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 4 years ago

Changed commit from 608bb6b to c6f0d3b

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

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

a652583 removal of typos/unnecessary methods

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

Changed commit from c6f0d3b to a652583

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

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

06063f8 changed morphisms to left morphisms, added a lot of methods for them, added orbits, stabilizers, flabby/coflabby resolutions for tori and a few more methods

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

Changed commit from a652583 to 06063f8

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

Changed commit from 06063f8 to ac6544a

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

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

ac6544a added some documentation

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

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

972c336 added some documentation, and several methods to construct morphisms of lattices, such as quotient, diagonal embedding, projection form square, and injection of sublattices

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

Changed commit from ac6544a to 972c336

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

Changed commit from 972c336 to 39aa76c

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

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

39aa76c fixed doctests, added Tamagawa number computation

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

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

a749abf fixed doctests for tori

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

Changed commit from 39aa76c to a749abf

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

Changed commit from a749abf to 617803a

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

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

617803a temporary skip of _test_pickling and _test_elements

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

Changed commit from 617803a to 00357c4

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

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

00357c4 fixed some documentation errors/typos

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

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

59982de added missing spaces in the documentation

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

Changed commit from 00357c4 to 59982de

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

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

537c4bd more spaces

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

Changed commit from 59982de to 537c4bd

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 537c4bd to 3301d80

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

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

3301d80 Merging develop

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

Changed commit from 3301d80 to 6d2832a

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

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

6d2832a Fix a few tabs, add a bit of documentation

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

Changed commit from 6d2832a to d92fe49

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

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

`06063f8`	`changed morphisms to left morphisms, added a lot of methods for them, added orbits, stabilizers, flabby/coflabby resolutions for tori and a few more methods`
`ac6544a`	`added some documentation`
`972c336`	`added some documentation, and several methods to construct morphisms of lattices, such as quotient, diagonal embedding, projection form square, and injection of sublattices`
`39aa76c`	`fixed doctests, added Tamagawa number computation`
`a749abf`	`fixed doctests for tori`
`617803a`	`temporary skip of _test_pickling and _test_elements`
`00357c4`	`fixed some documentation errors/typos`
`59982de`	`added missing spaces in the documentation`
`537c4bd`	`more spaces`
`d92fe49`	`Merge branch 'u/rud/algebraicTori' of git://trac.sagemath.org/sage into t/25902/algebraicTori`

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

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

d6c6323 Add indirect doctest marker

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

Changed commit from d92fe49 to d6c6323

roed314 commented 3 years ago

Dependencies: #29031

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

Changed commit from d6c6323 to 8f8b372

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

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

`4958fdb`	Adding custom `__reduce__` methods to Action and subclasses.
`cbf439f`	`Merge branch 'public/pickling/actions-29031' of git://trac.sagemath.org/sage into t/29031/actions`
`d4991d3`	`is can`
`8f8b372`	`Merge branch 't/29031/public/pickling/actions-29031' into t/25902/algebraicTori`

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

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

ff7f430 Update TestSuite calls

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

Changed commit from 8f8b372 to ff7f430

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:

9b88614 added missing documentation/doctests

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

Changed commit from ff7f430 to 9b88614

roed314 commented 3 years ago

Changed dependencies from #29031 to #29031, 28782

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:

`1ac12b4`	`Fixing doctests elsewhere in Sage`
`6ce601e`	`Fix more doctests`
`2abc75b`	`Merge branch 't/28782/galois_update' into t/25902/algebraicTori`

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

Changed commit from 9b88614 to 2abc75b

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

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

`52dc1e7`	`Fix pyflakes`
`4480e4a`	`Fix blocks plugin report`
`94687b1`	`Fix doctest (embeddings)`
`e6fa91b`	`Merge branch 't/28782/gal_revision' into t/25902/algebraicTori`

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

Changed commit from 2abc75b to e6fa91b

roed314 commented 3 years ago

Author: Thomas Rüd

roed314 commented 3 years ago

comment:89

Marking as needs review so patchbot tests it

roed314 commented 3 years ago

Reviewer: David Roe

roed314 commented 3 years ago

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

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

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

ad67cff Fix doctests, pickling for matrix actions

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

Changed commit from e6fa91b to ad67cff

sagemath / sage

Algebraic tori #25902