def _apply_to(self, expression: Expression, from_side: Expression, to_side: Expression) -> List[Expression]:
application_possibilities = []
template = from_side
# Apply to general structure
logger.debug("Trying to apply: " + self.name +
" to the general structure: " + str(expression))
analysis = self.analyzer.analyze(template, self.conditions, expression)
if analysis.expression_match_template:
application_possibilities.append(
self.transform_side(to_side, analysis.equalities))
# Apply to children
logger.debug("Trying to apply: " + self.name +
" to expression CHILDREN: " + str(expression))
children_transformations = self.apply_to_children(
expression, from_side, to_side)
for child_transformation in children_transformations:
result = expression.get_copy()
result.replace(child_transformation.before,
child_transformation.after)
application_possibilities.append(result)
return application_possibilities
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
class Theorem:
# left and right could be expressions or str
def __init__(self,
name: str,
left: Union['Expression', str],
right: Union['Expression', str],
conditions: dict):
self.name = name
if left is not None and right is not None:
self.left = Expression(left)
self.right = Expression(right)
else:
self.left = Expression(sympy.nan)
self.right = Expression(sympy.nan)
self.conditions = conditions
self.analyzer = TemplateMatchAnalyzer()
def to_json(self) -> dict:
left = ''
right = ''
if self.left is not None:
left = self.left.to_latex_with_derivatives()
if self.right is not None:
right = self.right.to_latex_with_derivatives()
return {
'name': self.name,
'right': right,
'left': left,
'conditions': self.conditions if 'conditions' is not None else {}
}
# Returns the application possibilities (could be more than 1)
def apply_reverse_to(self, expression: Expression) -> List[Expression]:
from_side = self.right
to_side = self.left
return self._apply_to(expression, from_side, to_side)
def there_is_a_chance_to_apply_to(self, expression: Expression):
return expression.operators_and_levels_match(self.left)
# Returns the application possibilities (could be more than 1)
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 _apply_to(self, expression: Expression, from_side: Expression, to_side: Expression) -> List[Expression]:
application_possibilities = []
template = from_side
# Apply to general structure
logger.debug("Trying to apply: " + self.name +
" to the general structure: " + str(expression))
analysis = self.analyzer.analyze(template, self.conditions, expression)
if analysis.expression_match_template:
application_possibilities.append(
self.transform_side(to_side, analysis.equalities))
# Apply to children
logger.debug("Trying to apply: " + self.name +
" to expression CHILDREN: " + str(expression))
children_transformations = self.apply_to_children(
expression, from_side, to_side)
for child_transformation in children_transformations:
result = expression.get_copy()
result.replace(child_transformation.before,
child_transformation.after)
application_possibilities.append(result)
return application_possibilities
def apply_to_children(self, expression: Expression, from_side: Expression, to_side: Expression) -> List[Expression]:
application_possibilities = []
template = from_side
already_tried = set()
# try applying to groups of children
# for example in x + y + z
# try with: x + y ; x + z : y + z
if expression.can_group_children():
logger.info("Trying to apply: " + self.name +
" to a group children: " + str(expression))
for size in range(2, expression.children_amount() + 1):
children_of_size_n_possibilities = expression.get_child_with_size_possibilities(
size)
for child_of_size_n in children_of_size_n_possibilities:
if str(child_of_size_n) not in already_tried:
analysis = self.analyzer.analyze(
template, self.conditions, child_of_size_n)
if analysis.expression_match_template:
application_possibilities.append(TheoremApplication(
child_of_size_n, self.transform_side(to_side, analysis.equalities)))
already_tried.add(str(child_of_size_n))
return application_possibilities
def transform_right_side(self, equalities: List[Equality]) -> Expression:
result = self.right.get_copy()
for equality in equalities:
result.replace(equality.template, equality.expression)
return result
def transform_side(self, side: Expression, equalities: List[Equality]) -> Expression:
result = side.get_copy()
for equality in equalities:
result.replace(equality.template, equality.expression)
return result
def __str__(self):
return self.name + ' - ' + self.left.to_string() + " = " + self.right.to_string()
def transform_side(self, side: Expression, equalities: List[Equality]) -> Expression:
result = side.get_copy()
for equality in equalities:
result.replace(equality.template, equality.expression)
return result
