def _expand_partial_derivative(self):
args, indices, free, dum = self._contract_indices_for_derivative(
self.expr, self.variables)
obj = self.func(*args)
obj._indices = indices
obj._free = free
obj._dum = dum
result = obj
if not args[0].free_symbols:
return S.Zero
elif isinstance(obj.expr, TensAdd):
# take care of sums of multi PDs
result = obj.expr.func(*[
self.func(a, *obj.variables)._expand_partial_derivative()
for a in result.expr.args
])
elif isinstance(obj.expr, TensMul):
# take care of products of multi PDs
if len(obj.variables) == 1:
# derivative with respect to single variable
terms = []
mulargs = list(obj.expr.args)
for ind in range(len(mulargs)):
if not isinstance(sympify(mulargs[ind]), Number):
# a number coefficient is not considered for
# expansion of PartialDerivative
d = self.func(
mulargs[ind],
*obj.variables)._expand_partial_derivative()
terms.append(
TensMul(*(mulargs[:ind] + [d] +
mulargs[(ind + 1):])))
result = TensAdd.fromiter(terms)
else:
# derivative with respect to multiple variables
# decompose:
# partial(expr, (u, v))
# = partial(partial(expr, u).doit(), v).doit()
result = obj.expr # init with expr
for v in obj.variables:
result = self.func(result, v)._expand_partial_derivative()
# then throw PD on it
return result
