12l[?25h[?25l[?7l_polynomial + adic_expansion  + adic_expansion_polynomial[?7h[?12l[?25h[?25l[?7l(2*x^15 + x^14 + 2*x^7 + x^6, f) + + +[?7h[?12l[?25h[?25l[?7l2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, f) +[?7h[?12l[?25h[?2004l[?7h(2*x^2 + 2)*t^5 + (x^2 + 2*x)*t^4 + (2*x^2 + 2)*t^3 + (2*x + 2)*t + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, f)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_expansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, 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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^15 + x^14 + 2*x^7 + x^6, f)[?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: adic_expansion_polynomial(2*x^15 + x^14 + 2*x^7 + x^6, x^3 - x) +[?7h[?12l[?25h[?2004l[?7h2*t^5 + (x^2 + x + 1)*t^4 + (2*x^2 + x + 2)*t^3 + (x^2 + 2*x)*t^2 + (x^2 + 2*x + 1)*t + 2*x^2 + x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^15 + x^14 + 2*x^7 + x^6, x^3 - x)[?7h[?12l[?25h[?25l[?7l72*x^14+ 2*x^13 + 2*11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, f)[?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: adic_expansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, x^3 - x) +[?7h[?12l[?25h[?2004l[?7h(2*x^2 + 1)*t^5 + (2*x^2 + 2*x + 2)*t^4 + (2*x^2 + 2*x + 1)*t^3 + x*t^2 + (2*x^2 + x + 2)*t + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + x + 1 over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, x^3 - x)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lexpansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^2, x^3 - x)[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lpansion_polynomial(2*x^17 + 2*x^14 + 2*x^13 + 2*x^11 + x^9 + x^8 + 2*x^7 + 2*x^5 + x^4 + 2*x^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)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?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)[?7h[?12l[?25h[?25l[?7l^)[?7h[?12l[?25h[?25l[?7l5)[?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[?7l4)[?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[?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[?7l)[?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)[?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[?7l+)[?7h[?12l[?25h[?25l[?7l )[?7h[?12l[?25h[?25l[?7l1)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lsage: adic_expansion_polynomial(x^5 + x^4 + x^3 + x, x^3 + x + 1) +[?7h[?12l[?25h[?2004l[?7h(x^2 + x)*t + x^2 +[?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--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Cell In [16], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :7 + +NameError: name 'a' 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[?2004lComputing 0. basis element +Computing 1. basis element +Computing 0. basis element +Computing 1. basis element +az^C--------------------------------------------------------------------------- +KeyboardInterrupt Traceback (most recent call last) +Cell In [17], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :13 + +File :44, in crystalline_cohomology_basis(self, prec, info) + +File :26, in de_rham_witt_lift(cech_class, prec) + +File :73, in diffn(self, dy_w) + +File :177, in dy_w(C) + +File :149, in auxilliary_derivative(P) + +File :55, in __rmul__(self, other) + +File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__() + 1959 return y + 1960 +-> 1961 return coercion_model.bin_op(left, right, operator.mul) + 1962 + 1963 cpdef _mul_(self, right): + +File /ext/sage/9.8/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 :55, in __rmul__(self, other) + +File :84, in __add__(self, other) + +File :27, in __add__(self, other) + +File /ext/sage/9.8/src/sage/rings/integer.pyx:1961, in sage.rings.integer.Integer.__mul__() + 1959 return y + 1960 +-> 1961 return coercion_model.bin_op(left, right, operator.mul) + 1962 + 1963 cpdef _mul_(self, right): + +File /ext/sage/9.8/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 :70, in __rmul__(self, constant) + +File :14, in __init__(self, C, g) + +File :248, in reduction(C, g) + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring_constructor.py:693, in PolynomialRing(base_ring, *args, **kwds) + 690 raise TypeError("variable names specified twice inconsistently: %r and %r" % (names, kwnames)) + 692 if multivariate or len(names) != 1: +--> 693 return _multi_variate(base_ring, names, **kwds) + 694 else: + 695 return _single_variate(base_ring, names, **kwds) + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring_constructor.py:813, in _multi_variate(base_ring, names, sparse, order, implementation) + 811 # "implementation" must be last + 812 key = [base_ring, names, n, order, implementation] +--> 813 R = _get_from_cache(key) + 814 if R is not None: + 815 return R + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_ring_constructor.py:715, in _get_from_cache(key) + 713 def _get_from_cache(key): + 714 key = tuple(key) +--> 715 return _cache.get(key) + +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/9.8/local/var/lib/sage/venv-python3.11.1/lib/python3.11/site-packages/IPython/core/interactiveshell.py:3433 in run_code + exec(code_obj, self.user_global_ns, self.user_ns) + + Cell In [18], 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/9.8/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :32 + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.8/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :37 + #print(M^3) + ^ +IndentationError: expected an indented block after 'for' statement on line 32 + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  +[?7h[?12l[?25h[?2004l[?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--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [19], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :25 + +File :19, in de_rham_witt_lift(cech_class, prec) + +AttributeError: 'list' object has no attribute 'curve' +[?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[?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( [0] d[x] + [2*a + 1] d[y] + V((2*x^5 + a*x^3 + x^2 + 2*a) dy) + dV(0), V((((2*a + 2)*x^2 + 2*a*x + 2*a + 1)/x)*y) ) +( [0] d[x] + [a + 2] d[y] + V((2*x^3 + (a + 1)*x + 2*a) dy) + dV(0), V(((x^6 + (2*a + 2)*x^4 + a*x^3 + 2*a + 1)/x^3)*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C1.y/C1.x^2).expansion_at_infty()[?7h[?12l[?25h[?25l[?7la^(-1))expansion_at_infy(prec = 100)[?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[?7h[?12l[?25h[?25l[?7l[?