Opened 15 months ago
Closed 13 months ago
#31609 closed enhancement (fixed)
Add method tangent_vector to differentiable manifolds
Reported by: | egourgoulhon | Owned by: | |
---|---|---|---|
Priority: | major | Milestone: | sage-9.4 |
Component: | manifolds | Keywords: | tangent vector |
Cc: | slelievre | Merged in: | |
Authors: | Eric Gourgoulhon | Reviewers: | Michael Jung |
Report Upstream: | N/A | Work issues: | |
Branch: | b5d7a8f (Commits, GitHub, GitLab) | Commit: | b5d7a8f800fb496de28a5e89cabac2250b124c6f |
Dependencies: | Stopgaps: |
Description (last modified by )
Currently, constructing a tangent vector v at some point p of a manifold M requires two steps: first construct the tangent space at p, TpM, and then construct v as an element of TpM. For instance:
sage: E.<x,y> = EuclideanSpace() sage: p = E((1, 2), name='p') sage: Tp = E.tangent_space(p) # step 1 sage: v = Tp((-1, 3)); v # step 2 Vector at Point p on the Euclidean plane E^2
This ticket endows the class DifferentiableManifold
with a method tangent_vector
, with vector
as an alias, to make it a 1-step process. We can now write:
sage: E.<x,y> = EuclideanSpace() sage: p = E((1, 2), name='p') sage: v = E.vector(p, -1, 3); v Vector at Point p on the Euclidean plane E^2
This feature is motivated by this ask.sagemath question.
Change History (20)
comment:1 Changed 15 months ago by
- Branch set to public/manifolds/tangent_vector-31609
- Cc slelievre added
- Commit set to 5b225961f67c6a01b238e657549cf6a9e7e11d05
- Status changed from new to needs_review
comment:2 Changed 15 months ago by
Sweet! I have just one comment. Since Python 3.6, we have f-strings which are way more convenient and easier to read than format
(and also faster). I'd propose to use f-strings more often in the future. For this ticket:
- raise ValueError("{} components must be provided".format(dim)) + raise ValueError(f"{dim} components must be provided")
comment:3 follow-up: ↓ 5 Changed 15 months ago by
Here is an explanation also elaborating on more advantages of f-strings over format
: https://realpython.com/python-f-strings/.
comment:4 Changed 15 months ago by
- Commit changed from 5b225961f67c6a01b238e657549cf6a9e7e11d05 to c4a76e92ff90733bf484265c1d0421152db252c8
Branch pushed to git repo; I updated commit sha1. New commits:
c4a76e9 | Use f-string in DifferentialManifold.vector
|
comment:5 in reply to: ↑ 3 Changed 15 months ago by
Replying to gh-mjungmath:
Here is an explanation also elaborating on more advantages of f-strings over
format
: https://realpython.com/python-f-strings/.
Thanks for the tip! The change to f-string is performed in the last commit.
comment:6 follow-up: ↓ 7 Changed 15 months ago by
Is there a reason why you chose vector
over tangent_vector
for the method's name? The latter would sound more intuitive to me.
comment:7 in reply to: ↑ 6 Changed 15 months ago by
Replying to gh-mjungmath:
Is there a reason why you chose
vector
overtangent_vector
for the method's name? The latter would sound more intuitive to me.
vector
is more adapted to elementary use, like in vector calculus in the Euclidean space, when the user might not know what "tangent space" means. Of course, we can make an alias for tangent_vector
if you feel it necessary.
comment:8 follow-up: ↓ 11 Changed 15 months ago by
Mh, I don't know. Manifolds usually don't constitute of vectors. So a vector
method wouldn't make much sense there as it sounds to me more like a method that should be reserved for vector spaces only. I'd advocate to rename vector
to tangent_vector
because mathematically precise.
This is a neat feature though, and I don't want to block it just because of my pedantry. An alias sounds like a good compromise.
comment:9 follow-up: ↓ 12 Changed 15 months ago by
Alternatively the Euclidean space, as a special case, can be endowed with an alias vector
whereas general (differentiable) manifolds only supposed to have tangent_vector
. I think that is the best solution to maintain preciseness and having that alias in the elementary case at the same time.
comment:10 Changed 15 months ago by
- Commit changed from c4a76e92ff90733bf484265c1d0421152db252c8 to b5d7a8f800fb496de28a5e89cabac2250b124c6f
Branch pushed to git repo; I updated commit sha1. New commits:
b5d7a8f | Rename vector to tangent_vector and make vector an alias to it
|
comment:11 in reply to: ↑ 8 ; follow-up: ↓ 15 Changed 15 months ago by
- Description modified (diff)
- Summary changed from Add method vector to differentiable manifolds to Add method tangent_vector to differentiable manifolds
Replying to gh-mjungmath:
Mh, I don't know. Manifolds usually don't constitute of vectors. So a
vector
method wouldn't make much sense there as it sounds to me more like a method that should be reserved for vector spaces only. I'd advocate to renamevector
totangent_vector
because mathematically precise.
OK, this is done in the last commit. Note however that saying simply "vector at point p of manifold M" is quite unambiguous and is in line with the terminology "vector field": we do not say "tangent vector field", do we?
This is a neat feature though, and I don't want to block it just because of my pedantry. An alias sounds like a good compromise.
Done. vector
is now an alias for tangent_vector
.
comment:12 in reply to: ↑ 9 Changed 15 months ago by
Replying to gh-mjungmath:
Alternatively the Euclidean space, as a special case, can be endowed with an alias
vector
whereas general (differentiable) manifolds only supposed to havetangent_vector
. I think that is the best solution to maintain preciseness and having that alias in the elementary case at the same time.
I oppose to this: we shall not introduce on Euclidean spaces method names that break for more general manifolds, while the functionality is exactly the same.
comment:13 follow-up: ↓ 14 Changed 15 months ago by
How about requiring
v = E.vector(p, (-1, 3))
instead of
v = E.vector(p, -1, 3)
I don't mind either way but there's a choice to make.
comment:14 in reply to: ↑ 13 Changed 15 months ago by
Replying to slelievre:
How about requiring
v = E.vector(p, (-1, 3))instead of
v = E.vector(p, -1, 3)I don't mind either way but there's a choice to make.
There is no choice to make ;-) Both work in the current implementation (cf. the examples).
comment:15 in reply to: ↑ 11 Changed 15 months ago by
Replying to egourgoulhon:
OK, this is done in the last commit. Note however that saying simply "vector at point p of manifold M" is quite unambiguous and is in line with the terminology "vector field": we do not say "tangent vector field", do we?
No, we don't say "tangent vector field". But I haven't heard or read the use of "vector" over "tangent vector" either. Historical burden I suppose.
It should be unambiguous though and having both is fine with me. Someone who seeks for (tangent) vectors will find them now.
comment:17 Changed 15 months ago by
- Reviewers set to Michael Jung
comment:18 Changed 15 months ago by
Thanks for the review and suggestions!
comment:19 Changed 15 months ago by
- Milestone changed from sage-9.3 to sage-9.4
Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review.
comment:20 Changed 13 months ago by
- Branch changed from public/manifolds/tangent_vector-31609 to b5d7a8f800fb496de28a5e89cabac2250b124c6f
- Resolution set to fixed
- Status changed from positive_review to closed
New commits:
Add method vector() to DifferentiableManifold