Opened 21 months ago
Last modified 3 months ago
#29581 closed enhancement
New Algorithm for Characteristic Classes — at Version 38
Reported by:  ghmjungmath  Owned by:  

Priority:  major  Milestone:  sage9.5 
Component:  manifolds  Keywords:  characteristic_classes, manifolds 
Cc:  slelievre, egourgoulhon, tscrim, mkoeppe, ghtobiasdiez  Merged in:  
Authors:  Michael Jung  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  u/ghmjungmath/new_algorithm (Commits, GitHub, GitLab)  Commit:  2cabd839d55e5c0f3ba2f8d0194bcae6ce31397c 
Dependencies:  #32270, #32272, #32396  Stopgaps: 
Description (last modified by )
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 subring 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 FaddeevLeVerrier?like algorithm (cf. #30681).
Change History (38)
comment:1 Changed 21 months ago by
 Branch set to u/ghmjungmath/new_algorithm
comment:2 Changed 21 months ago by
 Commit set to 1a803eba5b9724ebfa93e726a474d957fd6915b4
 Milestone changed from sage9.1 to sage9.2
comment:3 Changed 21 months ago by
 Cc slelievre added
 Component changed from PLEASE CHANGE to geometry
comment:4 Changed 21 months ago by
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
 Commit changed from 1a803eba5b9724ebfa93e726a474d957fd6915b4 to cb442eb8919ca33a5db63a17bac52f99f55553dd
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 nongeneric 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

comment:6 Changed 21 months ago by
 Commit changed from cb442eb8919ca33a5db63a17bac52f99f55553dd to 15c7341d071327a04fd229c3d2f78d583564f476
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

comment:7 Changed 21 months ago by
 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
Correct syntax for crosslinks is
.. SEEALSO::
comment:9 Changed 21 months ago by
 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
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
Thanks for your advice. :)
comment:12 Changed 21 months ago by
 Commit changed from 15c7341d071327a04fd229c3d2f78d583564f476 to d37229341effff46ea2fa4b3287e32997c8422b0
Branch pushed to git repo; I updated commit sha1. New commits:
d372293  Trac #29581: Strange typos reverted

comment:13 Changed 21 months ago by
 Status changed from new to needs_review
comment:14 Changed 21 months ago by
 Status changed from needs_review to needs_info
comment:15 Changed 21 months ago by
An example for the application of the new algorithm would be really nice. For instance a Todd class or AHat 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
 Commit changed from d37229341effff46ea2fa4b3287e32997c8422b0 to 19815c4257cee7dcf503d94e3b9bb651150bef5f
comment:17 Changed 18 months ago by
 Component changed from geometry to manifolds
 Dependencies set to #30211
comment:18 Changed 15 months ago by
 Milestone changed from sage9.2 to sage9.3
comment:19 Changed 10 months ago by
 Milestone changed from sage9.3 to sage9.4
Setting new milestone based on a cursory review of ticket status, priority, and last modification date.
comment:20 Changed 6 months ago by
 Milestone changed from sage9.4 to sage9.5
Setting a new milestone for this ticket based on a cursory review.
comment:21 Changed 6 months ago by
 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
 Commit changed from 19815c4257cee7dcf503d94e3b9bb651150bef5f to 3c9b80a2551994493f23640344e9ade63240cb01
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
3c9b80a  Trac #29581: implement algorithms for chern, pontryagin and euler

comment:23 Changed 6 months ago by
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
 Description modified (diff)
comment:25 Changed 6 months ago by
 Status changed from needs_work to needs_info
comment:26 Changed 6 months ago by
 Description modified (diff)
comment:27 Changed 6 months ago by
 Commit changed from 3c9b80a2551994493f23640344e9ade63240cb01 to 03529f8919357f98b65ee033e8dc5c7d48b2fa42
Branch pushed to git repo; I updated commit sha1. New commits:
03529f8  Trac #29581: return mixed form

comment:28 Changed 5 months ago by
 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

de5863a  Merge branch 't/32270/turn_de_rham_cohomology_into_algebra' into t/29581/new_algorithm

d22ee9a  Trac #32315: support iteration and enumerated sets

16c4737  Trac #32272: allow infinite max degree

6a320a0  Trac #32272: fix docstring

c1d4fce  Trac #32272: fix rst file + rename module

25e6b1d  Trac #32272: fix doctest

5a4c7ac  Trac #32272: narrow to finite dimensions

3b81085  Merge branch 't/32272/finitely_generated_graded_algebras_with_finite_degree' into t/29581/new_algorithm

ab288d6  Trac #29581: algorithm for complex vbundles

comment:29 Changed 5 months ago by
 Dependencies set to #32270, #32272
comment:30 Changed 5 months ago by
 Commit changed from ab288d62786a40b9f314d40ca932506d7b6932d9 to 6688740017097a79d7995101889cea097ee5c653
comment:31 Changed 5 months ago by
 Commit changed from 6688740017097a79d7995101889cea097ee5c653 to 61291f406b886abb9a509955355da749fc99a8d6
Branch pushed to git repo; I updated commit sha1. New commits:
61291f4  Trac #29581: minor fixes

comment:32 Changed 5 months ago by
 Commit changed from 61291f406b886abb9a509955355da749fc99a8d6 to 60318775e9c530c32280ba1bfa819cb9ac978bd1
Branch pushed to git repo; I updated commit sha1. New commits:
6031877  Trac #29581: return only list of generators

comment:33 Changed 5 months ago by
 Commit changed from 60318775e9c530c32280ba1bfa819cb9ac978bd1 to 0c7587f759b9555404fd417ee042e99fbb4ae02d
Branch pushed to git repo; I updated commit sha1. New commits:
0c7587f  Trac #29581: parent deals with different cases, element stays generic

comment:34 Changed 5 months ago by
 Commit changed from 0c7587f759b9555404fd417ee042e99fbb4ae02d to 28d2d84271a3e1516556a8364b1114dd6edaa992
Branch pushed to git repo; I updated commit sha1. New commits:
28d2d84  Trac #29581: revert mistaken merge

comment:35 Changed 5 months ago by
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
 Commit changed from 28d2d84271a3e1516556a8364b1114dd6edaa992 to 2cabd839d55e5c0f3ba2f8d0194bcae6ce31397c
Branch pushed to git repo; I updated commit sha1. New commits:
2cabd83  Trac #29581: add some comments

comment:37 Changed 5 months ago by
 Dependencies changed from #32270, #32272 to #32270, #32272, #32396
comment:38 Changed 5 months ago by
 Description modified (diff)
New commits:
Trac #29570: alternating_form returns correct element
Trac #29570: Typo fixed, doctest added, returned element preferably nonzero
Trac #29581: New Algorithm for Char Classes