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/xx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?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/(2*a+1) +[?7h[?12l[?25h[?2004l[?7h2*a +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbor b in B1:[?7h[?12l[?25h[?25l[?7l1[?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[?7lsage: b1.curve +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^9 + (a + 2)*x^3 + 2*a*x + 1 over Finite Field in a of size 3^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l1[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[4].omega0.regular_form()[?7h[?12l[?25h[?25l[?7lde_rham_basis()[4].omega0.regular_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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: C1.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^7 + (a - 1)*x)/y) dx, 2/x*y, (((-a)*x - 1)/(x^2*y)) dx), + (((-x^6 + (-a + 1))/y) dx, 2/x^2*y, (1/(x^3*y)) dx), + (0 dx, 2/x^3*y, (a/(x^3*y)) dx), + ((x^4/y) dx, 2/x^4*y, (((-a + 1)*x^3 + (-a)*x - 1)/(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( [0] d[x] + [2*a + 1] d[y] + V((2*x^5 + a*x^3 + x^2 + 2*a) dy) + dV(0), V((((2*a + 2)*x^2 + 2*a*x + 2*a + 1)/x)*y) ) +( [0] d[x] + [(a + 2)*x^2] d[y] + V(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1) dy) + dV(0), V(((x^12 + (2*a + 2)*x^10 + a*x^9 + (2*a + 1)*x^6 + 2*a*x^4 + x^3 + (a + 2)*x^2 + (2*a + 2)*x + a + 2)/x^3)*y) ) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(x^5 + x^4 + x^3 + x, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc_expansion_polynomial(x^5 + x^4 + x^3 + x, x^3 + x + 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, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l, x^3 + x + 1)[?7h[?12l[?25h[?25l[?7l((2*a1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1) dy, x^3 + x + 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 x)[?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[?7lsage: adic_expansion_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1) dy, x^3 - x) +[?7h[?12l[?25h[?2004l Cell In [25], line 1 + adic_expansion_polynomial(((Integer(2)*a + Integer(1))*x**Integer(17) + a*x**Integer(15) + Integer(2)*x**Integer(14) + Integer(2)*x**Integer(9) + (a + Integer(1))*x**Integer(7) + Integer(2)*a*x**Integer(6) + a*x**Integer(5) + (Integer(2)*a + Integer(1))*x**Integer(3) + (a + Integer(1))*x**Integer(2) + Integer(1)) dy, x**Integer(3) - x) + ^ +SyntaxError: invalid syntax. Perhaps you forgot a comma? + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1) dy, 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()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l, x^3 - x)[?7h[?12l[?25h[?25l[?7l(), 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[?7lsage: adic_expansion_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1), x^3 - x) +[?7h[?12l[?25h[?2004l[?7h((2*a + 1)*x^2 + 2*a + 2)*t^5 + (2*x^2 + 2*a*x + 2)*t^4 + ((2*a + 2)*x^2 + 2*x + a + 2)*t^3 + (2*x^2 + (a + 1)*x + 2*a + 1)*t^2 + (2*a*x^2 + a*x + a + 2)*t + (a + 2)*x + 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$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. 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--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [1], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +AttributeError: 'superelliptic_form' object has no attribute 'mult_by_p' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC1.de_rham_basis()[?7h[?12l[?25h[?25l[?7l.de_rham_basis()[0][?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lx.expansion_at_infty()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: C.dx.expansion_at_infty() + C.dx.cartier C.dx.expansion_at_infty C.dx.is_regular_on_U0 C.dx.reduce2 C.dx.verschiebung  + C.dx.coordinates C.dx.form C.dx.is_regular_on_Uinfty C.dx.regular_form  + C.dx.curve C.dx.int C.dx.jth_component C.dx.residue  + C.dx.expansion C.dx.inv_cartier C.dx.reduce C.dx.serre_duality_pairing  + [?7h[?12l[?25h[?25l[?7lm + + + +[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.dx.mult_by_p() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [2], line 1 +----> 1 C.dx.mult_by_p() + +AttributeError: 'superelliptic_form' object has no attribute 'mult_by_p' +[?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[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +V((x^5/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +V((x^8/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +V((x^11/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +V(((x^23 + (-a)*x^5)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +V(((-x^20 + a*x^2)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +0 +V((x^14/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?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) +File /ext/sage/9.8/src/sage/rings/finite_rings/integer_mod.pyx:379, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() + 378 try: +--> 379 z = integer_ring.Z(value) + 380 except (TypeError, ValueError): + +File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__() + 895 if no_extra_args: +--> 896 return mor._call_(x) + 897 else: + +File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:287, in sage.structure.coerce_maps.NamedConvertMap._call_() + 286 cdef Map m +--> 287 cdef Element e = method(C) + 288 if e is None: + +File /ext/sage/9.8/src/sage/rings/finite_rings/element_givaro.pyx:1405, in sage.rings.finite_rings.element_givaro.FiniteField_givaroElement._integer_() + 1404 return Integer(a) +-> 1405 raise TypeError("not in prime subfield") + 1406 + +TypeError: not in prime subfield + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +File /ext/sage/9.8/src/sage/rings/finite_rings/hom_prime_finite_field.pyx:43, in sage.rings.finite_rings.hom_prime_finite_field.SectionFiniteFieldHomomorphism_prime._call_() + 42 try: +---> 43 return self._codomain._element_constructor(x) + 44 except TypeError: + +File /ext/sage/9.8/src/sage/rings/finite_rings/integer_mod_ring.py:1191, in IntegerModRing_generic._element_constructor_(self, x) + 1190 try: +-> 1191 return integer_mod.IntegerMod(self, x) + 1192 except (NotImplementedError, PariError): + +File /ext/sage/9.8/src/sage/rings/finite_rings/integer_mod.pyx:200, in sage.rings.finite_rings.integer_mod.IntegerMod() + 199 t = modulus.element_class() +--> 200 return t(parent, value) + 201 + +File /ext/sage/9.8/src/sage/rings/finite_rings/integer_mod.pyx:387, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__() + 386 if isinstance(value, Element) and value.parent().is_exact(): +--> 387 value = sage.rings.rational_field.QQ(value) + 388 z = value % self.