discriminant method

@override Complex discriminant()

The discriminant of the algebraic equation if it exists.

Implementation

@override
Complex discriminant() {
  // Say that P(x) is the polynomial represented by this instance and
  // P'(x) is the derivative of P. In order to calculate the discriminant of
  // a polynomial, we need to first compute the resultant Res(A, A') which
  // is equivalent to the determinant of the Sylvester matrix.
  final sylvester = SylvesterMatrix(coefficients: coefficients);

  // Computes Res(A, A') and then determines the sign according with the
  // degree of the polynomial.
  return sylvester.polynomialDiscriminant();
}