#3021: add curl and divergence functions to symbolic vectors
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Reporter: jason | Owner: was
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.0.2
Component: calculus | Keywords:
Reviewer: | Author:
Merged: |
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Comment(by ncalexan):
{{{
# 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
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/3021#comment:2>
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