__modulus.sageInteger + +File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__() + 895 if no_extra_args: +--> 896 return mor._call_(x) + 897 else: + +File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + +File /ext/sage/9.8/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + +File /ext/sage/9.8/src/sage/rings/rational.pyx:538, in sage.rings.rational.Rational.__init__() + 537 if x is not None: +--> 538 self.__set_value(x, base) + 539 + +File /ext/sage/9.8/src/sage/rings/rational.pyx:683, in sage.rings.rational.Rational.__set_value() + 682 else: +--> 683 raise TypeError("unable to convert {!r} to a rational".format(x)) + 684 + +TypeError: unable to convert 2*a to a rational + +During handling of the above exception, another exception occurred: + +ValueError Traceback (most recent call last) +Cell In [4], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :82, in regular_drw_form(omega) + +File :27, in decomposition_omega0_hpdh(omega) + +File :70, in cartier(self) + +File :133, in polynomial_part(p, h) + +File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__() + 894 if mor is not None: + 895 if no_extra_args: +--> 896 return mor._call_(x) + 897 else: + 898 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.8/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/9.8/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/9.8/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/9.8/src/sage/rings/polynomial/polynomial_zmod_flint.pyx:124, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint.__init__() + 122 except AttributeError: + 123 pass +--> 124 Polynomial_template.__init__(self, parent, x, check, is_gen, construct) + 125 + 126 cdef Polynomial_template _new(self): + +File /ext/sage/9.8/src/sage/rings/polynomial/polynomial_template.pxi:170, in sage.rings.polynomial.polynomial_zmod_flint.Polynomial_template.__init__() + 168 elif isinstance(x, Polynomial): + 169 k = (self)._parent.base_ring() +--> 170 x = [k(w) for w in list(x)] + 171 Polynomial_template.__init__(self, parent, x, check=True, is_gen=False, construct=construct) + 172 elif isinstance(x, FractionFieldElement) and (x.parent().base() is parent or x.parent().base() == parent) and x.denominator() == 1: + +File /ext/sage/9.8/src/sage/structure/parent.pyx:896, in sage.structure.parent.Parent.__call__() + 894 if mor is not None: + 895 if no_extra_args: +--> 896 return mor._call_(x) + 897 else: + 898 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.8/src/sage/rings/finite_rings/hom_prime_finite_field.pyx:45, in sage.rings.finite_rings.hom_prime_finite_field.SectionFiniteFieldHomomorphism_prime._call_() + 43 return self._codomain._element_constructor(x) + 44 except TypeError: +---> 45 raise ValueError("%s is not in the image of %s" % (x, self._inverse)) + 46 + 47 + +ValueError: 2*a is not in the image of (map internal to coercion system -- copy before use) +Ring morphism: + From: Finite Field of size 3 + To: Finite Field in a of size 3^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7larent(A.h2.function)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(x) +[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field in a of size 3^2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(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[?7lbparent(x)[?7h[?12l[?25h[?25l[?7laparent(x)[?7h[?12l[?25h[?25l[?7lsparent(x)[?7h[?12l[?25h[?25l[?7leparent(x)[?7h[?12l[?25h[?25l[?7l_parent(x)[?7h[?12l[?25h[?25l[?7lrparent(x)[?7h[?12l[?25h[?25l[?7liparent(x)[?7h[?12l[?25h[?25l[?7lnparent(x)[?7h[?12l[?25h[?25l[?7lgparent(x)[?7h[?12l[?25h[?25l[?7l(parent(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[?7lsage: base_ring(parent(x)) +[?7h[?12l[?25h[?2004l[?7hFinite Field in a of size 3^2 +[?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--------------------------------------------------------------------------- +UnboundLocalError Traceback (most recent call last) +Cell In [7], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :82, in regular_drw_form(omega) + +File :27, in decomposition_omega0_hpdh(omega) + +File :70, in cartier(self) + +File :131, in polynomial_part(p, h) + +UnboundLocalError: cannot access local variable 'x' where it is not associated with a value +[?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--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [8], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :84, in regular_drw_form(omega) + +File :10, in decomposition_g0_pth_power(fct) + +File :150, in pth_root(self) + +File :70, in cartier(self) + +File :138, in polynomial_part(p, h) + +File /ext/sage/9.8/src/sage/rings/integer.pyx:655, in sage.rings.integer.Integer.__init__() + 653 otmp = getattr(x, "_integer_", None) + 654 if otmp is not None: +--> 655 set_from_Integer(self, otmp(the_integer_ring)) + 656 return + 657 + +File /ext/sage/9.8/src/sage/rings/finite_rings/element_givaro.pyx:1405, in sage.rings.finite_rings.element_givaro.FiniteField_givaroElement._integer_() + 1403 if a < self._cache.objectptr.characteristic(): + 1404 return Integer(a) +-> 1405 raise TypeError("not in prime subfield") + 1406 + 1407 def _log_to_int(FiniteField_givaroElement self): + +TypeError: not in prime subfield +[?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[?2004lFinite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Cell In [9], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :84, in regular_drw_form(omega) + +File :10, in decomposition_g0_pth_power(fct) + +File :150, in pth_root(self) + +File :70, in cartier(self) + +File :139, in polynomial_part(p, h) + +File /ext/sage/9.8/src/sage/rings/integer.pyx:655, in sage.rings.integer.Integer.__init__() + 653 otmp = getattr(x, "_integer_", None) + 654 if otmp is not None: +--> 655 set_from_Integer(self, otmp(the_integer_ring)) + 656 return + 657 + +File /ext/sage/9.8/src/sage/rings/finite_rings/element_givaro.pyx:1405, in sage.rings.finite_rings.element_givaro.FiniteField_givaroElement._integer_() + 1403 if a < self._cache.objectptr.characteristic(): + 1404 return Integer(a) +-> 1405 raise TypeError("not in prime subfield") + 1406 + 1407 def _log_to_int(FiniteField_givaroElement self): + +TypeError: not in prime subfield +[?