#28600 closed defect (fixed)

Use standard notation for pullback and pushforward on manifolds

Reported by: gh-DeRhamSource Owned by:
Priority: major Milestone: sage-9.0
Component: geometry Keywords: manifolds, pushforward, pullback
Cc: egourgoulhon Merged in:
Authors: Eric Gourgoulhon Reviewers: Michael Jung
Report Upstream: N/A Work issues:
Branch: cb3c97e (Commits) Commit: cb3c97ec7d4575725eedfcf12f4b02c48fc35a49
Dependencies: Stopgaps:

Description

At this stage, the pushforward of a vector field v along a differentiable map Phi reads Phi^*v. This contradicts the common literature where the pushforward usually writes Phi_*v.

In this ticket, a discussion is wanted and eventually a correction is performed.

Change History (11)

comment:1 follow-up: Changed 11 months ago by egourgoulhon

It seems to me that in some texts, Phi^* and Phi_* are used to denote respectively the pushforward and the pullback. I'll look for some precise references.

comment:2 Changed 11 months ago by gh-DeRhamSource

Yeah, it's always about conventions and historical remains...

Basically, this is not completely trustworthy, but here is an approach of explaination on stackexchange.

comment:3 in reply to: ↑ 1 ; follow-up: Changed 11 months ago by egourgoulhon

Replying to egourgoulhon:

It seems to me that in some texts, Phi^* and Phi_* are used to denote respectively the pushforward and the pullback. I'll look for some precise references.

Well, I could not find any such reference... Moreover, I agree that in the common literature, the pushforward is denoted by Phi_* while the pullback is denoted by Phi^*. In particular, this holds for Lee's textbooks, which we use as references in the documentation of manifolds. So I am fully OK in adopting such notation. By the way, where in the current Sage documentation have you seen the opposite convention?

comment:4 in reply to: ↑ 3 Changed 11 months ago by egourgoulhon

Replying to egourgoulhon:

By the way, where in the current Sage documentation have you seen the opposite convention?

OK, I found it: it is not in the documentation but in the code of the method pushforward(), in lines 1273 and 1275 of src/sage/manifolds/differentiable/diff_map.py.

comment:5 Changed 11 months ago by egourgoulhon

  • Authors set to Eric Gourgoulhon
  • Branch set to public/manifolds/pullback_pushforward_notation
  • Commit set to cb3c97ec7d4575725eedfcf12f4b02c48fc35a49
  • Status changed from new to needs_review

New commits:

cb3c97eChange notation of pullback and pushforward

comment:6 Changed 11 months ago by egourgoulhon

  • Keywords pullback added
  • Summary changed from Manifolds: Pushforward to Use standard notation for pullback and pushforward on manifolds

comment:7 Changed 11 months ago by egourgoulhon

  • Priority changed from minor to major
  • Type changed from enhancement to defect

comment:8 follow-up: Changed 11 months ago by gh-DeRhamSource

Looks good to me. All tests passed and the docbuild looks fine. The notebooks run fine as well. Remember, you should edit the comments in the notebook files on your homepage, too.

Should I give a positive review?

comment:9 in reply to: ↑ 8 Changed 11 months ago by egourgoulhon

Replying to gh-DeRhamSource:

Looks good to me. All tests passed and the docbuild looks fine. The notebooks run fine as well. Remember, you should edit the comments in the notebook files on your homepage, too.

Should I give a positive review?

Given what you said above, I think you may ;-)

comment:10 Changed 11 months ago by gh-DeRhamSource

  • Reviewers set to Michael Jung
  • Status changed from needs_review to positive_review

comment:11 Changed 11 months ago by vbraun

  • Branch changed from public/manifolds/pullback_pushforward_notation to cb3c97ec7d4575725eedfcf12f4b02c48fc35a49
  • Resolution set to fixed
  • Status changed from positive_review to closed
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