From 22872e266bfbcb6a3801bc25927a8be14c12e4de Mon Sep 17 00:00:00 2001 From: jgarnek Date: Fri, 24 Feb 2023 12:51:49 +0000 Subject: [PATCH] rozniczkowanie form drw zrobione (?) --- sage/.run.term-0.term | 1221 ++++++++++++++++- sage/drafty/draft.sage | 12 +- sage/drafty/second_patch.sage | 30 + sage/drafty/superelliptic_drw.sage | 259 +++- .../superelliptic_form_class.sage | 8 + .../superelliptic_function_class.sage | 5 + 6 files changed, 1466 insertions(+), 69 deletions(-) create mode 100644 sage/drafty/second_patch.sage diff --git a/sage/.run.term-0.term b/sage/.run.term-0.term index d659c25..ef85aec 100644 --- a/sage/.run.term-0.term +++ b/sage/.run.term-0.term @@ -38646,4 +38646,1223 @@ Untracked files: no changes added to commit (use "git add" and/or "git commit -a") ]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ add sage/drafty/addgit add sage/drafty/superelliptic_drw.sage sage/drafty/superelliptic/decomposition_into_g0_g8.sage -]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ g \ 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 "superelliptic de rham witt - poczatek" +[master 856d742] superelliptic de rham witt - poczatek + 12 files changed, 12077 insertions(+), 105 deletions(-) + rewrite sage/drafty/draft.sage (91%) + create mode 100644 sage/drafty/superelliptic_drw.sage + create mode 100644 sage/superelliptic/decomposition_into_g0_g8.sage +]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: 31, done. +Counting objects: 3% (1/31) Counting objects: 6% (2/31) Counting objects: 9% (3/31) Counting objects: 12% (4/31) Counting objects: 16% (5/31) Counting objects: 19% (6/31) Counting objects: 22% (7/31) Counting objects: 25% (8/31) Counting objects: 29% (9/31) Counting objects: 32% (10/31) Counting objects: 35% (11/31) Counting objects: 38% (12/31) Counting objects: 41% (13/31) Counting objects: 45% (14/31) Counting objects: 48% (15/31) Counting objects: 51% (16/31) Counting objects: 54% (17/31) Counting objects: 58% (18/31) Counting objects: 61% (19/31) Counting objects: 64% (20/31) Counting objects: 67% (21/31) Counting objects: 70% (22/31) Counting objects: 74% (23/31) Counting objects: 77% (24/31) Counting objects: 80% (25/31) Counting objects: 83% (26/31) Counting objects: 87% (27/31) Counting objects: 90% (28/31) Counting objects: 93% (29/31) Counting objects: 96% (30/31) Counting objects: 100% (31/31) Counting objects: 100% (31/31), done. +Delta compression using up to 4 threads +Compressing objects: 5% (1/18) Compressing objects: 11% (2/18) Compressing objects: 16% (3/18) Compressing objects: 22% (4/18) Compressing objects: 27% (5/18) Compressing objects: 33% (6/18) Compressing objects: 38% (7/18) Compressing objects: 44% (8/18) Compressing objects: 50% (9/18) Compressing objects: 55% (10/18) Compressing objects: 61% (11/18) Compressing objects: 66% (12/18) Compressing objects: 72% (13/18) Compressing objects: 77% (14/18) Compressing objects: 83% (15/18) Compressing objects: 88% (16/18) Compressing objects: 94% (17/18) Compressing objects: 100% (18/18) Compressing objects: 100% (18/18), done. +Writing objects: 5% (1/18) Writing objects: 11% (2/18) Writing objects: 16% (3/18) Writing objects: 22% (4/18) Writing objects: 27% (5/18) Writing objects: 33% (6/18) Writing objects: 38% (7/18) Writing objects: 44% (8/18) Writing objects: 50% (9/18) Writing objects: 55% (10/18) Writing objects: 61% (11/18) Writing objects: 66% (12/18) Writing objects: 72% (13/18) Writing objects: 77% (14/18) Writing objects: 83% (15/18) Writing objects: 88% (16/18) Writing objects: 94% (17/18) Writing objects: 100% (18/18) Writing objects: 100% (18/18), 91.43 KiB | 1.63 MiB/s, done. +Total 18 (delta 8), reused 0 (delta 0) +remote: . Processing 1 references +remote: Processed 1 references in total +To https://git.wmi.amu.edu.pl/jgarnek/DeRhamComputation.git + f683017..856d742 master -> master +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: 2021 De Rham/DeRhamComputation[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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--------------------------------------------------------------------------- +OSError Traceback (most recent call last) +Input In [1], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:244, in load(filename, globals, attach) + 242 break + 243 else: +--> 244 raise IOError('did not find file %r to load or attach' % filename) + 246 ext = os.path.splitext(fpath)[1].lower() + 247 if ext == '.py': + +OSError: did not find file 'init.sage' to load or attach +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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~/Research/2021 De Rham/DeRhamComputation$ cd sage/ +]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.genus()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.genus()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.expansion_at_infty()[1][?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lv[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.curve() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [3], in () +----> 1 C.x.curve() + +TypeError: 'superelliptic' object is not callable +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.curve()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: C.x.curve +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbbb[0].cartier().coordinates()[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lbin[?7h[?12l[?25h[?25l[?7lbino[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: binomial + binomial  + binomial_coefficients + + + [?7h[?12l[?25h[?25l[?7l + binomial  + + [?7h[?12l[?25h[?25l[?7l + + +[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l4[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: binomial(4, 2) +[?7h[?12l[?25h[?2004l[?7h6 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lstr(f).replace("x", "[x]")[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7lrw_form[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lon[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l,[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: superelliptic_drw_form(C.one, 0, 0) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [2], in () +----> 1 superelliptic_drw_form(C.one, Integer(0), Integer(0)) + +TypeError: superelliptic_drw_form.__init__() missing 1 required positional argument: 'h' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsage: superelliptic_drw_form(C.one, 0, 0) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [3], in () +----> 1 superelliptic_drw_form(C.one, Integer(0), Integer(0)) + +TypeError: superelliptic_drw_form.__init__() missing 1 required positional argument: 'h' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lbinomial(4, 2)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsage: superelliptic_drw_form(C.one, 0, 0) +[?7h[?12l[?25h[?2004l[?7h[1] d[x] + V(0) + dV([0]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx+1[?7h[?12l[?25h[?25l[?7lsage: x +[?7h[?12l[?25h[?2004l[?7hx +[?2004h[?25l[?7lsage: [?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[?7lx[?7h[?12l[?25h[?25l[?7lsage: x - x +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx - 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[?7l0[?7h[?12l[?25h[?25l[?7lsage: x - x == 0 +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTraceback (most recent call last): + + File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code + exec(code_obj, self.user_global_ns, self.user_ns) + + Input In [9] in  + load('init.sage') + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :26 in  + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :83 + if result ="": + ^ +SyntaxError: invalid syntax. Maybe you meant '==' or ':=' instead of '='? + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lx - x == 0[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsage: superelliptic_drw_form(C.one, 0, 0) +[?7h[?12l[?25h[?2004l[?7h) failed: AttributeError: 'sage.rings.integer.Integer' object has no attribute 'form'> +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*, 0)[?7h[?12l[?25h[?25l[?7lC, 0)[?7h[?12l[?25h[?25l[?7l., 0)[?7h[?12l[?25h[?25l[?7ld, 0)[?7h[?12l[?25h[?25l[?7lx, 0)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?7lC)[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7lx)[?7h[?12l[?25h[?25l[?7lsage: superelliptic_drw_form(C.one, 0*C.dx, 0*C.x) +[?7h[?12l[?25h[?2004l[?7h[1] d[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2+2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupere[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuper[?7h[?12l[?25h[?25l[?7lsupe[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lasupereliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l supereliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l=supereliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l supereliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0, 0) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbinomial(4, 2)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: b = a+b +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [14], in () +----> 1 b = a+b + +NameError: name 'b' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+b[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: b = a+a +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [15], in () +----> 1 b = a+a + +File :106, in __add__(self, other) + +File :27, in __add__(self, other) + +TypeError: superelliptic_witt.