Opened 15 years ago
Closed 8 years ago
#3021 closed enhancement (fixed)
add curl and divergence functions to vectors
Reported by:  Jason Grout  Owned by:  William Stein 

Priority:  major  Milestone:  sage6.4 
Component:  calculus  Keywords:  
Cc:  Eviatar Bach  Merged in:  
Authors:  Robert Bradshaw  Reviewers:  Eviatar Bach, Samuel Lelièvre, Travis Scrimshaw 
Report Upstream:  N/A  Work issues:  
Branch:  7b49240 (Commits, GitHub, GitLab)  Commit:  7b49240972f369a441432b2e2736b9dbc65d1337 
Dependencies:  Stopgaps: 
Description
Make curl work if the vector has 2 or 3 components. Is there a higherdimensional analogue for curl?
Change History (30)
comment:1 Changed 15 years ago by
comment:2 Changed 13 years ago by
# a possible implementation of div, for irc user hedgehog var('x, y, z') (x, y, z) f1 = x^2 + 2*y; f2 = x^3 + sin(z); f3 = y*z + 2 F = vector([f1, f2, f3]) print F(x=0, y=2, z=3) def _variables(F): # this is a little funky  we're finding all the variables that occur # in the components of F, and somehow choosing an ordering. There are # other (better ways) but I'm not sure what the correct interface is. # For now, the user can specify the variables if they choose, just # like the gradient method. variables = list(set(flatten([ list(f.variables()) for f in F ]))) variables.sort() return variables def div(F, variables=None): assert len(F) == 3 if variables is None: variables = _variables(F) s = 0 for i in range(len(F)): s += F[i].derivative(variables[i]) return s print F print div(F) print div(F, variables=(y, x, z)) def curl(F, variables=None): assert len(F) == 3 if variables is None: variables = _variables(F) assert len(variables) == 3 x, y, z = variables Fx, Fy, Fz = F i = Fz.derivative(y)  Fy.derivative(z) j = Fz.derivative(z)  Fx.derivative(x) k = Fy.derivative(x)  Fz.derivative(y) return vector([i, j, k]) print curl(F) print curl(F, variables=(y, x, z)) # let's assert that div(curl) == 0 # we need the variables because the ordering is suspect otherwise: for me, # sage: _variables(F) # [x, y, z] # sage: _variables(curl(F)) # [z, x, y] assert div(curl(F, variables=(x, y, z)), variables=(x, y, z)) == 0
comment:3 Changed 13 years ago by
Report Upstream:  → N/A 

See #5506 for a collection of things to add to a symbolic vectors class
comment:5 Changed 13 years ago by
Summary:  add curl and divergence functions to symbolic vectors → add curl and divergence functions to vectors 

What generic curl (I don't think it's in Sage right now)? Or are you saying we should just add curl to generic vectors? I agree; no reason to add this to just the callable symbolic vectors class (what was I thinking?).
comment:6 Changed 11 years ago by
Note that in the code above, it should be:
k = Fy.derivative(x)  Fx.derivative(y)
The "Fz
" should be "Fx
".
comment:8 Changed 9 years ago by
Milestone:  sage5.11 → sage5.12 

comment:9 Changed 9 years ago by
Milestone:  sage6.1 → sage6.2 

comment:10 Changed 9 years ago by
Cc:  Eviatar Bach added 

comment:11 Changed 9 years ago by
Branch:  → u/robertwb/ticket/3021 

Modified:  Mar 11, 2014, 7:34:59 AM → Mar 11, 2014, 7:34:59 AM 
comment:12 followup: 14 Changed 9 years ago by
Commit:  → 4e34d0d90624c54e233be003c460c3bbaf6e3dcf 

Status:  new → needs_review 
New commits:
4e34d0d  Add divergence and curl to vectors.

