cohomology of str sheaf dodany; zaczynamy zmieniac wspolrzedne w superelliptic holo
This commit is contained in:
parent
be66e7bc64
commit
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@ -26748,4 +26748,133 @@ Input [0;32mIn [81][0m, in [0;36m<cell line: 1>[0;34m()[0m
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]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ git add draft/sup[K[K[K[K[K[K[K[K[Ksage/drafty/superelliptic_cohomology_class.sage [K
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]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ gid add -u
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bash: gid: command not found
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]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ gid add -u[C[C
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]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ gid add -u[C[C[1P[1@t
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]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ git commit -m ""C"o"h"o"m"o"l"o"g"y" "o"f" "s"t"r"u"c"t"u"r"e" "s"h"e"a"f" "o"f" "s"u"p"e"r"e"l"l"i"p"t"i"c"
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[master be66e7b] Cohomology of structure sheaf of superelliptic
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11 files changed, 7056 insertions(+), 82 deletions(-)
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delete mode 100644 sage/as_covers/as_cover/uniformizer.sage
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rewrite sage/drafty/draft3.sage (90%)
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create mode 100644 sage/drafty/superelliptic_cohomology_class.sage
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]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ git push
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Username for 'https://git.wmi.amu.edu.pl': jgarnek
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Password for 'https://jgarnek@git.wmi.amu.edu.pl':
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Enumerating objects: 37, done.
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Counting objects: 2% (1/37)
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Counting objects: 100% (37/37), done.
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Delta compression using up to 4 threads
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Compressing objects: 4% (1/23)
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Compressing objects: 100% (23/23), done.
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Writing objects: 4% (1/23)
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Writing objects: 100% (23/23), 73.16 KiB | 337.00 KiB/s, done.
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Total 23 (delta 15), reused 0 (delta 0)
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remote: . Processing 1 references[K
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remote: Processed 1 references in total[K
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To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git
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d77adde..be66e7b master -> master
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]0;~/Research/2021 De Rham/DeRhamComputation[01;34m~/Research/2021 De Rham/DeRhamComputation[00m$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$
[K]0;~/Research/2021 De Rham/DeRhamComputation/sage[01;34m~/Research/2021 De Rham/DeRhamComputation/sage[00m$ sage
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┌────────────────────────────────────────────────────────────────────┐
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│ SageMath version 9.7, Release Date: 2022-09-19 │
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│ Using Python 3.10.5. Type "help()" for help. │
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└────────────────────────────────────────────────────────────────────┘
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[22;0t]0;IPython: DeRhamComputation/sage[6n[?2004h[?1l[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m
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[J[?7h[0m[?12l[?25h[?2004l[5]
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[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.is_smooth()[12D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mC[7D[0m
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[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
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[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mis_smooth()[11D[?7h[0m[?12l[?25h[?25l[?7l[0mf[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mbenius_matrix[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[26D[0m[J[0;94msage: [0mC.frobenius_matrix()[26D[0m
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[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