__init__() takes 3 positional arguments but 4 were given +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsuperelliptic_drwform(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0, 0) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.curve[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [19], in () +----> 1 a+a + +File :106, in __add__(self, other) + +File :95, in __rmul__(self, other) + +NameError: name 'f0' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la+[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0, 0) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0, 0)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l*, 0)[?7h[?12l[?25h[?25l[?7lC, 0)[?7h[?12l[?25h[?25l[?7l., 0)[?7h[?12l[?25h[?25l[?7ld, 0)[?7h[?12l[?25h[?25l[?7lx, 0)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l*)[?7h[?12l[?25h[?25l[?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[?7lsage: a = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0)[?7h[?12l[?25h[?25l[?7l*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+a[?7h[?12l[?25h[?25l[?7lsage: b = a+a +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [23], in () +----> 1 b = a+a + +File :106, in __add__(self, other) + +File :95, in __rmul__(self, other) + +NameError: name 'h0' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l, 0)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lsage: b = a+a +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [26], in () +----> 1 b = a+a + +File :107, in __add__(self, other) + +File :105, in __add__(self, other) + +File :38, in __add__(self, other) + +AttributeError: 'superelliptic_form' object has no attribute 'function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lsage: b = a+a +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lsage: b +[?7h[?12l[?25h[?2004l[?7h[1] d[x]V(x dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = a+a[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[x^5 + x^4 + z0*z1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = a+a[?7h[?12l[?25h[?25l[?7lasuperelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lsage: a = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = a+a[?7h[?12l[?25h[?25l[?7lsage: b = a+a +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = a+a[?7h[?12l[?25h[?25l[?7lsage: b +[?7h[?12l[?25h[?2004l[?7h[1] d[x] + V(x dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l = a+a[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: b = b+a +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = b+a[?7h[?12l[?25h[?25l[?7lsage: b +[?7h[?12l[?25h[?2004l[?7h[1] d[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = b+a[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lb+a[?7h[?12l[?25h[?25l[?7lsage: b = b+a +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = b+a[?7h[?12l[?25h[?25l[?7lsage: b +[?7h[?12l[?25h[?2004l[?7h[1] d[x] + V(x dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x over Finite Field of size 2 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l = superelliptic(x^4 + x, 2)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^1 = x^3 + 2*x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1] d[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1] d[x] + V((-x^2) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l[1] d[x] + V((-x^2) 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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h[1] d[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a+a +[?7h[?12l[?25h[?2004l[?7hV((x^2) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lhelp(second_patch)[?7h[?12l[?25h[?25l[?7l = yy*v^2 - yy^2*v[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: h = x/x +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lg.change_ring(Integers(9))[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lh = x/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[?7l1[?7h[?12l[?25h[?25l[?7lsage: h == 1 +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lpatch(C)[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lrent(g)[?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 of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx - x == 0[?7h[?12l[?25h[?25l[?7l+1[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7lsage: x+y +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [51], in () +----> 1 x+y + +NameError: name 'y' 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[?2004l0 +[?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[?7lx[?7h[?12l[?25h[?25l[?7lsage: -C.x +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [53], in () +----> 1 -C.x + +TypeError: superelliptic_function.__neg__() missing 1 required positional argument: 'other' +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l-C.x[?7h[?12l[?25h[?25l[?7lsage: -C.x +[?7h[?12l[?25h[?2004l[?7h2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-C.x[?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: -C.dx +[?7h[?12l[?25h[?2004l[?7h(-1) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTraceback (most recent call last): + + File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code + exec(code_obj, self.user_global_ns, self.user_ns) + + Input In [1] in  + load('init.sage') + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :26 in  + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :43 + ????? + ^ +SyntaxError: invalid syntax + +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la+a+a[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h[1] d[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2+2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 2*a +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [4], in () +----> 1 Integer(2)*a + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :108, in __rmul__(self, other) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.integer.Integer' object has no attribute 't' +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.curve[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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: C.x.teichmuller() +[?7h[?12l[?25h[?2004l[?7h[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004lTraceback (most recent call last): + + File /ext/sage/9.7/local/var/lib/sage/venv-python3.10.5/lib/python3.10/site-packages/IPython/core/interactiveshell.py:3398 in run_code + exec(code_obj, self.user_global_ns, self.user_ns) + + Input In [7] in  + load('init.sage') + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :26 in  + + File sage/misc/persist.pyx:175 in sage.misc.persist.load + sage.repl.load.load(filename, globals()) + + File /ext/sage/9.7/src/sage/repl/load.py:272 in load + exec(preparse_file(f.read()) + "\n", globals) + + File :75 + dy = [f(x)]'/2*y dx + ^ +SyntaxError: unterminated string literal (detected at line 75) + +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lteichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h[1] d[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*a[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 2*a +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*a[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 2*a +[?7h[?12l[?25h[?2004l[?7h[2] d[x] + V((x^2) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l3^4[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 3*a +[?7h[?12l[?25h[?2004l[?7hV((x^2) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: 9*a +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-C.dx[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: -3*a +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [15], in () +----> 1 -Integer(3)*a + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :127, in __rmul__(self, other) + +TypeError: bad operand type for unary -: 'superelliptic_drw_form' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-3*a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-3*a[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()*a[?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: (-3)*a +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [16], in () +----> 1 (-Integer(3))*a + +File /ext/sage/9.7/src/sage/rings/integer.pyx:1964, in sage.rings.integer.Integer.