Opened 18 months ago
Closed 18 months ago
#27581 closed enhancement (fixed)
Initializing the components of a tensor field while declaring it
Reported by:  egourgoulhon  Owned by:  

Priority:  major  Milestone:  sage8.8 
Component:  geometry  Keywords:  tensor field, manifold 
Cc:  tscrim  Merged in:  
Authors:  Eric Gourgoulhon  Reviewers:  Travis Scrimshaw 
Report Upstream:  N/A  Work issues:  
Branch:  990a858 (Commits)  Commit:  990a858f1ce18c6537f9c6de7603dcc58f4b9cc2 
Dependencies:  Stopgaps: 
Description (last modified by )
Currently (Sage 8.7), the definition of a tensor field on a differentiable manifold is a 2step operation. For instance, for a vector field:
sage: M = Manifold(2, 'M') sage: X.<x,y> = M.chart() sage: v = M.vector_field() # step 1: declaration sage: v[:] = y, x # step 2: initialization of components sage: v.display() y d/dx + x d/dy
This ticket adds the possibility to perform the definition in a single step:
sage: v = M.vector_field(y, x) sage: v.display() y d/dx + x d/dy
Moreover, some flexibility is introduced in passing the components: it can be a list:
sage: M.vector_field([y, x]).display() y d/dx + x d/dy
or more generally any iterable, like a vector of symbolic expressions:
sage: M.vector_field(vector([y, x])).display() y d/dx + x d/dy
The components can also be provided in a vector frame distinct from the default one:
sage: f = M.vector_frame('f') sage: M.vector_field(y^2, 1, frame=f).display(f) y^2 f_0  f_1
An alternative is passing a dictionary, the keys of which are the vector frames in which the components are defined:
sage: M.vector_field({f: [y^2, 1]}).display(f) y^2 f_0  f_1
The dictionary is mandatory if the components are given in various frames at once:
sage: M.vector_field({X.frame(): [y, x], f: [y^2, 1]}).display(f) y^2 f_0  f_1
Note that the possibility of initializing the components while declaring a vector field was introduced on Euclidean spaces in #24623. This ticket extends this to any kind of differentiable manifold and any kind of tensor field. Accordingly, the redefinition of the method vector_field
in the class EuclideanSpace
has been suppressed: it falls back now to the method vector_field
of the mother class DifferentiableManifold
.
Basically the (optional) component initialization is performed by the method TensorField._init_components
, which is invoked by all the enduser methods devoted to the creation of tensor fields on manifolds, i.e. the methods automorphism_field
, diff_form
, multivector_field
, one_form
, sym_bilin_form_field
, tensor_field
and vector_field
of class DifferentiableManifold
.
Change History (8)
comment:1 Changed 18 months ago by
 Branch set to public/manifolds/tensor_init_comp
 Cc tscrim added
 Commit set to ce2b064f6be21e4e4b1f321d79fb15725dd8d53c
 Status changed from new to needs_review
comment:2 Changed 18 months ago by
 Status changed from needs_review to needs_work
Have to fix some merge conflict with Sage 8.8.beta0.
comment:3 Changed 18 months ago by
 Commit changed from ce2b064f6be21e4e4b1f321d79fb15725dd8d53c to 990a858f1ce18c6537f9c6de7603dcc58f4b9cc2
Branch pushed to git repo; I updated commit sha1. New commits:
990a858  Merge branch 'public/manifolds/tensor_init_comp' of git://trac.sagemath.org/sage into Sage 8.8.beta0

comment:4 Changed 18 months ago by
 Status changed from needs_work to needs_review
Merge conflict solved.
comment:5 Changed 18 months ago by
 Description modified (diff)
comment:6 Changed 18 months ago by
 Reviewers set to Travis Scrimshaw
 Status changed from needs_review to positive_review
LGTM.
comment:7 Changed 18 months ago by
Thanks for the review!
comment:8 Changed 18 months ago by
 Branch changed from public/manifolds/tensor_init_comp to 990a858f1ce18c6537f9c6de7603dcc58f4b9cc2
 Resolution set to fixed
 Status changed from positive_review to closed
New commits:
Add possibility to initialize the components while creating a vector field
Add possibility to initialize the components while creating a differential form
Add possibility to initialize the components while creating a tensor field
Add possibility to initialize the components while creating a field of tangentspace automorphisms
Add possibility to initialize the components while creating a multivector field
Final clean up regarding the initialization of components at tensor field construction