def apply_to(self, expression: Expression) -> List[Expression]:
from_side = self.left
to_side = self.right
# Get the subtrees of the expression that have the same root as from side.
# by level means that we also get the level of that subtree to know if the
# subtree could match from_side
subtrees = expression.get_subtrees_with_root_func_by_level(from_side)
from_side_depth = from_side.get_depth()
expression_depth = expression.get_depth()
results = []
for subtree in subtrees:
sub_expression = subtree['expression']
level = subtree['level']
# Example Derivative(x) have depth 2 and Derivative(f(x)+g(x)) have depth 3
# So, if the depth of the subtree is less than the from_side of the theorem
# it can't be applied
if level <= expression_depth - from_side_depth:
application_possibilities = self._apply_to(sub_expression, from_side, to_side)
for possibility in application_possibilities:
if sub_expression != expression:
# Example:
# expression cos(x) + Derivative(2*x)
# sub_expression = Derivative(2*x)
# possibility = 2 * Derivative(x)
# replace sub_expression with possibility
# result = cos(x) + 2 * Derivative(x)
result = expression.get_copy()
result.replace(sub_expression,
possibility)
else:
result = possibility
results += [result]
return results
def test_get_depth_with_user_defined_func(self):
expression = Expression("Derivative(f(x) + g(x), x)", is_latex=False)
self.assertEquals(3, expression.get_depth())