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[?2004lFinite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +Finite Field in a of size 3^2 +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [10], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :85, in regular_drw_form(omega) + +File :206, in inv_cartier(omega) + +AttributeError: 'NoneType' 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--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [11], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :85, in regular_drw_form(omega) + +File :206, in inv_cartier(omega) + +AttributeError: 'NoneType' 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[?2004l0 +1 +0 +0 +0 +1 +0 +0 +0 +x^27 + (a + 2)*x^19 + x^13 + (a + 1)*x^11 + (2*a + 1)*x^10 + (a + 2)*x^9 + a*x^7 + (a + 2)*x^5 + x^4 + a*x^3 + (a + 1)*x^2 + (a + 2)*x + 1 +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [12], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :85, in regular_drw_form(omega) + +File :206, in inv_cartier(omega) + +AttributeError: 'NoneType' 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[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [13], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :86, in regular_drw_form(omega) + +File :206, in inv_cartier(omega) + +AttributeError: 'NoneType' 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[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [14], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :86, in regular_drw_form(omega) + +File :206, in inv_cartier(omega) + +AttributeError: 'NoneType' 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[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +0 ((x^28 + (a + 2)*x^20 + x^14 + (a + 1)*x^12 + (2*a + 1)*x^11 + (a + 2)*x^10 + a*x^8 + (a + 2)*x^6 + x^5 + a*x^4 + (a + 1)*x^3 + (a + 2)*x^2 + x)/(x^36 + (a + 2)*x^30 + 2*a*x^28 + x^27 + 2*a*x^18 + (a + 1)*x^12 + (a + 1)*x^10 + (2*a + 1)*x^9 + (2*a + 2)*x^6 + 2*x^4 + (2*a + 1)*x^3 + 2*a*x + 1))*y +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [15], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :87, in regular_drw_form(omega) + +File :206, in inv_cartier(omega) + +AttributeError: 'NoneType' 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[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [16], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :87, in regular_drw_form(omega) + +File :206, in inv_cartier(omega) + +AttributeError: 'NoneType' 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[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y +(A.diffn()).inv_cartier() ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [17], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :88, in regular_drw_form(omega) + +File :206, in inv_cartier(omega) + +AttributeError: 'NoneType' 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[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y +(A.diffn()).is_regular_on_U0() False +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Cell In [18], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :88, in regular_drw_form(omega) + +File :206, in inv_cartier(omega) + +AttributeError: 'NoneType' 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[?2004lV((x^2/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y +(A.diffn()).is_regular_on_U0() False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [19], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :88, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :103, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [20], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :85, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :100, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004lomega_aux.dx.teichmuller()*C.x.teichmuller().diffn() + omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() 0 +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [21], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :86, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :101, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004laux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [22], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :86, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :101, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004laux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [23], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :87, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :102, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004lTrue +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [24], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :88, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :103, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004lTrue +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True +True +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [25], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :89, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :104, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004lTrue +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True +True +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [26], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :89, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :104, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004lTrue +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True +True True +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [27], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :90, in regular_drw_form(omega) + +File :104, in regular_form(omega) + +ValueError: The form ((x^92 + (a - 1)*x^86 + (-a - 1)*x^84 + x^83 + (-a)*x^78 - x^76 + (-a - 1)*x^72 + (-a)*x^70 + a*x^69 + a*x^68 + x^67 + (a - 1)*x^66 + (-a - 1)*x^64 + (-a - 1)*x^63 + x^62 + (-a)*x^61 + (-a)*x^60 + a*x^59 + (a + 1)*x^58 + (-a + 1)*x^54 - x^52 + (a - 1)*x^51 - x^50 + (-a - 1)*x^49 - x^48 + a*x^45 + (-a - 1)*x^44 + a*x^43 + (-a)*x^42 + (-a - 1)*x^41 + (-a - 1)*x^40 + (a - 1)*x^39 + a*x^38 + x^37 + (-a - 1)*x^36 + (a + 1)*x^34 + (-a + 1)*x^33 + x^32 - x^31 + (-a - 1)*x^30 + (-a)*x^29 - x^28 + a*x^27 + x^26 + (a + 1)*x^25 + (a - 1)*x^24 + (a + 1)*x^23 + a*x^21 + a*x^20 + x^19 + (a - 1)*x^18 + x^17 + x^16 + (-a - 1)*x^15 + x^14 + (a - 1)*x^13 - x^12 - x^11 + a*x^10 + (-a + 1)*x^9 - x^8 + (-a + 1)*x^7 + (-a - 1)*x^6 + (-a - 1)*x^5 - x^4 + (-a - 1)*x^3 + x^2)/(x^99*y + (-a + 1)*x^93*y + a*x^91*y - x^90*y + (-a - 1)*x^87*y + x^85*y + (-a + 1)*x^84*y + (a + 1)*x^83*y + a*x^82*y + x^81*y + (a - 1)*x^45*y + (a + 1)*x^39*y + x^37*y + (-a + 1)*x^36*y + (-a)*x^33*y + (a - 1)*x^31*y + (a + 1)*x^30*y + a*x^29*y + x^28*y - x^27*y + x^21*y + (-a - 1)*x^19*y + (a + 1)*x^18*y + (-a + 1)*x^15*y + (-a)*x^13*y + (-a - 1)*x^12*y + (a - 1)*x^11*y - x^10*y + (-a - 1)*x^9*y + (-a - 1)*x^6*y + x^4*y + (-a + 1)*x^3*y + (a + 1)*x^2*y + a*x*y + y)) dx is not regular on U0. +[?