Opened 20 months ago
Closed 18 months ago
#31609 closed enhancement (fixed)
Add method tangent_vector to differentiable manifolds
Reported by:  Eric Gourgoulhon  Owned by:  

Priority:  major  Milestone:  sage9.4 
Component:  manifolds  Keywords:  tangent vector 
Cc:  Samuel Lelièvre  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, T_{p}M, and then construct v as an element of T_{p}M. 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 1step 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 20 months ago by
Branch:  → public/manifolds/tangent_vector31609 

Cc:  Samuel Lelièvre added 
Commit:  → 5b225961f67c6a01b238e657549cf6a9e7e11d05 
Status:  new → needs_review 
comment:2 Changed 20 months ago by
Sweet! I have just one comment. Since Python 3.6, we have fstrings which are way more convenient and easier to read than format
(and also faster). I'd propose to use fstrings 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 followup: 5 Changed 20 months ago by
Here is an explanation also elaborating on more advantages of fstrings over format
: https://realpython.com/pythonfstrings/.
comment:4 Changed 20 months ago by
Commit:  5b225961f67c6a01b238e657549cf6a9e7e11d05 → c4a76e92ff90733bf484265c1d0421152db252c8 

Branch pushed to git repo; I updated commit sha1. New commits:
c4a76e9  Use fstring in DifferentialManifold.vector

comment:5 Changed 20 months ago by
Replying to ghmjungmath:
Here is an explanation also elaborating on more advantages of fstrings over
format
: https://realpython.com/pythonfstrings/.
Thanks for the tip! The change to fstring is performed in the last commit.
comment:6 followup: 7 Changed 20 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 Changed 20 months ago by
Replying to ghmjungmath:
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 followup: 11 Changed 20 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 followup: 12 Changed 20 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 20 months ago by
Commit:  c4a76e92ff90733bf484265c1d0421152db252c8 → 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 followup: 15 Changed 20 months ago by
Description:  modified (diff) 

Summary:  Add method vector to differentiable manifolds → Add method tangent_vector to differentiable manifolds 
Replying to ghmjungmath:
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 Changed 20 months ago by
Replying to ghmjungmath:
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 followup: 14 Changed 20 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 Changed 20 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 in the doctests).
comment:15 Changed 20 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 20 months ago by
Reviewers:  → Michael Jung 

comment:19 Changed 20 months ago by
Milestone:  sage9.3 → sage9.4 

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 18 months ago by
Branch:  public/manifolds/tangent_vector31609 → b5d7a8f800fb496de28a5e89cabac2250b124c6f 

Resolution:  → fixed 
Status:  positive_review → closed 
New commits:
Add method vector() to DifferentiableManifold