Class Polynomial

algorithms/math/polynomial.py:344–708

A polynomial represented as a set of Monomial terms.

class Polynomial:
    """A polynomial represented as a set of Monomial terms."""

    def __init__(
        self, monomials: Iterable[int | float | Fraction | Monomial]
    ) -> None:
        """Create a polynomial from an iterable of monomials or scalars.

        Args:
            monomials: An iterable of Monomial, int, float, or Fraction values.

        Raises:
            ValueError: If an element is not a valid type.
        """
        self.monomials: set = set()
        for m in monomials:
            if any(map(lambda x: isinstance(m, x), [int, float, Fraction])):
                self.monomials |= {Monomial({}, m)}
            elif isinstance(m, Monomial):
                self.monomials |= {m}
            else:
                raise ValueError(
                    "Iterable should have monomials, int, float, or Fraction."
                )
        self.monomials -= {Monomial({}, 0)}

    @staticmethod
    def _rationalize_if_possible(
        num: int | float | Fraction,
    ) -> Fraction | float:
        """Convert numbers to Fraction when possible.

        Args:
            num: A numeric value.

        Returns:
            A Fraction if the input is Rational, otherwise the original value.
        """
        if isinstance(num, Rational):
            res = Fraction(num, 1)
            return Fraction(res.numerator, res.denominator)
        else:
            return num

    def __add__(self, other: int | float | Fraction | Monomial) -> Polynomial:
        """Add a polynomial, monomial, or scalar to this polynomial.

        Args:
            other: Value to add.

        Returns:
            The resulting Polynomial.

        Raises:
            ValueError: If other is not a valid type.
        """
        if isinstance(other, (int, float, Fraction)):
            return self.__add__(