def add(self, other: 'Polynomial') -> 'Polynomial':
if (self.is_zero):
return other
if (other.is_zero):
return self
# Assume this polynomial is smaller than the other one
smaller = self.coefficients
larger = other.coefficients
# Assumption is wrong. exchange the two arrays
if (len(smaller) > len(larger)):
smaller = other.coefficients
larger = self.coefficients
result = list([0] * len(larger))
delta = len(larger) - len(smaller)
# Copy high-order terms only found in higher-degree polynomial's coefficients
# Array.Copy(Larger, 0, Result, 0, Delta);
for i in range(len(larger)):
result[i] = larger[i]
# Add the coefficients of the two polynomials
# for(int Index = Delta; Index < Larger.Length; Index++)
for i in range(delta, len(larger)):
# Result[Index] = Modulus.Add(Smaller[Index - Delta], Larger[Index]);
result[i] = Modulus.add(smaller[i - delta], larger[i])
return Polynomial(0, 0, result)
def evaluate_at(self, x) -> int:
""" Evaluation of this polynomial at a given point """
if (x == 0): return self.coefficients[0]
result = 0
# Return the x^1 coefficient
if (x == 1):
# Return the sum of the coefficients
for coefficient in self.coefficients:
result = Modulus.add(result, coefficient)
else:
result = self.coefficients[0]
for i in range (1, self.length):
multiply_result = Modulus.multiply(x, result)
add_result = Modulus.add(multiply_result, self.coefficients[i])
result = add_result
return result
def multiply(self, other: 'Polynomial') -> 'Polynomial':
""" Multiply two polynomials """
if (self.is_zero or other.is_zero): return ZERO
result = list([0] * (self.length + other.length - 1))
for i in range(self.length):
coeff = self.coefficients[i]
for j in range(other.length):
result[i+j] = Modulus.add(result[i+j], Modulus.multiply(coeff, other.coefficients[j]))
return Polynomial(0, 0, result)