def __add__(self, value):
if isinstance(value, Monomial) and count_variables(
value.variables) == count_variables(self.variables):
if self.coefficient + value.coefficient == 1 and len(
self.variables) == 1:
return algebra.Variable(name=self.variables)
return Monomial(coefficient=self.coefficient + value.coefficient,
variables=self.variables)
elif isinstance(value, algebra.Variable):
if value.name == self.variables:
return Monomial(coefficient=self.coefficient + 1,
variables=self.variables)
else:
return algebra.Polynomial(
monomials=[self,
algebra.Monomial(variables=value.name)])
elif isinstance(value, Fraction):
value.numerator += self * value.denominator
return value
elif isinstance(value, Monomial):
return algebra.Polynomial(monomials=[
algebra.Monomial(coefficient=self.coefficient,
variables=self.variables), value
])
elif isinstance(value, int):
return algebra.Polynomial(monomials=[
self,
], numerical_term=value)
raise TypeError(f'Cannot add Monomial to {type(value)}')
def __sub__(self, value):
if isinstance(value, algebra.Monomial) and value.variables == self.name:
return algebra.Monomial(coefficient=1 - value.coefficient, variables=self.name)
elif isinstance(value, Variable) and value.name == self.name:
return 0
elif isinstance(value, int):
return algebra.Polynomial(monomials=[algebra.Monomial(variables=self.name), ],
numerical_term=-value)
elif isinstance(value, Fraction):
return Fraction(value.numerator - self * value.denominator, value.denominator)
raise ValueError(f'Cannot subtract Variable to {type(value)}')
def __mul__(self, value):
if isinstance(value, algebra.Monomial):
return algebra.Monomial(variables=value.variables + self.name,
coefficient=value.coefficient)
elif isinstance(value, int):
return algebra.Monomial(variables=self.name, coefficient=value)
elif isinstance(value, Variable):
return algebra.Monomial(variables=self.name + value.name)
elif isinstance(value, Fraction):
return algebra.Monomial(variables=self.name, coefficient=value)
elif isinstance(value, algebra.Polynomial):
return value * self
raise TypeError(f'Cannot multiply Variable by {type(value)}')
def __sub__(self, value):
if isinstance(value, algebra.Monomial):
result = Polynomial(numerical_term=self.numerical_term)
found = False
for monomial in self.monomials:
if algebra.monomial.count_variables(monomial.variables) == algebra.monomial.count_variables(
value.variables):
if not found:
if monomial.coefficient - value.coefficient != 0:
result.monomials.append(monomial - value)
found = True
else:
result.monomials.append(monomial)
if not found:
result.monomials.append(value)
return result
elif isinstance(value, Polynomial):
result = Polynomial()
for monomial in self.monomials:
result -= monomial
for monomial in value.monomials:
result -= monomial
result.numerical_term += self.numerical_term - value.numerical_term
return result
elif isinstance(value, int):
self.numerical_term -= value
return self
elif isinstance(value, algebra.Variable):
return self - algebra.Monomial(variables=value.name, coefficient=-1)
elif isinstance(value, Fraction):
frac = Fraction(1, value.denominator) * value.numerator + self
return frac
raise TypeError(f'Cannot subtract a Polynomial to {type(value)}')
def __add__(self, value):
if isinstance(value, algebra.Monomial):
result = Polynomial(numerical_term=self.numerical_term)
found = False
for monomial in self.monomials:
if algebra.monomial.count_variables(monomial.variables) == algebra.monomial.count_variables(
value.variables):
if not found:
if monomial.coefficient + value.coefficient != 0:
result.monomials.append(monomial + value)
found = True
else:
result.monomials.append(monomial)
if not found:
result.monomials.append(value)
return result
elif isinstance(value, Polynomial):
result = algebra.Polynomial()
for monomial in self.monomials:
result += monomial
for monomial in value.monomials:
result += monomial
result += self.numerical_term + value.numerical_term
return result
elif isinstance(value, int):
self.numerical_term += value
return self
elif isinstance(value, algebra.Variable):
return self + algebra.Monomial(variables=value.name)
elif isinstance(value, Fraction):
return Fraction(value.numerator - (value.denominator * self), value.denominator)
raise TypeError(f'Cannot add a Polynomial to {type(value)}')
def __add__(self, value):
if isinstance(value, algebra.Monomial):
if value.variables == self.name:
return algebra.Monomial(coefficient=1 + value.coefficient, variables=self.name)
else:
return algebra.Polynomial(monomials=[algebra.Monomial(variables=self.name), value])
elif isinstance(value, Variable):
if value.name == self.name:
return algebra.Monomial(coefficient=2, variables=self.name)
else:
return algebra.Polynomial(
monomials=[algebra.Monomial(variables=self.name),
algebra.Monomial(variables=value.name)])
elif isinstance(value, int):
return algebra.Polynomial(monomials=[algebra.Monomial(variables=self.name)],
numerical_term=value)
elif isinstance(value, Fraction):
return Fraction(value.numerator + self * value.denominator, value.denominator)
raise TypeError(f'Cannot add Variable to {type(value)}')
def __neg__(self):
return algebra.Monomial(variables=self.name, coefficient=-1)
def __pow__(self, value, mod=None):
if mod:
raise NotImplementedError
return algebra.Monomial(variables=self.name * value)