Algebraic tori - Githubissues

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 3 years ago

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

c559ad0 Fix syntax bug

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from ad67cff to c559ad0

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

b0b7efc Fix comparison for matrix actions

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from c559ad0 to b0b7efc

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from b0b7efc to 7af7689

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

7af7689 Fix pickling

toadrush commented 3 years ago

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

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

cef0413 fixed some patchbot errors

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 7af7689 to cef0413

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from cef0413 to b69a190

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

b69a190 fixed more patchbot errors

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from b69a190 to 964a7f6

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

964a7f6 added lazy attributes to tori

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

ec0770e added splitting fields for tori

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 964a7f6 to ec0770e

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

09c3209 added splitting fields for tori

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from ec0770e to 09c3209

roed314 commented 3 years ago

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

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 09c3209 to 2074bf6

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`539b0ca`	`Fix some test failures, factor _GaloisMixin for subgrous`
`61873da`	`Fix bitsize`
`2142390`	`Merge branch 't/31489/galois_sub' into t/25902/algebraicTori`
`5d4098d`	`fixed some doctests`
`cef0413`	`fixed some patchbot errors`
`b69a190`	`fixed more patchbot errors`
`964a7f6`	`added lazy attributes to tori`
`ec0770e`	`added splitting fields for tori`
`09c3209`	`added splitting fields for tori`
`2074bf6`	`Merge branch 'u/rud/algebraicTori' of git://trac.sagemath.org/sage into t/25902/algebraicTori`

roed314 commented 3 years ago

Changed dependencies from #29031, #28782 to #29031, #31489

toadrush commented 3 years ago

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

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 2074bf6 to 7375224

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

7375224 fixed doctests

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

d96ee06 added temporary methods for norm one tori for non-galois fields

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 7375224 to d96ee06

roed314 commented 3 years ago

Changed dependencies from #29031, #31489 to #29031, #31489, #31737

roed314 commented 3 years ago

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

mkoeppe commented 3 years ago

comment:109

Tate_Cohomology should probably be renamed tate_cohomology to match our coding standards

Last 10 new commits:

`25c62c1`	`fixed bugs`
`4d9fd9a`	`changed the error type`
`8f17598`	`added a test for the fix`
`a6898b0`	`merged with t/31818`
`fa796d1`	`fixed a typo`
`15807ec`	`Merge branch 'u/rud/creating_a_module_homomorphism_with_a_matrix_may_build_the_wrong_codomain' of git://trac.sagemath.org/sage into t/31737/matrixmorphism__add_support_for_morphisms_acting_on_the_left`
`dd528ed`	`completed a test`
`da7a09b`	`Merge branch 'u/rud/creating_a_module_homomorphism_with_a_matrix_may_build_the_wrong_codomain' of git://trac.sagemath.org/sage into t/31737/matrixmorphism__add_support_for_morphisms_acting_on_the_left`
`0548148`	`changed the pushout to hom`
`7000ae1`	`Merge branch 'u/rud/matrixmorphism__add_support_for_morphisms_acting_on_the_left' of trac.sagemath.org:sage into t/25902/algebraicTori`

mkoeppe commented 3 years ago

Changed commit from d96ee06 to 7000ae1

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

`a19088c`	`fixed a test`
`4b66508`	`fixed typos`
`2f73c05`	`fixed a typo`
`ed87b99`	`Merge branch 'u/rud/matrixmorphism__add_support_for_morphisms_acting_on_the_left' of git://trac.sagemath.org/sage into t/25902/algebraicTori`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 7000ae1 to ed87b99

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from ed87b99 to 4d8bed2

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

4d8bed2 Change capitalization of Tate_Cohomology

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

`9f8420d`	`White space changes and some code improvements that shouldn't change output`
`8410bee`	`Change capitalization of tamagawa number`
`a0a4864`	`Getting rid of some abbreviations`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 4d8bed2 to a0a4864

mkoeppe commented 3 years ago

comment:113

Needs rebase

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

`37f25b3`	`Merge branch 'u/rud/matrixmorphism__add_support_for_morphisms_acting_on_the_left' of git://trac.sagemath.org/sage into t/31737/matrix_morphism`
`2999315`	`fixed some bugs by adding side arguments to hecke morphisms, and morphisms of abelian varieties`
`cb41278`	`merged with develop`
`536aaff`	`removed the pushout in hom`
`c9fab37`	`fixed the restrict method`
`0acd41a`	`Merge branch 'u/rud/matrixmorphism__add_support_for_morphisms_acting_on_the_left' of git://trac.sagemath.org/sage into t/31737/matrix_morphism`
`178bac9`	`fixed typo`
`b1aad89`	`Merge branch 'u/rud/matrixmorphism__add_support_for_morphisms_acting_on_the_left' of git://trac.sagemath.org/sage into t/31737/matrix_morphism`
`9d62ddf`	`Fix some doctest failures, remove trailing whitespace, add pushout back in`
`d54aeb7`	`Merge branch 'u/roed/algebraicTori' of git://trac.sagemath.org/sage into t/25902/algebraicTori`

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from a0a4864 to d54aeb7

roed314 commented 3 years ago

comment:115

Rebased; resetting to needs review so the patchbot runs.

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from d54aeb7 to 67761e7

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

`3fb6c65`	`fixed blocks`
`c4ebbea`	`Merge branch 'u/rud/matrixmorphism__add_support_for_morphisms_acting_on_the_left' of git://trac.sagemath.org/sage into t/31737/matrix_morphism`
`a9a0271`	`Merge branch 't/31737/matrix_morphism' into t/25902/algebraicTori`
`67761e7`	`Fix pyflakes`

toadrush commented 3 years ago

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

roed314 commented 3 years ago

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

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

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

9caf319 Small improvement to stabilizer method

7ed8c4ca-6d56-4ae9-953a-41e42b4ed313 commented 3 years ago

Changed commit from 67761e7 to 9caf319

fchapoton commented 2 years ago

comment:120

red branch => needs work

sagemath / sage

Algebraic tori #25902