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[?2004lTrue +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True +True True +A.diffn().is_regular_on_U0() False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [28], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :90, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :105, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004lTrue +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True +True True +aux == omega False +A.diffn().is_regular_on_U0() False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [29], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :91, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :106, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004lTrue +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True +True True +True False +aux == omega False +A.diffn().is_regular_on_U0() False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [30], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :91, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :106, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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 9.8, Release Date: 2023-02-11 │ +│ Create a "Sage Worksheet" file for the notebook interface. │ +│ Enhanced for CoCalc. │ +│ Using Python 3.11.1. 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[?2004lTrue +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True +True True +aux == omega False +A.diffn().is_regular_on_U0() False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [1], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :91, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :106, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004lTrue +aux == omega True +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True +True True +aux == omega False +A.diffn().is_regular_on_U0() False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [2], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :92, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :107, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004lTrue +aux == omega True +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True +True True +aux == omega False +A.diffn().is_regular_on_U0() False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [3], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :92, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :107, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004lTrue +aux == omega True +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True +True True +aux - omega + V(((-x^2)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((x^30 + 2*a*x^12 + (2*a + 1)*x^6 + x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y]) +A.diffn().is_regular_on_U0() False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [4], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :92, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :107, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?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[?2004lTrue +aux == omega True +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True +mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() False +True True +aux - omega + V(((-x^2)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((x^30 + 2*a*x^12 + (2*a + 1)*x^6 + x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y]) +A.diffn().is_regular_on_U0() False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [5], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :93, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :108, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.dx.mult_by_p()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + a*x + 1 over Finite Field in a of size 3^2 +[?2004h[?25l[?7lsage: [?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[?7l[?7h[?12l[?25h[?25l[?7lparent(x)[?7h[?12l[?25h[?25l[?7lsage: p +[?7h[?12l[?25h[?2004l[?7h3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf2 - x^2*f1[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?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[?7lx[?7h[?12l[?25h[?25l[?7lsage: fct = C.x +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lfct = C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: fct = C.y +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().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[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l (fct^p).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l (fct^p).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l()(fct^p).verschiebung().difn()[?7h[?12l[?25h[?25l[?7l(), (fct^p).verschiebung().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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: mult_by_p(fct.diffn()), (fct^p).verschiebung().diffn() +[?7h[?12l[?25h[?2004l[?7h(V((((a - 1)*x^2)/(x^3*y + a*x*y + y)) dx), dV([(x^3 + a*x + 1)*y])) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(f, m)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lFxy, Rxy, x, y=C1.fct_field[?7h[?12l[?25h[?25l[?7l = GF(p)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lGF(p)[?7h[?12l[?25h[?25l[?7lsage: F = GF(p) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(f, m)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lsuperelliptic(f, m)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l, m)[?7h[?12l[?25h[?25l[?7lx, m)[?7h[?12l[?25h[?25l[?7l^, m)[?7h[?12l[?25h[?25l[?7l3, m)[?7h[?12l[?25h[?25l[?7l , m)[?7h[?12l[?25h[?25l[?7l-, m)[?7h[?12l[?25h[?25l[?7l , m)[?7h[?12l[?25h[?25l[?7lx, m)[?7h[?12l[?25h[?25l[?7l[?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 - x, m) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7l = C.y[?7h[?12l[?25h[?25l[?7lsage: fct = C.y +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lC =superelliptic(x^3 - x, m)[?7h[?12l[?25h[?25l[?7lFGF(p)[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()), (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7l == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() +[?7h[?12l[?25h[?2004l[?7hTrue +[?