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Algebraic tori #25902

Open roed314 opened 6 years ago

roed314 commented 6 years ago

Sage currently doesn't have much support for linear algebraic groups. This ticket is for creating some infrastructure for working with them, by starting with algebraic tori.

Sage does have support for matrix groups (sage/groups/matrix_gps/), for root systems (sage/combinat/root_systems/) and for affine schemes (sage/schemes/generic/scheme.py). Algebraic groups will be built out of these ingredients.

Magma's functionality for algebraic groups includes invariant theory (https://magma.maths.usyd.edu.au/magma/handbook/invariant_theory). In this ticket we will focus more on questions of rationality and Galois cohomology.

We also note that the functionality we envision for algebraic groups is fairly distinct from that of finitely presented matrix groups (e.g. as summarized in https://arxiv.org/pdf/1805.05984.pdf).

Depends on #29031 Depends on #31489 Depends on #31737

CC: @tscrim @dwbump

Component: group theory

Keywords: padicIMA

Author: Thomas Rüd

Branch/Commit: u/roed/algebraicTori @ 9caf319

Reviewer: David Roe

Issue created by migration from https://trac.sagemath.org/ticket/25902

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

ff4e9e1added group extension, sublattice, and action display methods
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from ff4e9e1 to bcf4e5c

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

bcf4e5cfixed doctests, fixed matrix and symmetric groups incorporation
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

d958b01added missing documentation, fixed Tate-Shafarevich
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from bcf4e5c to d958b01

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from d958b01 to 6616e7a

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

6616e7afixed documentation style
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

e705db3fixed documentation style
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 6616e7a to e705db3

fchapoton commented 4 years ago
comment:37

Patchbot is not happy, see the plugins.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from e705db3 to 426beb4

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

426beb4fixed documentation style
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

1261f3emore fixes
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 426beb4 to 1261f3e

roed314 commented 4 years ago

Changed branch from u/rud/algebraicTori to u/roed/algebraicTori

toadrush commented 4 years ago

Changed branch from u/roed/algebraicTori to u/rud/algebraicTori

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 1261f3e to 82ad12e

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

82ad12eswitched all GAP to libgap
roed314 commented 4 years ago

Changed branch from u/rud/algebraicTori to u/roed/algebraicTori

toadrush commented 4 years ago

Changed branch from u/roed/algebraicTori to u/rud/algebraicTori

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

f7ca62dadded operands for sublattices
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 82ad12e to f7ca62d

roed314 commented 4 years ago

Changed branch from u/rud/algebraicTori to u/roed/algebraicTori

fchapoton commented 4 years ago
comment:47

Now doc builds, but patchbot is still not happy. Please care about that.

New commits:

42f38ceMove Tate_Cohomology to generic
8dbcde3Merge branch 'u/rud/algebraicTori' of git://trac.sagemath.org/sage into t/25902/algebraicTori
fchapoton commented 4 years ago

Changed commit from f7ca62d to 8dbcde3

roed314 commented 4 years ago
comment:48

Yep, we're still working on various parts of the code, and will address the patchbot failures.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 8dbcde3 to d7ca975

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

15a5319Documentation tweaks, minor code changes
d7ca975Fixing patchbot issues, going through code
roed314 commented 4 years ago
comment:50

Still need to make various changes, but I think I've addressed the patchbot problems (though there may still be some failing tests)

fchapoton commented 4 years ago
comment:51

here, the doctests should be indented more

+        EXAMPLES::
+
+        sage: T1 = AlgebraicTorus(Lattice_ambient([], 1));
+        sage: T2 = T1.norm_one_restriction(G)
+        sage: G = SymmetricGroup(3)
fchapoton commented 4 years ago
comment:52

patchbot is almost happy (excluding the doctests):

+src/sage/modules/glattice.py:290: 'sage.combinat.permutation.Permutation' imported but unused
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from d7ca975 to 2157bb0

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

2157bb0Fixing a few more patchbot issues
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 2157bb0 to 63e13a6

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

63e13a6parent->ambient, combining some functions, other small changes
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 63e13a6 to 81a9d62

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

81a9d62Combining a few methods, changing print representations
fchapoton commented 4 years ago
comment:56

patchbot is still not happy, and moreover there are really many failing doctests...

roed314 commented 4 years ago
comment:57

Yep, we know about the doctests. The code is still in progress, and I recently changed the print representation without updating the test results. I'm pretty busy this coming week and won't have time time to work on this ticket much, though Thomas might. I'm planning on coming back to it once I get back to Boston though.

Thanks for the interest in the ticket!

toadrush commented 4 years ago

Changed branch from u/roed/algebraicTori to u/rud/algebraicTori

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 81a9d62 to 87d9c6f

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

0854831Merge branch 'u/pbruin/26816-GaloisGroup_subgroup' of git://trac.sagemath.org/sage into t/26816/gal_subgroup
2346140Use pari functions for ramification groups
3efc05eWorking on galois group revisions
ff53640Merge branch 'u/roed/gal_revision' of git://trac.sagemath.org/sage into t/25902/algebraicTori
87d9c6fmore fixes
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

8f62f4bimplemented morphisms, early stage
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 87d9c6f to 8f62f4b

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 8f62f4b to 586f11b

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

586f11badded file
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

608bb6bchanges to tori to start incorporating new galois groups
7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Changed commit from 586f11b to 608bb6b

tscrim commented 4 years ago
comment:63

So I talked with Thomas yesterday, and he told me you were having a pickling issue. The problem comes from the fact that actions cannot be pickled:

sage: V = QQ^3
sage: v = V((1, 2, 3))
sage: cm = get_coercion_model()
sage: a = cm.get_action(V, QQ, operator.mul)
sage: dumps(a)
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
[snip]
/home/travis/sage-build/local/lib/python3.7/site-packages/sage/categories/functor.pyx in sage.categories.functor.Functor.__reduce__ (build/cythonized/sage/categories/functor.c:2242)()
    212         """
    213         return (_Functor_unpickle,
--> 214                 (self.__class__, list(self.__dict__.items()),
    215                  self.__domain, self.__codomain))
    216 

AttributeError: 'sage.structure.coerce_actions.RightModuleAction' object has no attribute '__dict__'

This is #29031.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 4 years ago

Branch pushed to git repo; I updated commit sha1. New commits:

c6f0d3badded exterior direct sum of lattices, new methods for tori based on new galois groups, fixed the creation of sublattices