__mul__() + 1962 return y + 1963 +-> 1964 return coercion_model.bin_op(left, right, operator.mul) + 1965 + 1966 cpdef _mul_(self, right): + +File /ext/sage/9.7/src/sage/structure/coerce.pyx:1242, in sage.structure.coerce.CoercionModel.bin_op() + 1240 mul_method = getattr(y, '__r%s__'%op_name, None) + 1241 if mul_method is not None: +-> 1242 res = mul_method(x) + 1243 if res is not None and res is not NotImplemented: + 1244 return res + +File :127, in __rmul__(self, other) + +TypeError: bad operand type for unary -: 'superelliptic_drw_form' +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-3*a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: -a +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [18], in () +----> 1 -a + +TypeError: superelliptic_drw_form.__neg__() missing 1 required positional argument: 'other' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-a[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l-a[?7h[?12l[?25h[?25l[?7lsage: -a +[?7h[?12l[?25h[?2004l[?7h[2] d[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = x^3 + 2*x - 1[?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[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: f = x^5 - x^4 + 2*x +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf = x^5 - x^4 + 2*x[?7h[?12l[?25h[?25l[?7lsage: f +[?7h[?12l[?25h[?2004l[?7hx^5 + 2*x^4 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lparent(x)[?7h[?12l[?25h[?25l[?7la[?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[?7lf[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: parent(f) +[?7h[?12l[?25h[?2004l[?7hUnivariate Polynomial Ring in x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l.valuation()[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l()[][?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lMf.monomials()[0][?7h[?12l[?25h[?25l[?7l f.monomials()[0][?7h[?12l[?25h[?25l[?7l=f.monomials()[0][?7h[?12l[?25h[?25l[?7l f.monomials()[0][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M = f.monomials()[0] +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM = f.monomials()[0][?7h[?12l[?25h[?25l[?7lsage: M +[?7h[?12l[?25h[?2004l[?7hx^5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lM[?7h[?12l[?25h[?25l[?7l.determinant()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: M. + M.abs M.all_roots_in_interval M.base_ring M.change_variable_name M.compose_trunc  + M.adams_operator M.any_root M.cartesian_product M.coefficients M.composed_op  + M.add_bigoh M.args M.category M.complex_roots M.constant_coefficient > + M.additive_order M.base_extend M.change_ring M.compose_power M.content_ideal  + [?7h[?12l[?25h[?25l[?7labs + M.abs  + + + + [?7h[?12l[?25h[?25l[?7lll_roots_in_interval + M.abs  M.all_roots_in_interval [?7h[?12l[?25h[?25l[?7lbase_ring + M.all_roots_in_interval  M.base_ring [?7h[?12l[?25h[?25l[?7lchange_variable_name + M.base_ring  M.change_variable_name [?7h[?12l[?25h[?25l[?7lompose_tunc + M.change_variable_name  M.compose_trunc [?7h[?12l[?25h[?25l[?7lycltomic_part + ll_roots_in_intervalbase_ring change_variable_nameompose_tunc ycltomic_part + ny_rot cartesian_productoefficients mposed_op degree  +<rgs categoryomplex_rootsnstant_cefficientdeomiator  + base_extend chang_rigompose_powerntentidealderivaive [?7h[?12l[?25h[?25l[?7ldit +base_ring change_variable_nameompose_tunc ycltomic_partdit  +cartesian_productoefficients mposed_op degree iff  +categoryomplex_rootsnstant_cefficientdeomiator iffereniate +chang_rigompose_powerntentidealderivaive iscrimnant[?7h[?12l[?25h[?25l[?7lspersion +change_variable_nameompose_tunc ycltomic_partdit spersion +oefficients mposed_op degree iff spersion_set +omplex_rootsnstant_cefficientdeomiator iffereniatevides  +ompose_powerntentidealderivaive iscrimnantump [?7h[?12l[?25h[?25l[?7lums +ompose_tunc ycltomic_partdit spersionums  +mposed_op degree iff spersion_seteuclidean_degree +nstant_cefficientdeomiator iffereniatevides exponnts +ntentidealderivaive iscrimnantump factor[?7h[?12l[?25h[?25l[?7leclidean_degree + M.dumps  + M.euclidean_degree [?7h[?12l[?25h[?25l[?7lxponents + + M.euclidean_degree  + M.exponents [?7h[?12l[?25h[?25l[?7lfactor + + + M.exponents  + M.factor [?7h[?12l[?25h[?25l[?7lexponents + + + M.exponents  + M.factor [?7h[?12l[?25h[?25l[?7l + + + + +[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: M.exponents() +[?7h[?12l[?25h[?2004l[?7h[5] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + + [?7h[?12l[?25h[?25l[?7lM.exponents()[?7h[?12l[?25h[?25l[?7l()[[?7h[?12l[?25h[?25l[?7l0[?7h[?12l[?25h[?25l[?7l[][?7h[?12l[?25h[?25l[?7lsage: M.exponents()[0] +[?7h[?12l[?25h[?2004l[?7h5 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7h[1] d[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = b+a[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(.teichmuler()[?7h[?12l[?25h[?25l[?7l().teichmuler()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7lC).teichmuler()[?7h[?12l[?25h[?25l[?7l.).teichmuler()[?7h[?12l[?25h[?25l[?7lx).teichmuler()[?7h[?12l[?25h[?25l[?7l^).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lx).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(()).teichmuler()[?7h[?12l[?25h[?25l[?7l^).teichmuler()[?7h[?12l[?25h[?25l[?7l3).teichmuler()[?7h[?12l[?25h[?25l[?7l ).teichmuler()[?7h[?12l[?25h[?25l[?7l+).teichmuler()[?7h[?12l[?25h[?25l[?7l ).teichmuler()[?7h[?12l[?25h[?25l[?7l(().teichmuler()[?7h[?12l[?25h[?25l[?7lC).teichmuler()[?7h[?12l[?25h[?25l[?7l.).teichmuler()[?7h[?12l[?25h[?25l[?7lx).teichmuler()[?7h[?12l[?25h[?25l[?7l(()).teichmuler()[?7h[?12l[?25h[?25l[?7l^).teichmuler()[?7h[?12l[?25h[?25l[?7l2).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 + (C.x)^2).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lsage: auxilliar + auxilliaries/  + auxilliary_derivative + + + [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lies/ + auxilliaries/  + + [?7h[?12l[?25h[?25l[?7ly_derivative + auxilliaries/  + auxilliary_derivative[?7h[?12l[?25h[?25l[?7l + + +[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [31], in () +----> 1 auxilliary_derivative(b) + +File :92, in auxilliary_derivative(P) + +TypeError: unsupported operand type(s) for -: 'superelliptic_witt' and 'superelliptic_witt' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?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[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 + (C.x)^2).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [34], in () +----> 1 auxilliary_derivative(b) + +File :97, in auxilliary_derivative(P) + +NameError: name 'superelliptic_drw' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 + (C.x)^2).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 + (C.x)^2).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7llliary_derivative(b)[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [38], in () +----> 1 auxilliary_derivative(b) + +File :97, in auxilliary_derivative(P) + +File :175, in __add__(self, other) + +TypeError: unsupported operand type(s) for +: 'PolynomialRing_field_with_category.element_class' and 'superelliptic_function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 + (C.x)^2).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [41], in () +----> 1 auxilliary_derivative(b) + +File :97, in auxilliary_derivative(P) + +File :132, in __repr__(self) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:356, in sage.cpython.getattr.getattr_from_other_class() + 354 dummy_error_message.cls = type(self) + 355 dummy_error_message.name = name +--> 356 raise AttributeError(dummy_error_message) + 357 cdef PyObject* attr = instance_getattr(cls, name) + 358 if attr is NULL: + +AttributeError: 'PolynomialRing_field_with_category.element_class' object has no attribute 'function' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 + (C.x)^2).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) +[?7h[?12l[?25h[?2004l0 +[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller()[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 + (C.x)^2).teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?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)^2).teichmuler()[?7h[?12l[?25h[?25l[?7l- (C.x)^2).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?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.teichmuler()[?7h[?12l[?25h[?25l[?7l.teichmuler()[?7h[?12l[?25h[?25l[?7l().teichmuler()[?7h[?12l[?25h[?25l[?7l(()).teichmuler()[?7h[?12l[?25h[?25l[?7l()()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 - (C.x)).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7llliary_derivative(b)[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) +[?7h[?12l[?25h[?2004l0 +[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lb = ((C.x)^3 - (C.x)).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: b = ((C.x)^3 - (C.x)).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(b) +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ ]0;~/Research/2021 De Rham/DeRhamComputation/sage~/Research/2021 De Rham/DeRhamComputation/sage$ sage +┌────────────────────────────────────────────────────────────────────┐ +│ SageMath version 9.7, Release Date: 2022-09-19 │ +│ Using Python 3.10.5. Type "help()" for help. │ +└────────────────────────────────────────────────────────────────────┘ +]0;IPython: DeRhamComputation/sage[?2004h[?1l[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.teichmuller()[?