Opened 2 years ago
Closed 2 years ago
#28600 closed defect (fixed)
Use standard notation for pullback and pushforward on manifolds
Reported by:  ghDeRhamSource  Owned by:  

Priority:  major  Milestone:  sage9.0 
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, GitHub, GitLab)  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 followup: ↓ 3 Changed 2 years ago by
comment:2 Changed 2 years ago by
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 ; followup: ↓ 4 Changed 2 years ago by
Replying to egourgoulhon:
It seems to me that in some texts,
Phi^*
andPhi_*
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 2 years ago by
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 2 years ago by
 Branch set to public/manifolds/pullback_pushforward_notation
 Commit set to cb3c97ec7d4575725eedfcf12f4b02c48fc35a49
 Status changed from new to needs_review
New commits:
cb3c97e  Change notation of pullback and pushforward

comment:6 Changed 2 years ago by
 Keywords pullback added
 Summary changed from Manifolds: Pushforward to Use standard notation for pullback and pushforward on manifolds
comment:7 Changed 2 years ago by
 Priority changed from minor to major
 Type changed from enhancement to defect
comment:8 followup: ↓ 9 Changed 2 years ago by
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 2 years ago by
Replying to ghDeRhamSource:
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 2 years ago by
 Reviewers set to Michael Jung
 Status changed from needs_review to positive_review
comment:11 Changed 2 years ago by
 Branch changed from public/manifolds/pullback_pushforward_notation to cb3c97ec7d4575725eedfcf12f4b02c48fc35a49
 Resolution set to fixed
 Status changed from positive_review to closed
It seems to me that in some texts,
Phi^*
andPhi_*
are used to denote respectively the pushforward and the pullback. I'll look for some precise references.