Issue 1139: Description and Differentiation of vector, tensor, and
multivector fields.
http://code.google.com/p/sympy/issues/detail?id=1139
Comment #24 by [EMAIL PROTECTED]:
I am almost there, but need to understand the following code:
import sympy,types
class ImplicitFunction(sympy.Function):
def __new__(cls,Fstr,vars):
vars = tuple(vars)
obj = sympy.Function.__new__(cls, Fstr, *vars)
return obj
def __init__(self,Fstr,vars):
self.vars = tuple(vars)
sympy.Function.__init__(self,Fstr,self.vars)
return
def deriv(self,var):
return(ImplicitDerivative(self,var))
class ImplicitDerivative(sympy.Derivative):
def __init__(self,f,var):
self.vars = f.vars
if type(var) == types.IntType:
xvar = self.vars[var]
print 'self.vars[var] =',xvar
sympy.Derivative(f,xvar)
else:
sympy.Derivative(f,var)
return
def deriv(self,var):
df = ImplicitDerivative(self,var)
return(df)
x = sympy.symbols('x1','x2')
x1 = x[0]
x2 = x[1]
print x
f = ImplicitFunction('f',x)
print 'f =',f
df = f.deriv(0)
print 'df =',df
d2f = df.deriv(1)
print d2f
df = f.deriv(x1)
print 'df =',df
d2f = df.deriv(x2)
print d2f
The output of this code is:
[x1, x2]
f = ImplicitFunction(f, x1, x2)
self.vars[var] = x1
df = D(ImplicitFunction(f, x1, x2))
self.vars[var] = x2
D(D(ImplicitFunction(f, x1, x2)))
df = D(ImplicitFunction(f, x1, x2), x1)
D(D(ImplicitFunction(f, x1, x2), x1), x2)
so we have
F.deriv(1) = D(ImplicitFunction(f, x1, x2))
but
F.deriv(x2) = D(ImplicitFunction(f, x1, x2), x1)
which is correct. From the code they should give the same answer. Why not?
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