Opened 3 years ago
Last modified 3 years ago
#28554 closed enhancement
Scalar Field Restrictions — at Version 3
Reported by:  ghDeRhamSource  Owned by:  

Priority:  major  Milestone:  sage9.0 
Component:  geometry  Keywords:  manifolds, scalar fields 
Cc:  tscrim, egourgoulhon  Merged in:  
Authors:  Reviewers:  
Report Upstream:  N/A  Work issues:  
Branch:  u/ghDeRhamSource/scalar_field_restrictions (Commits, GitHub, GitLab)  Commit:  0c645ca987eb13c63cfc7841aac1c4d320eec253 
Dependencies:  Stopgaps: 
Description (last modified by )
How is a scalar field implemented which is split into different expressions in one particular chart?
Take for instance a scalar field f
on the real line with standard "top" chart x
, defined via f(x)=0 for x<1
, f(x)=x+1 for 1<=x<0
, f(x)=1x for 0<=x<1
and f(x)=0 for x>=1
. Currently, this is solved by using
f = M.scalar_field( unit_step(x + 1)*unit_step(1  x)*(1  abs(x)) )
(see https://trac.sagemath.org/ticket/28519#comment:46).
This solution is quite unhandy and becomes even more so for more complicated scalar fields.
How is a scalar field implemented which is split into different expressions in one particular chart?
Take for instance a scalar field f
on the real line with standard "top" chart x
, defined via f(x)=0 for x<1
, f(x)=x+1 for 1<=x<0
, f(x)=1x for 0<=x<1
and f(x)=0 for x>=1
. Currently, this is solved by using
f = M.scalar_field( unit_step(x + 1)*unit_step(1  x)*(1  abs(x)) )
(see https://trac.sagemath.org/ticket/28519#comment:46).
This solution is quite unhandy and becomes even more so for more complicated scalar fields.
This ticket includes:
 modification of namings after algebraic operations, such as
f*g
(f \cdot g
for LaTeX code),f/g
andf+g
display
method modified in such a way that all distinct expressions are shown (a small slowdown in computation time)set_restriction
method added smilar to tensor fields_is_zero
attribute copied for a copy
Change History (3)
comment:1 Changed 3 years ago by
comment:2 Changed 3 years ago by
 Branch set to u/ghDeRhamSource/scalar_field_restrictions
comment:3 Changed 3 years ago by
 Commit set to 0c645ca987eb13c63cfc7841aac1c4d320eec253
 Description modified (diff)
New commits:
0c645ca  'set_restriction' added + 'display' modified + naming modified

Eric, in the ticket mentioned above, I suggested to display all known expressions (on the greatest domain) and compute new expressions only if a particular chart is stated. It seems, there is no big difference to the previous code then, and the additional computation time might be negligible. What do you say? Is this a good compromise for you? Moreover, this approach seems to be the easiest one.
Or one implements an additional flag
display_all
for which the user is aware of additional computation time when using it?However, do you have an example for me with much computation time to test my current algorithm how long it takes? Then, I can compare computation times. I have a feeling that the current algorithm is not that much slower than before because it starts from the top charts  what happens anyway and, I guess, it only makes a significant difference if the scalar field is picewisely defined.