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[?7h[?12l[?25h[?25l[?7l('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTrue +aux == omega True +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True +mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() False +True True +aux - omega + V(((-x^2)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((x^30 + 2*a*x^12 + (2*a + 1)*x^6 + x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y]) +A.diffn().is_regular_on_U0() False +--------------------------------------------------------------------------- +ValueError Traceback (most recent call last) +Cell In [17], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :93, in regular_drw_form(omega) + +File :203, in inv_cartier(omega) + +File :108, in regular_form(omega) + +ValueError: The form ((x^36 + (a - 1)*x^30 + x^28 + x^27 + a*x^22 + (a - 1)*x^18 + (a + 1)*x^16 + (-a)*x^13 + (a + 1)*x^12 + a*x^9 + (a + 1)*x^7 + (-a + 1)*x^4 + x^3 + x + 1)/(x^36*y + (a - 1)*x^30*y + (-a)*x^28*y + x^27*y + (-a)*x^18*y + (a + 1)*x^12*y + (a + 1)*x^10*y + (-a + 1)*x^9*y + (-a - 1)*x^6*y - x^4*y + (-a + 1)*x^3*y + (-a)*x*y + y)) dx is not regular on U0. +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?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: om = ((3*C1.x^9 + 2*C1.x^5)*C1.y).teichmuller() * C1.x.teichmuller().diffn() + (2*C1.x^14 + C1.x^10 + 2*C1.x^6 + 3*C1.x^4).teichmuller() * C1.y.teichmuller( ) +....: .diffn() + (((C1.x^119 + 4*C1.x^115 + 4*C1.x^111 + C1.x^107 + 3*C1.x^105 + 3*C1.x^103 + C1.x^101 + 3*C1.x^99 + C1.x^97 + 4*C1.x^95 + 3*C1.x^93 + 3*C1.x^89 +   +....: 2*C1.x^87 + 4*C1.x^85 + 2*C1.x^83 + 4*C1.x^81 + C1.x^79 + 4*C1.x^69 + C1.x^65 + 4*C1.x^63 + 4*C1.x^59 + 3*C1.x^57 + 3*C1.x^55 + C1.x^53 + C1.x^51 + 4*C1.x^4 7 +....:  + 3*C1.x^45 + 4*C1.x^43 + 2*C1.x^41 + 2*C1.x^39 + 3*C1.x^37 + 4*C1.x^35 + 3*C1.x^33 + 2*C1.x^31 + 3*C1.x^29 + 4*C1.x^25 + C1.x^23 + 3*C1.x^21 + 4*C1.x^19 +   +....: 2*C1.x^17 + C1.x^15 + C1.x^13 + 2*C1.x^9 + C1.x^7 + 2*C1.x^5 + 4*C1.x)*C1.y) *C1.x.diffn() + (4*C1.x^124 + 2*C1.x^120 + C1.x^114 + 3*C1.x^112 + 2*C1.x^110 +   +....: 3*C1.x^108 + C1.x^106 + 2*C1.x^100 + C1.x^98 + 3*C1.x^96 + C1.x^94 + 3*C1.x^92 + 4*C1.x^90 + 3*C1.x^88 + 2*C1.x^84 + C1.x^82 + C1.x^80 + 4*C1.x^78 + 4*C1.x^ 7 +....: 6 + C1.x^74 + 4*C1.x^72 + 3*C1.x^70 + C1.x^66 + 3*C1.x^64 + 2*C1.x^62 + C1.x^58 + C1.x^56 + 4*C1.x^54 + 4*C1.x^52 + 3*C1.x^50 + 3*C1.x^48 + 3*C1.x^46 + 4*C1 . +....: x^40 + 2*C1.x^34 + 3*C1.x^32 + 3*C1.x^28 + 4*C1.x^26 + 4*C1.x^24 + 4*C1.x^22 + 4*C1.x^20 + 2*C1.x^14 + 4*C1.x^10 + 3*C1.x^8 + 2*C1.x^6 + 4*C1.x^4 + 4*C1.x^2   +....: + C1.one)*C1.y.diffn()).verschiebung()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lega.curve +  +  +  +  +  +  +  + [?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = B[0].omega0[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?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(C.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[?7l1[?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[?7lsage: omega = (C.x)^(-1)*C.dx +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + + + [?7h[?12l[?25h[?25l[?7lomega = (C.x)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.curve[?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: omega.cartier() +[?7h[?12l[?25h[?2004l[?7h(1/x) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + + [?7h[?12l[?25h[?25l[?7lomega.cartier()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l = (C.x)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: omega = a*omega +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7lomega = a*omega[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.cartier()[?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: omega.cartier() +[?7h[?12l[?25h[?2004l[?7h(a/x) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7ladic_expansion_polynomial(((2*a + 1)*x^17 + a*x^15 + 2*x^14 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6 + a*x^5 + (2*a + 1)*x^3 + (a + 1)*x^2 + 1), x^3 - x)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbn[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7lh[?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[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.nth_root(p) +[?7h[?12l[?25h[?2004l[?7h2*a + 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF = GF(p)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?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: F.cardinality() +[?7h[?12l[?25h[?2004l[?7h9 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lsage: f +[?7h[?12l[?25h[?2004l[?7hx^3 + a*x + 1 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: f[2] +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[2][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l1][?7h[?12l[?25h[?25l[?7lsage: f[1] +[?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[?2004lTrue +aux == omega False +--------------------------------------------------------------------------- +UnboundLocalError Traceback (most recent call last) +Cell In [27], line 1 +----> 1 load('init.sage') + +File /ext/sage/9.8/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/9.8/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 :32 + +File /ext/sage/9.8/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/9.8/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 :30 + +File :85, in regular_drw_form(omega) + +File :27, in decomposition_omega0_hpdh(omega) + +File :70, in cartier(self) + +UnboundLocalError: cannot access local variable 'polynomial_part' where it is not associated with a value +[?