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[0;31mTypeError[0m Traceback (most recent call last)
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Input [0;32mIn [3][0m, in [0;36m<cell line: 1>[0;34m()[0m
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[0;32m----> 1[0m [43mC[49m[38;5;241;43m.[39;49m[43mfrobenius_matrix[49m[43m([49m[43m)[49m
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File [0;32m<string>:163[0m, in [0;36mfrobenius_matrix[0;34m(self, prec)[0m
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[0;31mTypeError[0m: unsupported operand type(s) for ** or pow(): 'superelliptic_cohomology' and 'method'
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[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC.frobenius_matrix[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[19D[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m
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[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.frobenius_matrix()[19D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mf[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mbenius_matrix[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mr[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0mc[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0m-[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m5[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m-[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m5[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;210;48;5;88m)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m=[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m5[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[0;38;5;210;48;5;88m)[?7h[0m[?12l[?25h[?25l[?7l[32D[0m[J[0;94msage: [0mC.frobenius_matrix(prec=[0;38;5;20;1m50[0m)[33D[0m
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[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
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[0;31mTypeError[0m Traceback (most recent call last)
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Input [0;32mIn [5][0m, in [0;36m<cell line: 1>[0;34m()[0m
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[0;32m----> 1[0m [43mC[49m[38;5;241;43m.[39;49m[43mfrobenius_matrix[49m[43m([49m[43mprec[49m[38;5;241;43m=[39;49m[43mInteger[49m[43m([49m[38;5;241;43m50[39;49m[43m)[49m[43m)[49m
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File [0;32m<string>:163[0m, in [0;36mfrobenius_matrix[0;34m(self, prec)[0m
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[0;31mTypeError[0m: unsupported operand type(s) for ** or pow(): 'superelliptic_cohomology' and 'method'
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[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0moad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m
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[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mload[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[17D[0mC.frobenius_matrix[0;38;5;16;48;5;152m([0mprec=[0;38;5;20;1m50[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[33D[0m[J[0;94msage: [0mC.frobenius_matrix(prec=[0;38;5;20;1m50[0m)[33D[0m
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[J[?7h[0m[?12l[?25h[?2004l[0;31m---------------------------------------------------------------------------[0m
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[0;31mTypeError[0m Traceback (most recent call last)
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File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2441[0m, in [0;36msage.rings.polynomial.polynomial_element.Polynomial.__pow__[0;34m()[0m
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[1;32m 2440[0m try:
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[0;32m-> 2441[0m right = Integer(right)
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[1;32m 2442[0m except TypeError:
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File [0;32m/ext/sage/9.7/src/sage/rings/integer.pyx:717[0m, in [0;36msage.rings.integer.Integer.__init__[0;34m()[0m
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[1;32m 716[0m
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[0;32m--> 717[0m raise TypeError("unable to coerce %s to an integer" % type(x))
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[1;32m 718[0m
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[0;31mTypeError[0m: unable to coerce <class 'method'> to an integer
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During handling of the above exception, another exception occurred:
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[0;31mTypeError[0m Traceback (most recent call last)
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Input [0;32mIn [7][0m, in [0;36m<cell line: 1>[0;34m()[0m
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[0;32m----> 1[0m [43mC[49m[38;5;241;43m.[39;49m[43mfrobenius_matrix[49m[43m([49m[43mprec[49m[38;5;241;43m=[39;49m[43mInteger[49m[43m([49m[38;5;241;43m50[39;49m[43m)[49m[43m)[49m
