New Algorithm for Characteristic Classes

[mjungmath]

The current algorithm for characteristic forms is comparably slow. The worst case scenario showed computations times about 1h in dimension four.

With this ticket, we want to replace the current algorithm and implement characteristic cohomology classes as sub-ring of the de Rham cohomology ring (cf. #31691).

The idea is that characteristic (cohomology) classes are generated by Chern/Pontryagin/Euler classes. The generators can be computed by an Faddeev-LeVerrier-like algorithm (cf. #30681).

Depends on #32270
Depends on #32272
Depends on #32396

CC: @slel @egourgoulhon @tscrim @mkoeppe @tobiasdiez

Component: manifolds

Keywords: characteristic_classes

Author: Michael Jung

Branch/Commit: ac5cbbf

Reviewer: Travis Scrimshaw, Eric Gourgoulhon

Issue created by migration from https://trac.sagemath.org/ticket/29581

[mjungmath]

Branch: u/gh-mjungmath/new_algorithm

[mkoeppe]

New commits:

3b36f0d	Trac #29570: alternating_form returns correct element
85e7970	Trac #29570: Typo fixed, doctest added, returned element preferably non-zero
1a803eb	Trac #29581: New Algorithm for Char Classes

[mkoeppe]

Commit: 1a803eb

[slel]

comment:4

Please add a short description in the "Description" field of the ticket,
and the author's full name in the "Authors" field of the ticket. Don't forget
to set to needs_review when this is ready for review.

[sagetrac-git]

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

730046c	Merge branch 'develop' into t/29570/diff_form_bug
130ae3f	Trac #29570: NotImplementedError for non-generic ring elements
bba21e1	Trac #29570: Strange typo fixed...
ba3b4b9	Trac #29570: correct parent, vectorfield_module changes reverted
841e1bf	Merge branch 't/29570/diff_form_bug' into t/29581/new_algorithm
cb442eb	Trac #29570: new algorithm added and code cleaned

[sagetrac-git]

Changed commit from 1a803eb to cb442eb

[sagetrac-git]

Changed commit from cb442eb to 15c7341

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

15c7341

Trac #29581: new algorithm added and code cleaned

[mjungmath]

Author: Michael Jung

[mjungmath]

Changed keywords from none to characteristic_classes

[mjungmath]

Description changed:

--- 
+++ 
@@ -1 +1 @@
-
+Alternative algorithm for characteristic classes involving chern roots.