Implement untwisted affine Lie algebras

[tscrim]

Part of #14901. Implement untwisted affine Lie algebras from their corresponding classical one (given by extending the corresponding current algebra).

Depends on #16821

CC: @bsalisbury1

Component: algebra

Keywords: lie algebras

Author: Travis Scrimshaw

Branch/Commit: 3cf54ac

Reviewer: Ben Salisbury

Issue created by migration from https://trac.sagemath.org/ticket/16825

[tscrim]

comment:1

Preliminary version.

---

Last 10 new commits:

921e2ca	Adding back support for creating a Lie algebra from a Cartan type.
721632b	Fixing bugs in structure coefficients of Chevalley basis.
23c1474	Implementing matrix Lie algebras in types E6, F4, and G2.
3862a22	Merge branch 't/16820/public/lie_algebras/fd_structure_coeff-16820' into t/16821/public/lie_algebras/classical-16821
abcf1e5	Fix citation problem
600a87a	Merge branch 'public/lie_algebras/classical-16821' of git://trac.sagemath.org/sage into public/lie_algebras/classical-16821
5cbde34	Doing rebasing due to changes in base ticket.
e3e309e	Merge branch 'develop' into public/lie_algebras/classical-16821
a7cede7	New data structure for elements.
321a6b3	Adding affine method and fixing highest root element for matrix Lie algebras.

[tscrim]

Commit: 321a6b3

[tscrim]

Branch: public/lie_algebras/untwisted_affine-16825

[sagetrac-git]

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

c75ce5e

Finishing initial implementation of untwisted affine Lie algebras.

[sagetrac-git]

Changed commit from 321a6b3 to c75ce5e

[sagetrac-git]

Changed commit from c75ce5e to a160cfd

[sagetrac-git]

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

a160cfd

Adding some coercions and exposing some more data.

[sagetrac-git]

Changed commit from a160cfd to e266372

[sagetrac-git]

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

2efa478	Merge branch 'develop' into public/lie_algebras/untwisted_affine-16825
e266372	Doctest fixes.

[sagetrac-git]

Changed commit from e266372 to 394de75

[sagetrac-git]

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

76feb75	Merge branch 'public/lie_algebras/untwisted_affine-16825' of git://trac.sagemath.org/sage into public/lie_algebras/untwisted_affine-16825
394de75	A few last little doc tweaks.

[sagetrac-git]

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

9796372	Merge branch 'develop' into t/16825/public/lie_algebras/untwisted_affine-16825
0014c81	Merge branch 'public/lie_algebras/untwisted_affine-16825' of git://trac.sagemath.org/sage into t/16825/public/lie_algebras/untwisted_affine-16825
76f940f	Merge branch 'develop' into t/16825/public/lie_algebras/untwisted_affine-16825
f308868	Changed naming conventions in the documentation introduction
e5a9a3b	Changed delta to d and Lie derivative to canonical derivation

[sagetrac-git]

Changed commit from 394de75 to e5a9a3b

[bsalisbury1]

comment:9

It's not working currently, but I'm hoping you can help. The current complaint I'm getting is

'sage.algebras.lie_algebras.lie_algebra_element.UntwistedAffineLieAlgebraElement' object has no attribute '_d_coeff'

This comes, for example, when trying to compute

sage: g = LieAlgebra(QQ, cartan_type=['A',1,1])
sage: list(g.lie_algebra_generators())

I went to the .pyx file and confirmed that the attribute _d_coeff is there, so I'm not sure what's going wrong.

[tscrim]

comment:10

You need to change cdef _delta_coeff in the pxd file to cdef _d_coeff.

[sagetrac-git]

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

cbf09d3

Fixed typo in pxd file

[sagetrac-git]

Changed commit from e5a9a3b to cbf09d3

[bsalisbury1]

comment:12

Hi Travis,

I made a bunch of changes. If you are okay with them, then you may set this to positive review. All documentation builds and tests passed on my machine.

Ben

[bsalisbury1]

Reviewer: Ben Salisbury

[tscrim]

comment:13

Looks good. Thank you!

[vbraun]

comment:14

sage -t --long src/sage/algebras/lie_algebras/lie_algebra_element.pyx
**********************************************************************
File "src/sage/algebras/lie_algebras/lie_algebra_element.pyx", line 774, in sage.algebras.lie_algebras.lie_algebra_element.UntwistedAffineLieAlgebraElement.__hash__
Failed example:
    hash(x)
Expected:
    1782435762440299943
Got:
    -684399193
**********************************************************************
1 item had failures:
   1 of   5 in sage.algebras.lie_algebras.lie_algebra_element.UntwistedAffineLieAlgebraElement.__hash__
    [202 tests, 1 failure, 1.05 s]

[sagetrac-git]

Changed commit from cbf09d3 to 3cf54ac

[sagetrac-git]

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

3cf54ac

Better hash test.

[tscrim]

comment:16

32-bit/64-bit hash failure. Fixed.

[vbraun]

Changed branch from public/lie_algebras/untwisted_affine-16825 to 3cf54ac