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[?7lauxilliary_derivative(b)[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7llliary_derivative(b)[?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[?7lt)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7li)[?7h[?12l[?25h[?25l[?7lc)[?7h[?12l[?25h[?25l[?7lh)[?7h[?12l[?25h[?25l[?7lm)[?7h[?12l[?25h[?25l[?7lu)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7ll)[?7h[?12l[?25h[?25l[?7le)[?7h[?12l[?25h[?25l[?7lr)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(C.x.teichmuller()) +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(C.x.teichmuller())[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(C.x.teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(C.x.teichmuller()) +[?7h[?12l[?25h[?2004lx 1 +0 +[?7h0 +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(C.x.teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(C.x.teichmuller()) +[?7h[?12l[?25h[?2004lx 1 +0 [1] d[x] +[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.teichmuller()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lbC.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7l=C.x.function[?7h[?12l[?25h[?25l[?7l C.x.function[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage: b = C.x.function +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = C.x.function[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7lsage: b.monomials()\ +[?7h[?12l[?25h[?2004l[?7h[1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.monomials()\[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b.monomials() +[?7h[?12l[?25h[?2004l[?7h[1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb.monomials()[?7h[?12l[?25h[?25l[?7lsage: b +[?7h[?12l[?25h[?2004l[?7hx +[?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[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l.monomials()[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7l = C.x.function[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(C.x.teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative(C.x.teichmuller()) +[?7h[?12l[?25h[?2004l1 x +1 [1] d[x] +[?7h[1] d[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative(C.x.teichmuller())[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7lxilliary_derivative(C.x.teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?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.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().teichmuler()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l^).teichmuler()[?7h[?12l[?25h[?25l[?7l3).teichmuler()[?7h[?12l[?25h[?25l[?7l ).teichmuler()[?7h[?12l[?25h[?25l[?7l-).teichmuler()[?7h[?12l[?25h[?25l[?7l ).teichmuler()[?7h[?12l[?25h[?25l[?7lC).teichmuler()[?7h[?12l[?25h[?25l[?7l.).teichmuler()[?7h[?12l[?25h[?25l[?7lx).teichmuler()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: auxilliary_derivative((C.x^3 - C.x).teichmuller()) +[?7h[?12l[?25h[?2004l1 x^3 +3 V((x^8) dx) +2 x +1 [2] d[x] +[?7h[2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lC.x.teichmuller())[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((C.x^3 - C.x).teichmuller()) +[?7h[?12l[?25h[?2004l1 x^3 +2 x +[?7h[2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((C.x^3 - C.x).teichmuller()) +[?7h[?12l[?25h[?2004l[?7h[2] d[x] + V((x^8) dx) + dV([2*x^7 + x^5]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lsage: C +[?7h[?12l[?25h[?2004l[?7hSuperelliptic curve with the equation y^2 = x^3 + 2*x over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3 - C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: auxilliary_derivative((C.x^3).teichmuller()) +[?7h[?12l[?25h[?2004l[?7hV((x^8) dx) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((C.x^3).teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l).teichmuler()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: auxilliary_derivative((-C.x).teichmuller()) +[?7h[?12l[?25h[?2004l[?7h[2] d[x] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l(())[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l()-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(()-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l()-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l(-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7lauxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l-auxiliary_derivative(C.x).teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: -auxilliary_derivative((C.x).teichmuller()) +[?7h[?12l[?25h[?2004l[?7h[2] d[x] +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l-auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lauxiliary_derivative((-) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) +[?7h[?12l[?25h[?2004leq1 True +try +[?7hFalse +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) +[?7h[?12l[?25h[?2004leq1 True +try +[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-3)*a[?7h[?12l[?25h[?25l[?7l0[?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[?7lp[?7h[?12l[?25h[?25l[?7l[?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[?7l()[?7h[?12l[?25h[?25l[?7lsage: (0*C.x).pth_root() +[?7h[?12l[?25h[?2004l[?7h0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(0*C.x).pth_root()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(0*C.x).pth_root()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) +[?7h[?12l[?25h[?2004leq1 True +0 +try +[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lteichmuller(C.x + 2*C.y)[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ltry[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7lsage: try: +....: [?7h[?12l[?25h[?25l[?7lprint(b.cartier())[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?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[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lrint(b.cartier())[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l"[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(b.cartier())[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l....:  print('a') +....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l() + [?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lexcept[?7h[?12l[?25h[?25l[?7l:[?7h[?12l[?25h[?25l[?7l....: except: +....: [?7h[?12l[?25h[?25l[?7l....:  +....: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lprint(b.cartier())[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lprint[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l'[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() +....: [?7h[?12l[?25h[?25l[?7lsage: try: +....:  print('a') +....: except: +....:  print('b') +....:  +[?7h[?12l[?25h[?2004la +[?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[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: try: +....:  print('a') +....: except: +....:  print('b')[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) +  +  + [?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) +[?7h[?12l[?25h[?2004leq1 True +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [32], in () +----> 1 auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) + +File :115, in __eq__(self, other) + +AttributeError: 'superelliptic_function' object has no attribute 'pthroot' +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7lsage: auxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller()) +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.x.teichmuller()[?7h[?12l[?25h[?25l[?7ly*v*(v - C.y)[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lchmuller[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller() +[?7h[?12l[?25h[?2004l[?7h[y] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lauxilliary_derivative((-C.x).teichmuller()) == -auxilliary_derivative((C.x).teichmuller())[?7h[?12l[?25h[?25l[?7l = supeelliptic_drw_form(Cone, 0*C.dx, 0*C.x)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC.dx[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lsage: a = C.dx + C.a_number C.basis_of_cohomology C.degrees_de_rham0 C.dx C.frobenius_matrix  + C.base_ring C.cartier_matrix C.degrees_de_rham1 C.exponent C.genus  + C.basis_de_rham_degrees C.characteristic C.degrees_holomorphic_differentials C.fct_field C.holomorphic_differentials_basis > + C.basis_holomorphic_differentials_degree C.de_rham_basis C.dr_frobenius_matrix C.final_type C.is_smooth  + [?7h[?12l[?25h[?25l[?7ly + + + +[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lchmuller[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = C.y.teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lsage:  + + + + [?7h[?12l[?25h[?25l[?7la = C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l+a+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a +[?7h[?12l[?25h[?2004l[?7h) failed: NameError: name 'f1' is not defined> +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7lsage:  + + [?