Opened 21 months ago

Last modified 3 months ago

#29581 closed enhancement

New Algorithm for Characteristic Classes — at Version 38

Reported by: gh-mjungmath Owned by:
Priority: major Milestone: sage-9.5
Component: manifolds Keywords: characteristic_classes, manifolds
Cc: slelievre, egourgoulhon, tscrim, mkoeppe, gh-tobiasdiez Merged in:
Authors: Michael Jung Reviewers:
Report Upstream: N/A Work issues:
Branch: u/gh-mjungmath/new_algorithm (Commits, GitHub, GitLab) Commit: 2cabd839d55e5c0f3ba2f8d0194bcae6ce31397c
Dependencies: #32270, #32272, #32396 Stopgaps:

Status badges

Description (last modified by gh-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).

Change History (38)

comment:1 Changed 21 months ago by gh-mjungmath

  • Branch set to u/gh-mjungmath/new_algorithm

comment:2 Changed 21 months ago by mkoeppe

  • Commit set to 1a803eba5b9724ebfa93e726a474d957fd6915b4
  • Milestone changed from sage-9.1 to sage-9.2

New commits:

3b36f0dTrac #29570: alternating_form returns correct element
85e7970Trac #29570: Typo fixed, doctest added, returned element preferably non-zero
1a803ebTrac #29581: New Algorithm for Char Classes

comment:3 Changed 21 months ago by slelievre

  • Cc slelievre added
  • Component changed from PLEASE CHANGE to geometry

comment:4 Changed 21 months ago by slelievre

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.

comment:5 Changed 21 months ago by git

  • Commit changed from 1a803eba5b9724ebfa93e726a474d957fd6915b4 to cb442eb8919ca33a5db63a17bac52f99f55553dd

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

730046cMerge branch 'develop' into t/29570/diff_form_bug
130ae3fTrac #29570: NotImplementedError for non-generic ring elements
bba21e1Trac #29570: Strange typo fixed...
ba3b4b9Trac #29570: correct parent, vectorfield_module changes reverted
841e1bfMerge branch 't/29570/diff_form_bug' into t/29581/new_algorithm
cb442ebTrac #29570: new algorithm added and code cleaned

comment:6 Changed 21 months ago by git

  • Commit changed from cb442eb8919ca33a5db63a17bac52f99f55553dd to 15c7341d071327a04fd229c3d2f78d583564f476

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

15c7341Trac #29581: new algorithm added and code cleaned

comment:7 Changed 21 months ago by gh-mjungmath

  • Authors set to Michael Jung
  • Cc egourgoulhon added
  • Description modified (diff)
  • Keywords characteristic_classes manifolds added
  • Type changed from PLEASE CHANGE to enhancement

comment:8 Changed 21 months ago by chapoton

Correct syntax for crosslinks is

.. SEEALSO::

comment:9 Changed 21 months ago by chapoton

  • do not use this:
    if distinct_real == False
    

but

if not distinct_real

(at least in two places)

  • The following change is wrong:
    -        - ``cmatrix`` -- curvature matrix
    -
    +            - ``cmatrix`` -- curvature matrix
             OUTPUT:
     
    -        - ``I/(2*pi)*cmatrix``
    +            - ``I/(2*pi)*cmatrix``
    

as one should not indent inside INPUT or OUTPUT blocks (because they end with only one colon). And moreover, one does want empty lines to separate these things.

This is also incorrect:

-            self._dual_exterior_powers[p] = ExtPowerDualFreeModule(self, p)
+                self._dual_exterior_powers[p] = ExtPowerDualFreeModule(self, p)

Why did you change the indentation ? it was ok.

comment:10 Changed 21 months ago by gh-mjungmath

I am sorry. At this stage, this is just a draft. The indentations are typos coming from using alt+tab (at least I guess so). I will fix this soon.

comment:11 Changed 21 months ago by gh-mjungmath

Thanks for your advice. :)

comment:12 Changed 21 months ago by git

  • Commit changed from 15c7341d071327a04fd229c3d2f78d583564f476 to d37229341effff46ea2fa4b3287e32997c8422b0

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

d372293Trac #29581: Strange typos reverted

comment:13 Changed 21 months ago by gh-mjungmath

  • Status changed from new to needs_review

comment:14 Changed 21 months ago by gh-mjungmath

  • Status changed from needs_review to needs_info

comment:15 Changed 21 months ago by gh-mjungmath

An example for the application of the new algorithm would be really nice. For instance a Todd class or A-Hat class. But I have no idea for a suitable one. If anyone does, or at least knows someone who does, I would really appreciate it. Thanks! :)

comment:16 Changed 21 months ago by git

  • Commit changed from d37229341effff46ea2fa4b3287e32997c8422b0 to 19815c4257cee7dcf503d94e3b9bb651150bef5f