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[?2004lTrue +aux == omega True +aux.omega, fct 0 dx ((x^10 + (a + 2)*x^4 + a*x^2 + x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True +mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True +True True +aux - omega + V(((-x^2)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((x^30 + 2*a*x^12 + (2*a + 1)*x^6 + x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y]) +A.diffn().is_regular_on_U0() True +[0] d[x] + [0] d[y] + V((2*a*x^9 + 2*x^3 + (a + 1)*x + 2*a) dy) + dV(0) +True +aux == omega True +aux.omega, fct (((a - 1)*x^36 + (-a - 1)*x^30 - x^28 + (a - 1)*x^27 - x^18 + a*x^12 + a*x^10 + (a + 1)*x^9 + (-a)*x^6 + (-a + 1)*x^4 + (a + 1)*x^3 - x + (a - 1))/y) dx (((a + 2)*x^19 + (a + 1)*x^13 + x^11 + (2*a + 1)*x^10 + 2*a*x^7 + (a + 2)*x^5 + (a + 1)*x^4 + x^2 + (a + 2)*x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y False False +mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True +True True +aux - omega + V((((a - 1)*x^45 + (a + 1)*x^39 + x^37 + (-a + 1)*x^36 + (-a)*x^33 + (a - 1)*x^31 + (a + 1)*x^30 + a*x^29 + x^28 + (a + 1)*x^27 + x^21 + (-a)*x^19 + a*x^18 + (-a + 1)*x^15 + (a + 1)*x^13 + x^12 + (-a - 1)*x^11 + (-a + 1)*x^10 + (-a - 1)*x^9 + (-a - 1)*x^7 + (-a + 1)*x^4 + a*x^2 + x + (a - 1))/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((2*a*x^57 + (2*a + 2)*x^39 + x^33 + a*x^30 + (a + 2)*x^21 + 2*a*x^15 + (2*a + 2)*x^12 + x^6 + 2*a*x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y]) +A.diffn().is_regular_on_U0() True +[0] d[x] + [0] d[y] + V((2*a*x^12 + 2*x^6 + (a + 1)*x^4 + 2*a*x^3) dy) + dV(0) +True +aux == omega True +aux.omega, fct ((x^63 + (a - 1)*x^57 + (-a)*x^55 + x^54 + a*x^45 + a*x^39 + (-a - 1)*x^37 + (a - 1)*x^36 + (-a - 1)*x^33 - x^31 + a*x^28 + a*x^27 + (a - 1)*x^21 + (a - 1)*x^19 + (-a + 1)*x^18 + (-a + 1)*x^15 + a*x^13 + (a - 1)*x^12 + (-a - 1)*x^10 + (a + 1)*x^9 + (-a - 1)*x^6 - x^4 + (-a + 1)*x^3 + (-a)*x + 1)/y) dx (((a + 1)*x^28 + (a + 2)*x^20 + (a + 1)*x^14 + (2*a + 1)*x^11 + (a + 2)*x^10 + 2*a*x^8 + (a + 1)*x^5 + 2*a*x^4 + (a + 2)*x^2 + (a + 1)*x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y False False +mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True +True True +aux - omega + V(((x^72 + (-a + 1)*x^66 + a*x^64 - x^63 + (-a - 1)*x^60 + x^58 + (-a + 1)*x^57 + (a + 1)*x^56 + a*x^55 + (a + 1)*x^54 + (a + 1)*x^48 + (a + 1)*x^46 + (-a - 1)*x^45 + (-a)*x^42 + (a + 1)*x^40 - x^39 + (-a + 1)*x^38 + x^37 + (a - 1)*x^36 + (a - 1)*x^34 + (-a - 1)*x^33 + a*x^32 + a*x^30 + (-a - 1)*x^29 + (a + 1)*x^28 + x^27 + a*x^24 + x^22 - x^21 - x^20 - x^19 + a*x^18 - x^16 - x^15 + (-a - 1)*x^14 + x^13 + a*x^12 + (-a + 1)*x^11 + (-a + 1)*x^10 - x^9 - x^8 + (a - 1)*x^7 + a*x^5 - x^4 + (a + 1)*x^2 + a*x + 1)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([(((2*a + 2)*x^84 + 2*a*x^60 + (2*a + 2)*x^42 + a*x^33 + 2*a*x^30 + (a + 2)*x^24 + (2*a + 2)*x^15 + (a + 2)*x^12 + 2*a*x^6 + (2*a + 2)*x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y]) +A.diffn().is_regular_on_U0() True +[0] d[x] + [0] d[y] + V((2*a*x^15 + 2*x^9 + (a + 1)*x^7 + 2*a*x^6) dy) + dV(0) +True +aux == omega True +aux.omega, fct 0 dx ((x^13 + (a + 2)*x^7 + a*x^5 + x^4)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True +mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True +True True +aux - omega + V(((-x^11)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((x^39 + 2*a*x^21 + (2*a + 1)*x^15 + x^12)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y]) +A.diffn().is_regular_on_U0() True +[0] d[x] + [0] d[y] + V((2*a*x^18 + 2*x^12 + (a + 1)*x^10 + 2*a*x^9) dy) + dV(0) +True +aux == omega True +aux.omega, fct (((a - 1)*x^54 + (-a - 1)*x^48 - x^46 + (a - 1)*x^45 + x^36 + x^30 + (-a)*x^28 + a*x^27 + (-a)*x^24 + (-a + 1)*x^22 + (a + 1)*x^21 - x^19 + (-a - 1)*x^18 + (-a - 1)*x^12 + (-a - 1)*x^10 + (a - 1)*x^9 + (a + 1)*x^6 + x^4 + (a - 1)*x^3 + a*x - 1)/y) dx (((a + 2)*x^25 + x^17 + (2*a + 1)*x^16 + (2*a + 1)*x^11 + (2*a + 2)*x^10 + x^8 + (a + 1)*x^7 + (2*a + 2)*x^5 + a*x^4 + (a + 2)*x^2 + (2*a + 2)*x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y False False +mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True +True True +aux - omega + V((((a - 1)*x^63 + (a + 1)*x^57 + x^55 + (-a + 1)*x^54 + (-a)*x^51 + (a - 1)*x^49 + (a + 1)*x^48 + a*x^47 + x^46 + a*x^45 + a*x^39 + a*x^37 + (a + 1)*x^36 - x^33 + a*x^31 + a*x^30 + (a + 1)*x^29 + (a + 1)*x^28 + x^27 + (-a - 1)*x^25 + (-a + 1)*x^22 + (-a)*x^21 + a*x^20 + (a - 1)*x^19 + x^18 + x^15 + (a - 1)*x^13 + (-a)*x^12 + (-a + 1)*x^11 + x^10 + (-a + 1)*x^9 + (-a + 1)*x^7 + x^4 + (-a - 1)*x^2 + (-a)*x - 1)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((2*a*x^75 + x^51 + a*x^48 + a*x^33 + (a + 1)*x^30 + x^24 + (2*a + 2)*x^21 + (a + 1)*x^15 + (2*a + 1)*x^12 + 2*a*x^6 + (a + 1)*x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y]) +A.diffn().is_regular_on_U0() True +[0] d[x] + [0] d[y] + V((2*a*x^30 + 2*x^24 + (a + 1)*x^22 + 2*a*x^21 + (a + 1)*x^12 + a*x^6 + (a + 2)*x^4 + (a + 1)*x^3) dy) + dV(0) +True +aux == omega True +aux.omega, fct 0 dx ((2*x^16 + (a + 2)*x^10 + 2*a*x^8 + 2*x^7 + (a + 1)*x^4 + 2*x^2 + (2*a + 1)*x)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y True True +mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True +True True +aux - omega + V(((x^20 + (-a)*x^2)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((2*x^48 + 2*a*x^30 + (a + 2)*x^24 + 2*x^21 + (2*a + 2)*x^12 + 2*x^6 + a*x^3)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y]) +A.diffn().is_regular_on_U0() True +[0] d[x] + [0] d[y] + V((a*x^27 + x^21 + (2*a + 2)*x^19 + a*x^18 + (2*a + 2)*x^9 + 2*a*x^3 + (2*a + 1)*x + 2*a + 2) dy) + dV(0) +True +aux == omega True +aux.omega, fct 0 dx 0 True True +mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True +True True +aux - omega 0 +A.diffn().is_regular_on_U0() True +[0] d[x] + [0] d[y] + V((0) dy) + dV(0) +True +aux == omega True +aux.omega, fct (((a - 1)*x^45 + (-a - 1)*x^39 - x^37 + (a - 1)*x^36 - x^27 + a*x^21 + a*x^19 + (a + 1)*x^18 + (-a)*x^15 + (-a + 1)*x^13 + (a + 1)*x^12 - x^10 + (a - 1)*x^9)/y) dx (((a + 2)*x^22 + (a + 1)*x^16 + x^14 + (2*a + 1)*x^13 + 2*a*x^10 + (a + 2)*x^8 + (a + 1)*x^7 + x^5 + (a + 2)*x^4)/(x^18 + (2*a + 1)*x^12 + a*x^10 + 2*x^9 + (2*a + 2)*x^6 + x^4 + (2*a + 1)*x^3 + (a + 1)*x^2 + a*x + 1))*y False False +mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() True +True True +aux - omega + V((((a - 1)*x^54 + (a + 1)*x^48 + x^46 + (-a + 1)*x^45 + (-a)*x^42 + (a - 1)*x^40 + (a + 1)*x^39 + a*x^38 + x^37 + (a + 1)*x^36 + x^30 + (-a)*x^28 + a*x^27 + (-a + 1)*x^24 + (a + 1)*x^22 + x^21 + (-a - 1)*x^20 + (-a + 1)*x^19 + (-a - 1)*x^18 + (-a - 1)*x^16 + (-a + 1)*x^13 + a*x^11 + x^10 + (a - 1)*x^9)/(x^9*y + (a - 1)*x^3*y + (-a)*x*y + y)) dx) + dV([((2*a*x^66 + (2*a + 2)*x^48 + x^42 + a*x^39 + (a + 2)*x^30 + 2*a*x^24 + (2*a + 2)*x^21 + x^15 + 2*a*x^12)/(x^45 + (2*a + 1)*x^39 + a*x^37 + 2*x^36 + (2*a + 2)*x^33 + x^31 + (2*a + 1)*x^30 + (a + 1)*x^29 + a*x^28 + (2*a + 1)*x^27 + a*x^21 + (2*a + 2)*x^19 + (a + 1)*x^18 + 2*x^15 + (2*a + 1)*x^13 + a*x^12 + (a + 2)*x^11 + 2*x^10 + (a + 2)*x^9 + (a + 2)*x^7 + a*x^5 + 2*x^4 + (a + 1)*x^2 + a*x + 1))*y]) +A.diffn().is_regular_on_U0() True +[0] d[x] + [0] d[y] + V((2*a*x^21 + 2*x^15 + (a + 1)*x^13 + 2*a*x^12) dy) + dV(0) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf[1][?