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la+[?7h[?12l[?25h[?25l[?7l = C.y.teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a = C.y.teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l+a[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7lsage: a+a +[?7h[?12l[?25h[?2004l[?7h[2*y] + V((x^3 + 2*x)*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l11/3-4[?7h[?12l[?25h[?25l[?7l/[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7lQ[?7h[?12l[?25h[?25l[?7lsage: 1/2 in QQ +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lI[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lg[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l3[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l5[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()([?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()^[?7h[?12l[?25h[?25l[?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[?7li[?7h[?12l[?25h[?25l[?7lin[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7lZ[?7h[?12l[?25h[?25l[?7lsage: Integers(25)(2)^(-1) in ZZ +[?7h[?12l[?25h[?2004l[?7hTrue +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l.teichmuller()[?7h[?12l[?25h[?25l[?7l()*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7lle[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.x.teichmuller()*C.y.teichmuller() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [44], in () +----> 1 C.x.teichmuller()*C.y.teichmuller() + +TypeError: unsupported operand type(s) for *: 'superelliptic_witt' and 'superelliptic_witt' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x.teichmuller()*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?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.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.y.teichmuler()[?7h[?12l[?25h[?25l[?7lsage: 2*C.y.teichmuller() +[?7h[?12l[?25h[?2004l[?7h[2*y] + V((x^3 + 2*x)*y) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l-[?7h[?12l[?25h[?25l[?7l7[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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: 2*C.y.teichmuller() == -7*C.y.teichmuller() +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.y.teichmuller() == -7*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.teichmuler()[?7h[?12l[?25h[?25l[?7lx.teichmuler()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller() +[?7h[?12l[?25h[?2004l[?7h[2*x] + V(x^3) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7ly() == -7*C.y.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.teichmuler()[?7h[?12l[?25h[?25l[?7lx.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.teichmuler() = -7*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7lx.teichmuler() = -7*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller() == -7*C.x.teichmuller() +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller() == -7*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l -7*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l -7*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l+ -7*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(-7*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l_*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l()*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller() + (-7)*C.x.teichmuller() +[?7h[?12l[?25h[?2004l[?7h[x] + V(x^3) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller() + (-7)*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?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: 2*C.x.teichmuller() +[?7h[?12l[?25h[?2004l[?7h[2*x] + V(x^3) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9*a[?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[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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: 9*C.x.teichmuller() +[?7h[?12l[?25h[?2004l[?7h[0] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l9*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l() + (-7)*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l (-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l()(-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l(), (-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller(), (-7)*C.x.teichmuller() +[?7h[?12l[?25h[?2004l[?7h([2*x] + V(x^3), [2*x] + V(x^3)) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller(), (-7)*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l() (-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l() (-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l= (-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7l= (-7)*C.x.teichmuler()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller() == (-7)*C.x.teichmuller() +[?7h[?12l[?25h[?2004l[?7hFalse +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l2*C.x.teichmuller() == (-7)*C.x.teichmuller()[?7h[?12l[?25h[?25l[?7lsage: 2*C.x.teichmuller() == (-7)*C.x.teichmuller() +[?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[?7lad('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [56], in () +----> 1 load('init.sage') + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :27, in  + +File /ext/sage/9.7/src/sage/misc/persist.pyx:175, in sage.misc.persist.load() + 173 + 174 if sage.repl.load.is_loadable_filename(filename): +--> 175 sage.repl.load.load(filename, globals()) + 176 return + 177 + +File /ext/sage/9.7/src/sage/repl/load.py:272, in load(filename, globals, attach) + 270 add_attached_file(fpath) + 271 with open(fpath) as f: +--> 272 exec(preparse_file(f.read()) + "\n", globals) + 273 elif ext == '.spyx' or ext == '.pyx': + 274 if attach: + +File :9, in  + +File :203, in __add__(self, other) + +File :54, in __mul__(self, other) + +AttributeError: 'superelliptic_drw_form' object has no attribute 't' +[?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 +[?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 +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldenominator(((C.y)^(-1)*C.dx).form) == y[?7h[?12l[?25h[?25l[?7limension_of_RHS = p*gY + (len(list_of_m) - 1)*(p-1) + sum(sum(i*alpha(i, m, p) for i in range(1, p)) for m in list_of_m)[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?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: diffn(C.y.teichmuller)\ +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [60], in () +----> 1 diffn(C.y.teichmuller) + +NameError: name 'diffn' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn(C.y.teichmuller)\[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?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: diffn(C.y.teichmuller()) +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [61], in () +----> 1 diffn(C.y.teichmuller()) + +NameError: name 'diffn' is not defined +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ldiffn(C.y.teichmuller())[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l(()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()[?7h[?12l[?25h[?25l[?7lC.y.teichmuler()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [62], in () +----> 1 C.y.teichmuller().diffn() + +File :86, in diffn(self) + +File :122, in auxilliary_derivative(P) + +File /ext/sage/9.7/src/sage/structure/element.pyx:494, in sage.structure.element.Element.__getattr__() + 492 AttributeError: 'LeftZeroSemigroup_with_category.element_class' object has no attribute 'blah_blah' + 493 """ +--> 494 return self.getattr_from_category(name) + 495 + 496 cdef getattr_from_category(self, name): + +File /ext/sage/9.7/src/sage/structure/element.pyx:507, in sage.structure.element.Element.getattr_from_category() + 505 else: + 506 cls = P._abstract_element_class +--> 507 return getattr_from_other_class(self, cls, name) + 508 + 509 def __dir__(self): + +File /ext/sage/9.7/src/sage/cpython/getattr.pyx:361, in sage.cpython.getattr.getattr_from_other_class() + 359 dummy_error_message.cls = type(self) + 360 dummy_error_message.name = name +--> 361 raise AttributeError(dummy_error_message) + 362 attribute = attr + 363 # Check for a descriptor (__get__ in Python) + +AttributeError: 'sage.rings.polynomial.polynomial_zmod_flint.Polynomial_zmod_flint' object has no attribute 't' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx*C.y.teichmuller()[?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[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lsage: C.x^3 - C.x +[?7h[?12l[?25h[?2004l[?7hx^3 + 2*x +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.x^3 - C.x[?7h[?12l[?25h[?25l[?7ly.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7ldiffn(C.y.teichmuller())[?7h[?12l[?25h[?25l[?7l()\[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lC.x^3 - C.x[?7h[?12l[?25h[?25l[?7ly.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: C.y.teichmuller().diffn() +[?7h[?12l[?25h[?2004l[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx^3 - 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(C.x[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y)[?7h[?12l[?25h[?25l[?7l*C.y)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)^(-1)*C.dx[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la(C.x*C.y)[?7h[?12l[?25h[?25l[?7l (C.x*C.y)[?7h[?12l[?25h[?25l[?7l=(C.x*C.y)[?7h[?12l[?25h[?25l[?7l (C.x*C.y)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l.)