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File [0;32m<string>:163[0m, in [0;36mfrobenius_matrix[0;34m(self, prec)[0m
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File [0;32m<string>:71[0m, in [0;36m__pow__[0;34m(self, exp)[0m
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File [0;32m/ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:2443[0m, in [0;36msage.rings.polynomial.polynomial_element.Polynomial.__pow__[0;34m()[0m
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[1;32m 2441[0m right = Integer(right)
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[1;32m 2442[0m except TypeError:
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[0;32m-> 2443[0m raise TypeError("non-integral exponents not supported")
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[1;32m 2444[0m
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[1;32m 2445[0m d = self.degree()
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[0;31mTypeError[0m: non-integral exponents not supported
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[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m([0;38;5;241m(C.x)*C.x*C.dx).cartier()[25D[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.one/[5D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0mx[0;38;5;241m*C.dx).cartier()[0m[K[16D[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m([3C)[0m[K[?7h[0m[?12l[?25h[?25l[?7l[5D[0m([3C)^[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[13D[0m[J[0;94msage: [0m(C.x)^p[13D[0m
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[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mx^7
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[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.frobenius_matrix(prec=50)[26D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mC[7D[0m
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[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
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[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mp[0;38;5;241mrint(len(lista))[16D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mp[7D[0m
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[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m7
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[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0ml[0;38;5;241moad('init.sage')[16D[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mad[0;38;5;16;48;5;152m([0;38;5;160;48;5;231m'init.sage'[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[23D[0m[J[0;94msage: [0mload([0;38;5;160;48;5;231m'init.sage'[0m)[23D[0m
|
||||
[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[?7h[0m[?12l[?25h[?25l[?7l[0m.[0;38;5;241mfrobenius_matrix(prec=50)[25D[?7h[0m[?12l[?25h[?25l[?7l[0mfrobenius_matrix[0;38;5;16;48;5;152m([0mprec=[0;38;5;20;1m50[0;38;5;16;48;5;152m)[?7h[0m[?12l[?25h[?25l[?7l[33D[0m[J[0;94msage: [0mC.frobenius_matrix(prec=[0;38;5;20;1m50[0m)[33D[0m
|
||||
[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[0 0 0 0 0 1]
|
||||
[0 0 1 0 0 0]
|
||||
[0 1 0 0 0 0]
|
||||
[1 0 0 0 0 0]
|
||||
[0 0 0 0 0 0]
|
||||
[0 0 0 0 0 0]
|
||||
[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.frobenius_matrix(prec=50)[26D[?7h[0m[?12l[?25h[?25l[?7l[0m.[?7h[0m[?12l[?25h[?25l[?7l[0md[0;38;5;241mx.cartier()[0m[K[11D[?7h[0m[?12l[?25h[?25l[?7l[0me[0;38;5;241m_rham_basis()[13D[?7h[0m[?12l[?25h[?25l[?7l[0m_rham_basis[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[2D[0m([0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mb[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[12D[0;94msage: [0mC.basis_[0m
|
||||
[14C[0;38;5;16;48;5;250m C.basis_de_rham_degrees [0m
|
||||
[14C[0;38;5;16;48;5;250m C.basis_holomorphic_differentials_degree[0m
|
||||
[14C[0;38;5;16;48;5;250m C.basis_of_cohomology [0m
|
||||
|
||||
[0m [5A[14C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mde_rham_degrees[0m
|
||||
[14C[0;38;5;231;48;5;102m C.basis_de_rham_degrees [0m
|
||||
|
||||
|
||||
[14C[0;38;5;16;48;5;248m <unknown> [4A[4C[?7h[0m[?12l[?25h[?25l[?7l[15D[0mholomorphic_differentials_degree[0m
|
||||
[14C[0;38;5;16;48;5;250m C.basis_de_rham_degrees [0m
|
||||
[14C[0;38;5;231;48;5;102m C.basis_holomorphic_differentials_degree[2A[9D[?7h[0m[?12l[?25h[?25l[?7l[32D[0mof_cohomology[0m[K[0m
|
||||
|
||||
[14C[0;38;5;16;48;5;250m C.basis_holomorphic_differentials_degree[0m
|
||||
[14C[0;38;5;231;48;5;102m C.basis_of_cohomology [3A[28D[?7h[0m[?12l[?25h[?25l[?7l[0m
|
||||
[C[0m[K[0m
|
||||
[C[0m[K[0m
|
||||
[C[0m[K[0m
|
||||
[C[0m[K[4A[26C[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[29D[0m[J[0;94msage: [0mC.basis_of_cohomology()[29D[0m
|
||||
[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[1/x*y, 1/x*y^2, 1/x^2*y^2, 1/x*y^3, 1/x^2*y^3, 1/x^3*y^3]
|
||||
[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0m
|
||||
|
||||