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

c975bd2Merge branch 'develop' into t/29581/new_algorithm
19815c4Trac #29581: Readability of one line

comment:17 Changed 18 months ago by gh-mjungmath

  • Component changed from geometry to manifolds
  • Dependencies set to #30211

comment:18 Changed 15 months ago by mkoeppe

  • Milestone changed from sage-9.2 to sage-9.3

comment:19 Changed 10 months ago by mkoeppe

  • Milestone changed from sage-9.3 to sage-9.4

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

comment:20 Changed 6 months ago by mkoeppe

  • Milestone changed from sage-9.4 to sage-9.5

Setting a new milestone for this ticket based on a cursory review.

comment:21 Changed 6 months ago by gh-mjungmath

  • Cc tscrim mkoeppe added
  • Dependencies #30211 deleted
  • Description modified (diff)
  • Status changed from needs_info to needs_work

comment:22 Changed 6 months ago by git

  • Commit changed from 19815c4257cee7dcf503d94e3b9bb651150bef5f to 3c9b80a2551994493f23640344e9ade63240cb01

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

3c9b80aTrac #29581: implement algorithms for chern, pontryagin and euler

comment:23 Changed 6 months ago by gh-mjungmath

Do you think it is necessary to give those cohomology classes an own parent or would DeRhamCohomologyRing as parent suffice?

The point is that addition and multiplication is performed differently among those elements. Moreover, it is possible to compare them.

comment:24 Changed 6 months ago by gh-mjungmath

  • Description modified (diff)

comment:25 Changed 6 months ago by gh-mjungmath

  • Status changed from needs_work to needs_info

comment:26 Changed 6 months ago by gh-mjungmath

  • Description modified (diff)

comment:27 Changed 6 months ago by git

  • Commit changed from 3c9b80a2551994493f23640344e9ade63240cb01 to 03529f8919357f98b65ee033e8dc5c7d48b2fa42

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

03529f8Trac #29581: return mixed form

comment:28 Changed 5 months ago by git

  • Commit changed from 03529f8919357f98b65ee033e8dc5c7d48b2fa42 to ab288d62786a40b9f314d40ca932506d7b6932d9

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

fb9c661#32270: de rham cohomology as algebra
de5863aMerge branch 't/32270/turn_de_rham_cohomology_into_algebra' into t/29581/new_algorithm
d22ee9aTrac #32315: support iteration and enumerated sets
16c4737Trac #32272: allow infinite max degree
6a320a0Trac #32272: fix docstring
c1d4fceTrac #32272: fix rst file + rename module
25e6b1dTrac #32272: fix doctest
5a4c7acTrac #32272: narrow to finite dimensions
3b81085Merge branch 't/32272/finitely_generated_graded_algebras_with_finite_degree' into t/29581/new_algorithm
ab288d6Trac #29581: algorithm for complex vbundles

comment:29 Changed 5 months ago by gh-mjungmath

  • Dependencies set to #32270, #32272

comment:30 Changed 5 months ago by git

  • Commit changed from ab288d62786a40b9f314d40ca932506d7b6932d9 to 6688740017097a79d7995101889cea097ee5c653

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

932e128Trac #29581: element constructor
6688740Trac #29581: naming

comment:31 Changed 5 months ago by git

  • Commit changed from 6688740017097a79d7995101889cea097ee5c653 to 61291f406b886abb9a509955355da749fc99a8d6

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

61291f4Trac #29581: minor fixes

comment:32 Changed 5 months ago by git

  • Commit changed from 61291f406b886abb9a509955355da749fc99a8d6 to 60318775e9c530c32280ba1bfa819cb9ac978bd1

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

6031877Trac #29581: return only list of generators

comment:33 Changed 5 months ago by git

  • Commit changed from 60318775e9c530c32280ba1bfa819cb9ac978bd1 to 0c7587f759b9555404fd417ee042e99fbb4ae02d

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

0c7587fTrac #29581: parent deals with different cases, element stays generic

comment:34 Changed 5 months ago by git

  • Commit changed from 0c7587f759b9555404fd417ee042e99fbb4ae02d to 28d2d84271a3e1516556a8364b1114dd6edaa992

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

28d2d84Trac #29581: revert mistaken merge

comment:35 Changed 5 months ago by gh-mjungmath

The ticket is not ready for review yet; the structure should be fixed though. Feedback at this stage is very much appreciated. :)

comment:36 Changed 5 months ago by git

  • Commit changed from 28d2d84271a3e1516556a8364b1114dd6edaa992 to 2cabd839d55e5c0f3ba2f8d0194bcae6ce31397c

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

2cabd83Trac #29581: add some comments

comment:37 Changed 5 months ago by gh-mjungmath

  • Dependencies changed from #32270, #32272 to #32270, #32272, #32396

comment:38 Changed 5 months ago by gh-mjungmath

  • Description modified (diff)
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