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).function() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).function()[?7h[?12l[?25h[?25l[?7lsage: a +[?7h[?12l[?25h[?2004l[?7hx*y +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.lift()[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7lp[?7h[?12l[?25h[?25l[?7lonents[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.exponents() +[?7h[?12l[?25h[?2004l[?7h[1] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.exponents()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lR. = PolynomialRing(GF(3))[?7h[?12l[?25h[?25l[?7lx. = PolynomialRing(GF(4)[?7h[?12l[?25h[?25l[?7ly. = PlynomalRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7l. = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7lsage: Rxy. = PolynomialRing(GF(3), 2) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.exponents()[?7h[?12l[?25h[?25l[?7l = (C.x*C.y.function()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lR(2)[?7h[?12l[?25h[?25l[?7lxyz(1)[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = Rxy(a) +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = Rxy(a)[?7h[?12l[?25h[?25l[?7lRxy.<, y> = PolynomialRing(GF(3), 2)[?7h[?12l[?25h[?25l[?7la.exponents()[?7h[?12l[?25h[?25l[?7lsage: a.exponents() +[?7h[?12l[?25h[?2004l[?7h[(1, 1)] +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.exponents()[?7h[?12l[?25h[?25l[?7l = Rxy(a)[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l [?7h[?12l[?25h[?25l[?7lC..teichmuller()[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l).function()[?7h[?12l[?25h[?25l[?7l).function()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l().function()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7l.exponents([?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [74], in () +----> 1 a.diffn() + +File :93, in diffn(self) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:6094, in sage.rings.polynomial.polynomial_element.Polynomial.monomial_coefficient() + 6092 """ + 6093 if not m.parent() is self._parent: +-> 6094 raise TypeError("monomial must have same parent as self.") + 6095 + 6096 d = m.degree() + +TypeError: monomial must have same parent as self. +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7l = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [77], in () +----> 1 a.diffn() + +File :94, in diffn(self) + +File /ext/sage/9.7/src/sage/rings/polynomial/polynomial_element.pyx:6094, in sage.rings.polynomial.polynomial_element.Polynomial.monomial_coefficient() + 6092 """ + 6093 if not m.parent() is self._parent: +-> 6094 raise TypeError("monomial must have same parent as self.") + 6095 + 6096 d = m.degree() + +TypeError: monomial must have same parent as self. +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7l = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +NameError Traceback (most recent call last) +Input In [82], in () +----> 1 a.diffn() + +File :96, in diffn(self) + +NameError: name 'P' 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[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7l = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +IndexError Traceback (most recent call last) +Input In [85], in () +----> 1 a.diffn() + +File :98, in diffn(self) + +IndexError: list index out of range +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7l = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +TypeError Traceback (most recent call last) +Input In [88], in () +----> 1 a.diffn() + +File :99, in diffn(self) + +File :79, in diffn(self) + +TypeError: superelliptic_form.__init__() takes 3 positional arguments but 4 were given +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7la.diffn()[?7h[?12l[?25h[?25l[?7l = (C.x*C.y).teichmuller()[?7h[?12l[?25h[?25l[?7l();[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a = (C.x*C.y).teichmuller(); a.diffn() +[?7h[?12l[?25h[?2004l[?7h[y + 1] d[x] + V(((-x^8*y - x^5*y - x^5 + x^3*y + x^3 - x^2*y)/y) dx) + dV([x^7 + 2*x^5]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7l = C.x.function[?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[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l_[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l+[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7lt[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lc[?7h[?12l[?25h[?25l[?7lh[?7h[?12l[?25h[?25l[?7lm[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7ll[?7h[?12l[?25h[?25l[?7le[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: b = C.x.teichmuller().diffn() + C.y.teichmuller().diffn() +[?7h[?12l[?25h[?2004l[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la = (C.x*C.y).teichmuller(); a.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[?7lb[?7h[?12l[?25h[?25l[?7lsage: a == b +[?7h[?12l[?25h[?2004l--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +Input In [93], in () +----> 1 a == b + +File :69, in __eq__(self, other) + +AttributeError: 'superelliptic_drw_form' object has no attribute 't' +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la == b[?7h[?12l[?25h[?25l[?7l.diffn()[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb[?7h[?12l[?25h[?25l[?7lsage: a.diffn() == b +[?7h[?12l[?25h[?2004l[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7la.diffn() == b[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: a.diffn() +[?7h[?12l[?25h[?2004l[?7h[y + 1] d[x] + V(((-x^8*y - x^5*y - x^5 + x^3*y + x^3 - x^2*y)/y) dx) + dV([x^7 + 2*x^5]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lb = C.x.teichmuller().diffn() + C.y.teichmuller().diffn()[?7h[?12l[?25h[?25l[?7lsage: b +[?7h[?12l[?25h[?2004l[?7h[(x + 1)/x] d[x] + V(((-x^6 + x^4 + x^2 - x - 1)/x) dx) + dV([x^4 + 2*x^2]) +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y.teichmuller().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(C.[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lx/C.y).expansion_at_infty()[?7h[?12l[?25h[?25l[?7lx[?7h[?12l[?25h[?25l[?7l*^(-1)*C.dx[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.x*C.y).diffn() +[?7h[?12l[?25h[?2004l[?7h(x^3/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.x*C.y).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7lC.y).difn()[?7h[?12l[?25h[?25l[?7l.y).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[?7lsage: (C.y).diffn() +[?7h[?12l[?25h[?2004l[?7h(1/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y).diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l.).difn()[?7h[?12l[?25h[?25l[?7lt).difn()[?7h[?12l[?25h[?25l[?7le).difn()[?7h[?12l[?25h[?25l[?7li).difn()[?7h[?12l[?25h[?25l[?7lc).difn()[?7h[?12l[?25h[?25l[?7lh).difn()[?7h[?12l[?25h[?25l[?7lm).difn()[?7h[?12l[?25h[?25l[?7lu).difn()[?7h[?12l[?25h[?25l[?7ll).difn()[?7h[?12l[?25h[?25l[?7ll).difn()[?7h[?12l[?25h[?25l[?7le).difn()[?7h[?12l[?25h[?25l[?7lr).difn()[?7h[?12l[?25h[?25l[?7l(().difn()[?7h[?12l[?25h[?25l[?7l(()).difn()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn() +[?7h[?12l[?25h[?2004l[?7h[1/x] d[x] + V(((-x^6 + x^4 - x^2 - 1)/x) dx) + dV([x^4 + 2*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[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn() +[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) +[?7h[1/x] d[x] + V(((-x^6 + x^4 - x^2 - 1)/x) dx) + dV([x^4 + 2*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[?7la[?7h[?12l[?25h[?25l[?7ld('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn() +[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) +[?7h[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) +[?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 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn()[?7h[?12l[?25h[?25l[?7l().[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lr[?7h[?12l[?25h[?25l[?7lo[?7h[?12l[?25h[?25l[?7lbe[?7h[?12l[?25h[?25l[?7lni[?7h[?12l[?25h[?25l[?7lu[?7h[?12l[?25h[?25l[?7ls[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius() +[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) + 705 try: +--> 706 x, y = resolve_fractions(x0, y0) + 707 except (AttributeError, TypeError): + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) + 682 def resolve_fractions(x, y): +--> 683 xn = x.numerator() + 684 xd = x.denominator() + +AttributeError: 'superelliptic_form' object has no attribute 'numerator' + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +Input In [105], in () +----> 1 (C.y.teichmuller()).diffn().frobenius() + +File :238, in frobenius(self) + +File :7, in __init__(self, C, g) + +File :245, in reduction_form(C, g) + +File :216, in reduction(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) + 706 x, y = resolve_fractions(x0, y0) + 707 except (AttributeError, TypeError): +--> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( + 709 x0, y0, self)) + 710 try: + 711 return self._element_class(self, x, y, coerce=coerce) + +TypeError: cannot convert ((x^3 - x)/y) dx/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius() +[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) +--------------------------------------------------------------------------- +AttributeError Traceback (most recent call last) +File /ext/sage/9.7/src/sage/rings/fraction_field.py:706, in FractionField_generic._element_constructor_(self, x, y, coerce) + 705 try: +--> 706 x, y = resolve_fractions(x0, y0) + 707 except (AttributeError, TypeError): + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:683, in FractionField_generic._element_constructor_..resolve_fractions(x, y) + 682 def resolve_fractions(x, y): +--> 683 xn = x.numerator() + 684 xd = x.denominator() + +AttributeError: 'superelliptic_form' object has no attribute 'numerator' + +During handling of the above exception, another exception occurred: + +TypeError Traceback (most recent call last) +Input In [106], in () +----> 1 (C.y.teichmuller()).diffn().frobenius() + +File :238, in frobenius(self) + +File :7, in __init__(self, C, g) + +File :245, in reduction_form(C, g) + +File :216, in reduction(C, g) + +File /ext/sage/9.7/src/sage/structure/parent.pyx:897, in sage.structure.parent.Parent.