|
||||
[0m [3A[6C[?7h[0m[?12l[?25h[?25l[?7l[0mC.basis_of_cohomology[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[2D[0m()[[?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m0[?7h[0m[?12l[?25h[?25l[?7l[2D[0;38;5;16;48;5;152m[[C][?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C].[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C][0m[K[?7h[0m[?12l[?25h[?25l[?7l[3D[0m[[C]^[?7h[0m[?12l[?25h[?25l[?7l[0m[[?7h[0m[?12l[?25h[?25l[?7l[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0m)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[4D[0;38;5;16;48;5;152m[[C[0;38;5;210;48;5;88m][?7h[0m[?12l[?25h[?25l[?7l[2D[0m[[C][2D[?7h[0m[?12l[?25h[?25l[?7l[3D[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[21D[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0m(C.basis_of_cohomology()[[0;38;5;20;1m0[0m]^p)[29D[?7h[0m[?12l[?25h[?25l[?7l[2C[?7h[0m[?12l[?25h[?25l[?7l[19C[0;38;5;210;48;5;88m([0;38;5;16;48;5;152m)[2D[?7h[0m[?12l[?25h[?25l[?7l[0m()[C[?7h[0m[?12l[?25h[?25l[?7l[3C[?7h[0m[?12l[?25h[?25l[?7l[28D[0;38;5;16;48;5;152m([28C)[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[30D[0m([28C).[?7h[0m[?12l[?25h[?25l[?7l[0mc[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mo[?7h[0m[?12l[?25h[?25l[?7l[0mr[?7h[0m[?12l[?25h[?25l[?7l[0md[?7h[0m[?12l[?25h[?25l[?7l[0mi[?7h[0m[?12l[?25h[?25l[?7l[0mn[?7h[0m[?12l[?25h[?25l[?7l[0ma[?7h[0m[?12l[?25h[?25l[?7l[0mt[?7h[0m[?12l[?25h[?25l[?7l[0me[?7h[0m[?12l[?25h[?25l[?7l[0ms[?7h[0m[?12l[?25h[?25l[?7l[0m([?7h[0m[?12l[?25h[?25l[?7l[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[50D[0m[J[0;94msage: [0m(C.basis_of_cohomology()[[0;38;5;20;1m0[0m]^p).coordinates()[50D[0m
|
||||
[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[0, 0, 0, 0, 1, 0]
|
||||
[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[6D[0;94msage: [0m
|
||||
[0m [A[6C[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mp[7D[0m
|
||||
[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m7
|
||||
[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mC[0;38;5;241m.basis_of_cohomology()[22D[?7h[0m[?12l[?25h[?25l[?7l[7D[0m[J[0;94msage: [0mC[7D[0m
|
||||
[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0mSuperelliptic curve with the equation y^4 = x^5 + x over Finite Field of size 3
|
||||
[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0m [0;38;5;241m= 5[3D[?7h[0m[?12l[?25h[?25l[?7l[0m=[?7h[0m[?12l[?25h[?25l[?7l[0m [?7h[0m[?12l[?25h[?25l[?7l[0;38;5;20;1m3[?7h[0m[?12l[?25h[?25l[?7l[11D[0m[J[0;94msage: [0mp = [0;38;5;20;1m3[11D[0m
|
||||
[J[?7h[0m[?12l[?25h[?2004l[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mp = [0;38;5;20;1m3[?7h[0m[?12l[?25h[?25l[?7l[5D[0mC[0m[K[?7h[0m[?12l[?25h[?25l[?7l[0mp[?7h[0m[?12l[?25h[?25l[?7l[0m(C.basis_of_cohomology()[[0;38;5;20;1m0[0m]^p).coordinates[0;38;5;16;48;5;152m()[?7h[0m[?12l[?25h[?25l[?7l[50D[0m[J[0;94msage: [0m(C.basis_of_cohomology()[[0;38;5;20;1m0[0m]^p).coordinates()[50D[0m
|
||||
[J[?7h[0m[?12l[?25h[?2004l[0m[?7h[0;91m[0m[0m[0, 0, 0, 0, 0, 1]
|
||||
[6n[?2004h[?25l[0m[?7l[0m[J[0;94msage: [6D[6C[?7h[0m[?12l[?25h[?25l[?7l[?7h[0m[?12l[?25h[?25l[?7l[0mq[0;38;5;241m = 5[4D[?7h[0m[?12l[?25h
|
||||
@ -18,7 +18,7 @@ load('auxilliaries/linear_combination_polynomials.sage')
|
||||
##############
|
||||
##############
|
||||
load('drafty/lift_to_de_rham.sage')
|
||||
load('drafty/superelliptic_cohomology_class.sage')
|
||||
#load('drafty/superelliptic_cohomology_class.sage')
|
||||
load('drafty/draft5.sage')
|
||||
load('drafty/pole_numbers.sage')
|
||||
#load('drafty/draft4.sage')
|
||||
@ -12,6 +12,7 @@ class superelliptic:
|
||||
self.exponent = m
|
||||
self.base_ring = F
|
||||
self.characteristic = F.characteristic()
|
||||
self.fct_field = RxyzQ, Rxyz, x, y, z
|
||||
r = Rx(f).degree()
|
||||
delta = GCD(r, m)
|
||||
self.nb_of_pts_at_infty = delta
|
||||
@ -26,6 +27,19 @@ class superelliptic:
|
||||
F = self.base_ring
|
||||
return 'Superelliptic curve with the equation y^' + str(m) + ' = ' + str(f)+' over ' + str(F)
|
||||
|
||||
def coordinates2(self, basis = 0):
|
||||
"""Find coordinates of the given holomorphic form self in terms of the basis forms in a list holo."""
|
||||
C = self.curve
|
||||
if basis == 0:
|
||||
basis = C.holomorphic_differentials_basis()
|
||||
RxyzQ, Rxyz, x, y, z = C.fct_field
|
||||
# We need to have only polynomials to use monomial_coefficients in linear_representation_polynomials,
|
||||
# and sometimes basis elements have denominators. Thus we multiply by them.
|
||||
denom = LCM([denominator(omega.form) for omega in basis])
|
||||
basis = [denom*omega for omega in basis]
|
||||
self_with_no_denominator = denom*self
|
||||
return linear_representation_polynomials(Rxyz(self_with_no_denominator.form), [Rxyz(omega.form) for omega in basis])
|
||||
|
||||
#Auxilliary algorithm that returns the basis of holomorphic differentials
|
||||
#of the curve and (as a second argument) the list of pairs (i, j)
|
||||
#such that x^i dx/y^j is holomorphic.
