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

toadrush commented 6 years ago

Branch: u/rud/algebraicTori

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

Commit: a3d5e84

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

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

a3d5e84 Updated file

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

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

0a41c93 Started the comments on lattices

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

Changed commit from a3d5e84 to 0a41c93

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

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

8bc7682 Documented the methods for lattices, and fixed a bug to compute cohomology of Symmetric groups

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

Changed commit from 0a41c93 to 8bc7682

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

Changed commit from 8bc7682 to 0f7aa2c

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

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

0f7aa2c Added documentation and fixed typesetting errors

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

Changed commit from 0f7aa2c to 2e48c0c

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

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

2e48c0c Added documentation for the Tori

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

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

d2e4c04 Implemented extended_xgcd to have more than two integers, implemented zero_sum_lattice() for sublattices, and updated the header

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

Changed commit from 2e48c0c to d2e4c04

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

Changed commit from d2e4c04 to bdb1f65

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

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

bdb1f65 added missing informations in the header

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

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

18f4566 added missing informations in the header, corrected others

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

Changed commit from bdb1f65 to 18f4566

roed314 commented 6 years ago

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

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

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

1d4829d Move docstring for induced_lattice down to method

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

Changed commit from 18f4566 to 1d4829d

toadrush commented 6 years ago

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

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

Changed commit from 1d4829d to 8688185

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

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

8688185 fixed some documentation

roed314 commented 6 years ago

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

toadrush commented 6 years ago

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

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

Changed commit from 8688185 to 0b58dcf

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

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

0b58dcf fixed some documentation style

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

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

ba95812 added test of rationality on the torus

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

Changed commit from 0b58dcf to ba95812

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

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

5c611ee added method to get rational characters

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

Changed commit from ba95812 to 5c611ee

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

Changed commit from 5c611ee to e4a1e7a

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

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

e4a1e7a bugfix on cohomology

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

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

e29a3e1 bugfix, and implementation of a method for quotient lattices

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

Changed commit from e4a1e7a to e29a3e1

roed314 commented 6 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

roed314 commented 4 years ago

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

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

Changed commit from e29a3e1 to 05a84f6

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

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

`d1147c5`	`Updating markdown, small changes`
`05a84f6`	`Split into two files`

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

Changed commit from 05a84f6 to fd6049d

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

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

`d7758a5`	`Merge branch 'u/roed/algebraicTori' of git://trac.sagemath.org/sage into t/25902/algebraicTori`
`fd6049d`	`Merge branch 'u/roed/algebraicTori' of git://trac.sagemath.org/sage into t/25902/algebraicTori`

toadrush commented 4 years ago

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

roed314 commented 4 years ago

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

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

Changed commit from fd6049d to 38a0ec0

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

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

38a0ec0 remove check, add GLattice to global namespace

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

Changed commit from 38a0ec0 to 4369c26

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

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

4369c26 Remove check actually

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 4369c26 to ff4e9e1

sagemath / sage

Algebraic tori #25902