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lF.cardinality()[?7h[?12l[?25h[?25l[?7lanth_root(p)[?7h[?12l[?25h[?25l[?7lomega.carier()[?7h[?12l[?25h[?25l[?7l = a*omega[?7h[?12l[?25h[?25l[?7l.cartier()[?7h[?12l[?25h[?25l[?7l = (C.x)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lC =superelliptic(x^3 - x, m)[?7h[?12l[?25h[?25l[?7lfct= C.y[?7h[?12l[?25h[?25l[?7lsage: fct = C.y +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lfct = C.y[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lf[1][?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lfct = 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[?7lmult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()[?7h[?12l[?25h[?25l[?7lsage: mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn() +[?7h[?12l[?25h[?2004l \ No newline at end of file diff --git a/sage/drafty/draft.sage b/sage/drafty/draft.sage index ca94803..7045bcd 100644 --- a/sage/drafty/draft.sage +++ b/sage/drafty/draft.sage @@ -1,13 +1,14 @@ -p = 5 +p = 3 m = 2 -F = GF(p) +F = GF(p^2, 'a') +a = F.gens()[0] Rxx. = PolynomialRing(F) #f = (x^3 - x)^3 + x^3 - x -f = x^3 + x -f1 = f(x = x^5 - x) +f = x^3 + a*x + 1 +f1 = f(x = x^p - x) C = superelliptic(f, m) -#C1 = superelliptic(f1, m, prec = 500) -B = C.crystalline_cohomology_basis(prec = 100, info = 1) +C1 = superelliptic(f1, m, prec = 500) +#B = C.crystalline_cohomology_basis(prec = 100, info = 1) #B1 = C1.crystalline_cohomology_basis(prec = 100, info = 1) def crystalline_matrix(C, prec = 50): @@ -20,8 +21,15 @@ def crystalline_matrix(C, prec = 50): M[i, :] = vector(autom(b).coordinates(basis = B)) return M -for b in B: - print(b.regular_form()) +#b0 = de_rham_witt_lift(C.de_rham_basis()[0], prec = 100) +#b1 = de_rham_witt_lift(C1.de_rham_basis()[2], prec = 300) +#print(b0.regular_form()) +#print(b1.regular_form()) +for b in C1.de_rham_basis(): + print(mult_by_p(b.omega0).regular_form()) + +#for b in B: +# print(b.regular_form()) #for b in B1: # print(b.regular_form()) diff --git a/sage/superelliptic/superelliptic_cech_class.sage b/sage/superelliptic/superelliptic_cech_class.sage index 05c7ed6..4f3f6c0 100644 --- a/sage/superelliptic/superelliptic_cech_class.sage +++ b/sage/superelliptic/superelliptic_cech_class.sage @@ -127,14 +127,14 @@ def cut(f, i): return sum(R(x^(j-i-1)) * coeff[j] for j in range(i+1, f.degree() + 1)) def polynomial_part(p, h): - F = GF(p) + F = base_ring(parent(h)) Rx. = PolynomialRing(F) h = Rx(h) result = Rx(0) for i in range(0, h.degree()+1): if (i%p) == p-1: power = Integer((i-(p-1))/p) - result += Integer(h[i]) * x^(power) + result += F(h[i]) * x^(power) return result #Find delta-th root of unity in field F diff --git a/sage/superelliptic/superelliptic_form_class.sage b/sage/superelliptic/superelliptic_form_class.sage index 257dac1..b27f4f9 100644 --- a/sage/superelliptic/superelliptic_form_class.sage +++ b/sage/superelliptic/superelliptic_form_class.sage @@ -66,7 +66,11 @@ class superelliptic_form: h = Rx(h) j1 = (p^(mult_order-1)*j)%m B = floor(p^(mult_order-1)*j/m) - result += superelliptic_form(C, polynomial_part(p, h)/(f^B*y^(j1)*h_denom)) + P = polynomial_part(p, h) + if F.cardinality() != p: + d = P.degree() + P = sum(P[i].nth_root(p)*x^i for i in range(0, d+1)) + result += superelliptic_form(C, P/(f^B*y^(j1)*h_denom)) return result def serre_duality_pairing(self, fct, prec=20): diff --git a/sage/superelliptic_drw/regular_form.sage b/sage/superelliptic_drw/regular_form.sage index a92ec4b..60ac5f4 100644 --- a/sage/superelliptic_drw/regular_form.sage +++ b/sage/superelliptic_drw/regular_form.sage @@ -73,14 +73,22 @@ class superelliptic_regular_drw_form: return "[" + str(self.dx) + "] d[x] + [" + str(self.dy) + "] d[y] + V(" + str(self.omega) + ") + dV(" + str(self.h2) + ")" def regular_drw_form(omega): + print(omega.frobenius().is_regular_on_U0()) C = omega.curve p = C.characteristic omega_aux = omega.r() omega_aux = omega_aux.regular_form() aux = omega - omega_aux.dx.teichmuller()*C.x.teichmuller().diffn() - omega_aux.dy.teichmuller()*C.y.teichmuller().diffn() + print("aux == omega", aux == omega) + aux1 = aux.omega aux.omega, fct = decomposition_omega0_hpdh(aux.omega) + print('aux.omega, fct', aux.omega, fct, aux1.cartier() == fct.diffn(), aux1.verschiebung() == mult_by_p(fct.diffn())) + print('mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()', mult_by_p(fct.diffn()) == (fct^p).verschiebung().diffn()) aux.h2 += fct^p + print(aux.omega.is_regular_on_U0(), aux.frobenius().is_regular_on_U0()) + print('aux - omega', aux - omega) aux.h2, A = decomposition_g0_pth_power(aux.h2) + print('A.diffn().is_regular_on_U0()', A.diffn().is_regular_on_U0()) aux.omega += (A.diffn()).inv_cartier() result = superelliptic_regular_drw_form(omega_aux.dx, omega_aux.dy, aux.omega.regular_form(), aux.h2) return result @@ -95,6 +103,8 @@ superelliptic_drw_cech.regular_form = regular_drw_cech def regular_form(omega): '''Given a form omega regular on U0, present it as P(x, y) dx + Q(x, y) dy for some polynomial P, Q. The output is A(x)*y, B(x), where omega = A(x) y dx + B(x) dy''' + if not omega.is_regular_on_U0(): + raise ValueError("The form " + str(omega) + " is not regular on U0.") C = omega.curve f = C.polynomial Fxy, Rxy, x, y = C.fct_field diff --git a/sage/superelliptic_drw/superelliptic_drw_cech.sage b/sage/superelliptic_drw/superelliptic_drw_cech.sage index 541e382..23b257b 100644 --- a/sage/superelliptic_drw/superelliptic_drw_cech.sage +++ b/sage/superelliptic_drw/superelliptic_drw_cech.sage @@ -13,7 +13,10 @@ class superelliptic_drw_cech: f_second_comp = fct.f decomp_first_comp = decomposition_g0_g8(f_first_comp) decomp_second_comp = decomposition_g0_g8(f_second_comp) - new = self + new = superelliptic_drw_cech(0*C.dx.verschiebung(), 0*C.x.verschiebung()) + new.omega0 = self.omega0 + new.omega8 = self.omega8 + new.f = self.f new.omega0 -= decomposition_g0_g8(f_first_comp)[0].teichmuller().diffn() new.omega0 -= decomposition_g0_g8(f_second_comp)[0].verschiebung().diffn() new.f = decomposition_g0_g8(f_first_comp)[2].teichmuller() + decomposition_g0_g8(f_second_comp)[2].verschiebung()