comment:13 Changed 9 years ago by
I was just going to work on this today!
I haven't tested the code, but looks good. Just a few things:
 Is there any reason why you're converting the variables to their string representations in
._variables()
?  The parameter in
Expression.gradient
is calledvariables
; I think it would be good to switchvars
tovariables
for consistency.  I think there should be test(s) for
.curl()
with the variables parameter.  I believe the
raise TypeError, "curl only defined for 3 dimensions"
syntax is deprecated, and that the string should be passed as an argument.
comment:14 Changed 9 years ago by
Nitpicking on the error message in div
: I would change it from "variable list must be equal to the dimension of self"
to "number of variables must equal dimension of self"
.
About point 4 in eviatarbach's comment:
 A reference for the change in exception raising syntax is PEP3109.
 the
ValueError
indiv
on follows the new syntax. By contrast, both theTypeError
andValueError
incurl
follow the old syntax.
comment:15 Changed 9 years ago by
More nitpicking:
 Use "Return" instead of "Returns" in docstrings, see PEP 0257:
The docstring is a phrase ending in a period. It prescribes the function or method's effect as a command ("Do this", "Return that"), not as a description; e.g. don't write "Returns the pathname ...".
 Should there be a docstring and tests for the
_variables
function?  In examples for
div
, remove extra space beforew
inR.<x,y,z, w> = QQ[]
comment:16 Changed 9 years ago by
Another thought:
The extracting of variables from each element and then sorting by name looks scary, and can give unexpected results (if your vector is (x1, x10, x2)
, I believe you would get 3 for the divergence instead of 1 as you might expect, since '10'
comes before '2'
in the alphanumeric sort). Unless there's a better solution, I think we should have it so that the variables list has to always be given explicitly.
comment:17 followup: 18 Changed 9 years ago by
If your vectors are callable symbolic vectors, you should be able to get the list of arguments from the base ring (since you've already explicitly given an order to the variables):
sage: f(x,y,z)=(x*y,y*z,z^2) sage: f (x, y, z) > (x*y, y*z, z^2) sage: type(f) <class 'sage.modules.vector_callable_symbolic_dense.Vector_callable_symbolic_dense'> sage: f.base_ring().arguments() (x, y, z)
comment:18 Changed 9 years ago by
That's a great idea. I think we should have that for callable vectors.
For the record, Mathematica and Maple both have default coordinate systems, which is how they deal with this issue.
comment:19 Changed 9 years ago by
Milestone:  sage6.2 → sage6.3 

comment:20 Changed 8 years ago by
Commit:  4e34d0d90624c54e233be003c460c3bbaf6e3dcf → f353c94832b7ddd0b76d18eba32a1dd5440c3a8e 

Branch pushed to git repo; I updated commit sha1. New commits:
f353c94  Missing doctest.

comment:21 Changed 8 years ago by
Commit:  f353c94832b7ddd0b76d18eba32a1dd5440c3a8e → 8ab298e3617a2a803db07f27ad6515a1a8551821 

comment:23 Changed 8 years ago by
Milestone:  sage6.3 → sage6.4 

comment:24 followup: 25 Changed 8 years ago by
I was going to look at this, but looks like Eviatar and Samuel are on top, so just think of this as a ping :)
comment:25 Changed 8 years ago by
Replying to kcrisman:
I was going to look at this, but looks like Eviatar and Samuel are on top, so just think of this as a ping :)
Feel free to look at this yourself :)
comment:26 Changed 8 years ago by
My 2 cents, I'd have curl also take 2dim inputs and return a vector. It might also be a good idea for a way (likely another method) which takes a 2dim input and return a scalar as a shorthand (a la Green's theorem).
+1 to getting these (fundamental) methods into Sage.
comment:27 Changed 8 years ago by
Are there any enhancements to this withpatch, 7yearold ticket that simply can't be deferred 'till later so we can finally get this in?
comment:28 Changed 8 years ago by
Authors:  → Robert Bradshaw 

Branch:  u/robertwb/ticket/3021 → u/tscrim/curl_divergence3021 
Commit:  8ab298e3617a2a803db07f27ad6515a1a8551821 → 7b49240972f369a441432b2e2736b9dbc65d1337 
Reviewers:  → Eviatar Bach, Samuel Lelièvre, Travis Scrimshaw 
comment:29 Changed 8 years ago by
Status:  needs_review → positive_review 

comment:30 Changed 8 years ago by
Branch:  u/tscrim/curl_divergence3021 → 7b49240972f369a441432b2e2736b9dbc65d1337 

Resolution:  → fixed 
Status:  positive_review → closed 
(After some discussion on IRC) It seems that Sage is really lacking in the differential geometry area. If some good work is done there, this request will likely automatically be satisfied.
A short term solution would be to write a vector field class.