__call__() + 895 if mor is not None: + 896 if no_extra_args: +--> 897 return mor._call_(x) + 898 else: + 899 return mor._call_with_args(x, args, kwds) + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 159 print(type(C), C) + 160 print(type(C._element_constructor), C._element_constructor) +--> 161 raise + 162 + 163 cpdef Element _call_with_args(self, x, args=(), kwds={}): + +File /ext/sage/9.7/src/sage/structure/coerce_maps.pyx:156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_() + 154 cdef Parent C = self._codomain + 155 try: +--> 156 return C._element_constructor(x) + 157 except Exception: + 158 if print_warnings: + +File /ext/sage/9.7/src/sage/rings/fraction_field.py:708, in FractionField_generic._element_constructor_(self, x, y, coerce) + 706 x, y = resolve_fractions(x0, y0) + 707 except (AttributeError, TypeError): +--> 708 raise TypeError("cannot convert {!r}/{!r} to an element of {}".format( + 709 x0, y0, self)) + 710 try: + 711 return self._element_class(self, x, y, coerce=coerce) + +TypeError: cannot convert ((x^3 - x)/y) dx/1 to an element of Fraction Field of Multivariate Polynomial Ring in x, y over Finite Field of size 3 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius()[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius() +[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) +[?7h((x^3 - x)/y) dx +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l=[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l^[?7h[?12l[?25h[?25l[?7l2[?7h[?12l[?25h[?25l[?7l*[?7h[?12l[?25h[?25l[?7lC[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ly[?7h[?12l[?25h[?25l[?7l.[?7h[?12l[?25h[?25l[?7ld[?7h[?12l[?25h[?25l[?7li[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7lf[?7h[?12l[?25h[?25l[?7ln[?7h[?12l[?25h[?25l[?7l([?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn() +[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) +[?7hFalse +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn()[?7h[?12l[?25h[?25l[?7l)[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l()[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7l C.y^2*C.y.difn()[?7h[?12l[?25h[?25l[?7l C.y^2*C.y.difn()[?7h[?12l[?25h[?25l[?7l()C.y^2*C.y.difn()[?7h[?12l[?25h[?25l[?7l(), C.y^2*C.y.difn()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius(), C.y^2*C.y.diffn() +[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) +[?7h(((x^3 - x)/y) dx, ((x^3 - x)/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[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius(), C.y^2*C.y.diffn()[?7h[?12l[?25h[?25l[?7l == C.y^2*Cy.diffn()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn() +[?7h[?12l[?25h[?2004l[(1/(x^3 + 2*x))*y] d[x] + V(((-x^7 + x^3 - x)/(x^2*y - y)) dx) + dV([(x^3/(x^2 + 2))*y]) +[?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('init.sage')[?7h[?12l[?25h[?25l[?7lsage: load('init.sage') +[?7h[?12l[?25h[?2004l0 +[?2004h[?25l[?7lsage: [?7h[?12l[?25h[?25l[?7l[?7h[?12l[?25h[?25l[?7lload('init.sage')[?7h[?12l[?25h[?25l[?7l(C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn()[?7h[?12l[?25h[?25l[?7lsage: (C.y.teichmuller()).diffn().frobenius() == C.y^2*C.y.diffn() +[?7h[?12l[?25h[?2004l[?7hTrue +[?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 status +On branch master +Your branch is up to date with 'origin/master'. + +Changes not staged for commit: + (use "git add ..." to update what will be committed) + (use "git restore ..." to discard changes in working directory) + modified: sage/.run.term-0.term + modified: sage/drafty/draft.sage + modified: sage/drafty/superelliptic_drw.sage + modified: sage/superelliptic/superelliptic_form_class.sage + modified: sage/superelliptic/superelliptic_function_class.sage + +Untracked files: + (use "git add ..." to include in what will be committed) + .crystalline_p2.ipynb.sage-jupyter2 + .deRhamComputation.ipynb.sage-jupyter2 + .elementary_covers_of_superelliptic_curves.ipynb.sage-jupyter2 + .git.x11-0.term + .superelliptic.ipynb.sage-jupyter2 + .superelliptic_alpha.ipynb.sage-jupyter2 + .superelliptic_arbitrary_field.ipynb.sage-jupyter2 + git.x11 + sage/as_covers/tests/cartier_test.sage + sage/drafty/as_cartier.sage + sage/drafty/better_trace.sage + sage/drafty/cartier_image_representation.sage + sage/drafty/draft4.sage + sage/drafty/draft5.sage + sage/drafty/draft6.sage + sage/drafty/draft7.sage + sage/drafty/lift_to_de_rham.sage + sage/drafty/pole_numbers.sage + sage/drafty/regular_on_U0.sage + sage/drafty/second_patch.sage + sage/superelliptic/frobenius_kernel.sage + sage/superelliptic/tests/ + superelliptic_arbitrary_field.ipynb + +no changes added to commit (use "git add" and/or "git commit -a") +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add sage/drqaafty/second_patch.sage +]0;~/Research/2021 De Rham/DeRhamComputation~/Research/2021 De Rham/DeRhamComputation$ git add -u \ No newline at end of file diff --git a/sage/drafty/draft.sage b/sage/drafty/draft.sage index 120f4e9..c9739b8 100644 --- a/sage/drafty/draft.sage +++ b/sage/drafty/draft.sage @@ -1,9 +1,9 @@ -p = 2 -m = 1 +p = 3 +m = 2 F = GF(p) Rx. = PolynomialRing(F) -f = x +f = x^3 - x C = superelliptic(f, m) -xx = C.x -AS = as_cover(C, [xx^5, xx^5 + xx^3]) -print(AS.magical_element()) \ No newline at end of file +a = superelliptic_drw_form(C.one, 0*C.dx, 0*C.x) +b = a+a+a+a+a+a+a+a+a +print(b) \ No newline at end of file diff --git a/sage/drafty/second_patch.sage b/sage/drafty/second_patch.sage new file mode 100644 index 0000000..7a85d09 --- /dev/null +++ b/sage/drafty/second_patch.sage @@ -0,0 +1,30 @@ +def patch(C): + if C.exponent != 2: + raise ValueError("Not implemented yet!") + Fxy, Rxy, x, y = C.fct_field + F = C.base_ring + Rx. = PolynomialRing(F) + f = C.polynomial + g = C.genus() + f_star = Rx(x^(2*g+2)*f(1/x)) + return superelliptic(f_star, 2) + +def second_patch(argument): + C = argument.curve + C1 = patch(C) + Fxy, Rxy, x, y = C.fct_field + g = C.genus() + if isinstance(argument, superelliptic_function): + fct = Fxy(argument.function) + fct1 = Fxy(fct.subs({x : 1/x, y : y/x^(g+1)})) + return superelliptic_function(C1, fct1) + if isinstance(argument, superelliptic_form): + fct = Fxy(argument.form) + fct1 = Fxy(fct.subs({x : 1/x, y : y/x^(g+1)})) + fct1 *= -x^(-2) + return superelliptic_form(C1, fct1) + +def lift_form_to_drw(omega): + A, B = regular_form(omega) + A, B = A.change_ring(QQ), B.change_ring(QQ) + print("%s dx + %s dy"%(A, B)) \ No newline at end of file diff --git a/sage/drafty/superelliptic_drw.sage b/sage/drafty/superelliptic_drw.sage index 1465dd6..ed4e80b 100644 --- a/sage/drafty/superelliptic_drw.sage +++ b/sage/drafty/superelliptic_drw.sage @@ -1,39 +1,105 @@ class superelliptic_witt: - def __init__(self, C, t, f0, f1): - ''' Define Witt function on C of the form [t] + f0([x], [y]) + V(f1). ''' - self.curve = C + def __init__(self, t, f): + ''' Define Witt function on C of the form [t] + V(f). ''' + self.curve = t.curve + C = t.curve p = C.characteristic self.t = t #superelliptic_function - self.f0 = reduce_rational_fct(f0, p) #polynomial/rational function over Z/p^2 - self.f1 = f1 #superelliptic_function + self.f = f #superelliptic_function def __repr__(self): - f0 = self.f0 - f1 = self.f1 + f = self.f t = self.t - return "[" + str(t) + "] + " + str(f0).replace("x", "[x]").replace("y", "[y]") + " + V(" + str(f1) + ")" + if f.function == 0: + return "[" + str(t) + "]" + if t.function == 0: + return "V(" + str(f) + ")" + return "[" + str(t) + "] + V(" + str(f) + ")" + + def __neg__(self): + f = self.f + t = self.t + return superelliptic_witt(-t, -f) def __add__(self, other): C = self.curve - return superelliptic_witt(C, self.t + other.t, self.f0 + other.f0, self.f1 + other.f1) - - def teichmuller_representation(self): - '''Represents as [f] + V(g), i.e. f0 = 0.''' - C = self.curve - Fxy, Rxy, x, y = self.fct_field - F = C.base_ring - function = Rxy(self.f0) - if self.f0 == 0: - return self - M = Rxy(function.monomials()[0]) - a = F(function.monomial_coefficient(M)) - fct1 = fct - superelliptic_function(C, a*M) - function1 = fct1.function - return teichmuller(fct1) + superelliptic_witt(C, (a.lift())^p*M.change_ring(QQ), superelliptic_function(C, function1^2*a*M + function1*(a*M)^2)) + second_coor = 0*C.x + X = self.t + Y = other.t + for i in range(1, p): + second_coor -= binomial_prim(p, i)*X^i*Y^(p-i) + return superelliptic_witt(self.t + other.t, self.f + other.f + second_coor) - def antiteichmuller_representation(self): - '''Represents as f([x], [y]) + V(g), i.e. teichmuller part is zero.''' - return 0 + def __sub__(self, other): + return self + (-other) + + def __rmul__(self, other): + p = self.curve.characteristic + if other in ZZ: + if other == 0: + return superelliptic_witt(0*C.x, 0*C.x) + if other > 0: + return self + (other-1)*self + if other < 0: + return (-other)*(-self) + if other in QQ: + other_integer = Integers(p^2)(other)^(-1) + return other_integer*self + + def __mul__(self, other): + if isinstance(other, superelliptic_witt): + t1 = self.t + f1 = self.f + p = self.curve.characteristic + t2 = other.t + f2 = other.f + return superelliptic_witt(t1*t2, t1^p*f2 + t2^p*f1) + if isinstance(other, superelliptic_drw_form): + h1 = other.h1 + h2 = other.h2 + omega = other.omega + p = other.curve.characteristic + t = self.t + f = self.f + aux_form = t^p*omega - h2*t^(p-1)*t.diffn() + f*h1^p*(C.x)^(p-1)*C.dx + return superelliptic_drw_form(t*h1, aux_form, t^p*h2) + + def __eq__(self, other): + return self.t == other.t and self.f == other.f + + def diffn(self): + C = self.curve + t = self.t + f = self.f + fC = C.polynomial + F = C.base_ring + Rxy. = PolynomialRing(F, 2) + if t.function == 0: + return superelliptic_drw_form(0*C.x, 0*C.dx, f) + t_polynomial = t.function + num = t_polynomial.numerator() + den = t_polynomial.denominator() + num_t_fct = superelliptic_function(C, num) + den_t_fct = superelliptic_function(C, den) + inv_den_t_fct = superelliptic_function(C, 1/den) + if den != 1: + # d([N/D] + V(f)) = [1/D]*d([N]) - [N]*[D^(-2)]*d([D]) + dV(f) + return ((den_t_fct)^(-1)).teichmuller()*num_t_fct.teichmuller().diffn() - ((den_t_fct)^(-2)).teichmuller()*num_t_fct.teichmuller()*den_t_fct.teichmuller().diffn() + superelliptic_drw_form(0*C.x, 0*C.dx, f) + t_polynomial = Rxy(t_polynomial) + fC = superelliptic_function(C, fC) + fC = fC.teichmuller() + dy_w = 1/2* ((C.y)^(-1)).teichmuller()*auxilliary_derivative(fC) + M = t_polynomial.monomials()[0] + a = t_polynomial.monomial_coefficient(M) + #[P] = [aM] + Q, where Q = ([P] - [aM]) + aM_fct = superelliptic_function(C, a*M) + Q = self - aM_fct.teichmuller() + exp_x = M.exponents()[0][0] + exp_y = M.exponents()[0][1] + return Q.diffn() + exp_x*superelliptic_drw_form(aM_fct/C.x, 0*C.dx, 0*C.x) + exp_y*(aM_fct/C.y).teichmuller()*dy_w + +def binomial_prim(p, i): + return binomial(p, i)/p def reduce_rational_fct(fct, p): Rxy. = PolynomialRing(QQ) @@ -53,58 +119,127 @@ def reduce_rational_fct(fct, p): def teichmuller(fct): C = fct.curve - Fxy, Rxy, x, y = C.fct_field - F = C.base_ring - function = Rxy(fct.function) - if function == 0: - return superelliptic_witt(C, 0, 0*C.x) - M = Rxy(function.monomials()[0]) - a = F(function.monomial_coefficient(M)) - fct1 = fct - superelliptic_function(C, a*M) - function1 = fct1.function - return teichmuller(fct1) + superelliptic_witt(C, (a.lift())^p*M.change_ring(QQ), superelliptic_function(C, function1^2*a*M + function1*(a*M)^2)) + return superelliptic_witt(fct, 0*C.x) +superelliptic_function.teichmuller = teichmuller + +#dy = [f(x)]'/2*y dx +#[f1 + M] = [f1] + [M] + V(cos) +#d[f1 + M] = d[f1] + d[M] + dV(f1*M) +#M = b x^a +#d[M] = a*[b x^(a-1)] + +def auxilliary_derivative(P): + '''Return "derivative" of P, where P depends only on x. ''' + P0 = P.t.function + P1 = P.f.function + C = P.curve + F = C.base_ring + Rx. = PolynomialRing(F) + P0 = Rx(P0) + P1 = Rx(P1) + if P0 == 0: + return superelliptic_drw_form(0*C.x, 0*C.dx, P.f) + M = P0.monomials()[0] + a = P0.monomial_coefficient(M) + #[P] = [aM] + Q, where Q = ([P] - [aM]) + aM_fct = superelliptic_function(C, a*M) + Q = P - aM_fct.teichmuller() + exp = M.exponents()[0] + return auxilliary_derivative(Q) + exp*superelliptic_drw_form(aM_fct/C.x, 0*C.dx, 0*C.x) + class superelliptic_drw_form: - def __init__(self, C, omega_x, omega_y, omega, h): - '''Form [omega_x] d[x] + [omega_y] d[y] + V(omega) + dV([h])''' - self.curve = C - self.omega_x = omega_x - self.omega_y = omega_y + def __init__(self, h1, omega, h2): + '''Form [h1] d[x] + V(omega) + dV([h])''' + self.curve = h1.curve + self.h1 = h1 self.omega = omega - self.h = h + self.h2 = h2 def __eq__(self, other): - eq1 = (self.omega1 == self.omega1) + eq1 = (self.h1 == self.h1) try: - H = (self.h - other.h).pthroot() + H = (self.h2 - other.h2).pth_root() except: return False - eq2 = (self.omega2 - other.omega2).cartier() - H.diffn() + eq2 = (self.omega - other.omega).cartier() - H.diffn() if eq1 and eq2: return True return False - + def __repr__(self): C = self.curve - omega_x = self.omega_x - omega_y = self.omega_y - h = self.h - return str(omega_x) + "] dx + [" + str(omega_x.form) + "] d[x] " + "+ V(" + str(omega2) + ") + dV([" + str(h) +"])" + h1 = self.h1 + omega = self.omega + h2 = self.h2 + result = "" + if h1.function != 0: + result += "[" + str(h1) + "] d[x]" + if h1.function !=0 and omega.form != 0: + result += " + " + if omega.form != 0: + result += "V(" + str(omega) + ")" + if h2.function !=0 and omega.form != 0: + result += " + " + if h2.function != 0: + result += "dV([" + str(h2) +"])" + if result == "": + result += "0" + return result + + def __rmul__(self, other): + h1 = self.h1 + h2 = self.h2 + omega = self.omega + p = self.curve.characteristic + if other in ZZ: + if other == 0: + return superelliptic_drw_form(0*C.x, 0*C.dx, 0*C.x) + if other > 0: + return self + (other-1)*self + if other < 0: + return (-other)*(-self) + if other in QQ: + other_integer = Integers(p^2)(other)^(-1) + return other_integer*self + t = other.t + f = other.f + aux_form = t^p*omega - h2*t^(p-1)*t.diffn() + f*h1^p*(C.x)^(p-1)*C.dx + return superelliptic_drw_form(t*h1, aux_form, t^p*h2) + + def __neg__(self): + C = self.curve + h1 = self.h1 + h2 = self.h2 + omega = self.omega + return superelliptic_drw_form(-h1, -omega, -h2) + + def __add__(self, other): + C = self.curve + h1 = self.h1 + h2 = self.h2 + omega = self.omega + H1 = other.h1 + H2 = other.h2 + OMEGA = other.omega + aux = (teichmuller(h1) + teichmuller(H1))*superelliptic_drw_form(C.one, 0*C.dx, 0*C.x) + h1_aux = aux.h1 + h2_aux = aux.h2 + omega_aux = aux.omega + return superelliptic_drw_form(h1_aux, omega + OMEGA + omega_aux, h2 + H2 + h2_aux) + + def frobenius(self): + C = self.curve + h1 = self.h1 + h2 = self.h2 + p = C.characteristic + return h1^p*C.x^(p-1)*C.dx + h2.diffn() def mult_by_p(omega): C = omega.curve fct = omega.form Fxy, Rxy, x, y = C.fct_field - omega2 = superelliptic_form(C, fct^p * x^(p-1)) - result = superelliptic_drw_form(C, 0*C.dx, omega2, 0*C.x) + omega = superelliptic_form(C, fct^p * x^(p-1)) + result = superelliptic_drw_form(C, 0*C.dx, omega, 0*C.x) return result - -def basis_W2Omega(C): - basis = C.holomorphic_differentials_basis() - result = [] - for omega in basis: - result += [mult_by_p(omega)] - - image_of_cartier = [] - - return result \ No newline at end of file + diff --git a/sage/superelliptic/superelliptic_form_class.sage b/sage/superelliptic/superelliptic_form_class.sage index 922003a..68ddf7f 100644 --- a/sage/superelliptic/superelliptic_form_class.sage +++ b/sage/superelliptic/superelliptic_form_class.sage @@ -21,6 +21,11 @@ class superelliptic_form: g = reduction(C, g1 - g2) return superelliptic_form(C, g) + def __neg__(self): + C = self.curve + g = self.form + return superelliptic_form(C, -g) + def __repr__(self): g = self.form if len(str(g)) == 1: @@ -32,6 +37,9 @@ class superelliptic_form: omega = self.form return superelliptic_form(C, constant*omega) + def __eq__(self, other): + return self.form == other.form + def cartier(self): '''Computes Cartier operator on the form. Idea: y^m = f(x) -> y^(p^r - 1) = f(x)^M, where r = ord_p(m), M = (p^r - 1)/m. Thus h(x)/y^j dx = h(x) f(x)^(M*j)/y^(p^r * j) dx. Thus C(h(x)/y^j dx) = 1/y^(p^(r-1)*j) C(h(x) f(x)^(M*j) dx).''' diff --git a/sage/superelliptic/superelliptic_function_class.sage b/sage/superelliptic/superelliptic_function_class.sage index 80516cb..c83aee1 100644 --- a/sage/superelliptic/superelliptic_function_class.sage +++ b/sage/superelliptic/superelliptic_function_class.sage @@ -38,6 +38,11 @@ class superelliptic_function: g = reduction(C, g1 + g2) return superelliptic_function(C, g) + def __neg__(self): + C = self.curve + g = self.function + return superelliptic_function(C, -g) + def __sub__(self, other): C = self.curve g1 = self.function