|
||||
@ -128,7 +142,7 @@ class superelliptic:
|
||||
M[i, :] = v
|
||||
return M
|
||||
|
||||
def frobenius_matrix(self):
|
||||
def dr_frobenius_matrix(self):
|
||||
basis = self.de_rham_basis()
|
||||
g = self.genus()
|
||||
p = self.characteristic
|
||||
@ -153,6 +167,16 @@ class superelliptic:
|
||||
M[i, :] = v
|
||||
return M
|
||||
|
||||
def frobenius_matrix(self, prec=20):
|
||||
g = self.genus()
|
||||
F = self.base_ring
|
||||
p = F.characteristic()
|
||||
M = matrix(F, g, g)
|
||||
for i, f in enumerate(self.basis_of_cohomology()):
|
||||
M[i, :] = vector((f^p).coordinates(prec=prec))
|
||||
M = M.transpose()
|
||||
return M
|
||||
|
||||
# def p_rank(self):
|
||||
# return self.cartier_matrix().rank()
|
||||
|
||||
@ -165,6 +189,23 @@ class superelliptic:
|
||||
V = self.verschiebung_matrix()
|
||||
p = self.characteristic
|
||||
return flag(Fr, V, p, test)
|
||||
|
||||
def basis_of_cohomology(self):
|
||||
'''Basis of cohomology of structure sheaf H1(X, OX).'''
|
||||
m = self.exponent
|
||||
f = self.polynomial
|
||||
r = f.degree()
|
||||
F = self.base_ring
|
||||
delta = self.nb_of_pts_at_infty
|
||||
Rx.<x> = PolynomialRing(F)
|
||||
Rxy.<x, y> = PolynomialRing(F, 2)
|
||||
Fxy = FractionField(Rxy)
|
||||
basis = []
|
||||
for j in range(1, m):
|
||||
for i in range(1, r):
|
||||
if (r*j - m*i >= delta):
|
||||
basis += [superelliptic_function(self, Fxy(m*y^(j)/x^i))]
|
||||
return basis
|
||||
|
||||
#Auxilliary. Given a superelliptic curve C : y^m = f(x) and a polynomial g(x, y)
|
||||
#it replaces repeteadly all y^m's in g(x, y) by f(x). As a result
|
||||
|
||||
@ -53,6 +53,14 @@ class superelliptic_form:
|
||||
B = floor(p^(mult_order-1)*j/m)
|
||||
result += superelliptic_form(C, polynomial_part(p, h)/(f^B*y^(j1)))
|
||||
return result
|
||||
|
||||
def serre_duality_pairing(self, fct, prec=20):
|
||||
result = 0
|
||||
C = self.curve
|
||||
delta = C.nb_of_pts_at_infty
|
||||
for i in range(delta):
|
||||
result += (fct*self).expansion_at_infty(place=i, prec=prec)[-1]
|
||||
return -result
|
||||
|
||||
def coordinates(self):
|
||||
C = self.curve
|
||||
|
||||
@ -69,7 +69,7 @@ class superelliptic_function:
|
||||
C = self.curve
|
||||
g = self.function
|
||||
return superelliptic_function(C, g^(exp))
|
||||
|
||||
|
||||
def diffn(self):
|
||||
C = self.curve
|
||||
f = C.polynomial
|
||||
@ -83,6 +83,18 @@ class superelliptic_function:
|
||||
B = g.derivative(y)*f.derivative(x)/(m*y^(m-1))
|
||||
return superelliptic_form(C, A+B)
|
||||
|
||||
def coordinates(self, basis = 0, basis_holo = 0, prec=20):
|
||||
'''Find coordinates in H1(X, OX) in given basis basis with dual basis basis_holo.'''
|
||||
C = self.curve
|
||||
if basis == 0:
|
||||
basis = basis_of_cohomology(C)
|
||||
if basis_holo == 0:
|
||||
basis_holo = C.holomorphic_differentials_basis()
|
||||
g = C.genus()
|
||||
coordinates = g*[0]
|
||||
for i, omega in enumerate(basis_holo):
|
||||
coordinates[i] = omega.serre_duality_pairing(self, prec=prec)
|
||||
return coordinates
|
||||
|
||||
def expansion_at_infty(self, place = 0, prec=10):
|
||||
C = self.curve
|
||||
|
||||
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Reference in New Issue
Block a user