Class Monomial

algorithms/math/polynomial.py:23–341

A monomial represented by a coefficient and variable-to-power mapping.

class Monomial:
    """A monomial represented by a coefficient and variable-to-power mapping."""

    def __init__(
        self, variables: dict[int, int], coeff: int | float | Fraction | None = None
    ) -> None:
        """Create a monomial with the given variables and coefficient.

        Args:
            variables: Dictionary mapping variable indices to their powers.
            coeff: The coefficient (defaults to 0 if empty, 1 otherwise).

        Examples:
            >>> Monomial({1: 1})  # (a_1)^1
            >>> Monomial({1: 3, 2: 2}, 12)  # 12(a_1)^3(a_2)^2
        """
        self.variables = dict()

        if coeff is None:
            coeff = Fraction(0, 1) if len(variables) == 0 else Fraction(1, 1)
        elif coeff == 0:
            self.coeff = Fraction(0, 1)
            return

        if len(variables) == 0:
            self.coeff = Monomial._rationalize_if_possible(coeff)
            return

        for i in variables:
            if variables[i] != 0:
                self.variables[i] = variables[i]
        self.coeff = Monomial._rationalize_if_possible(coeff)

    @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 equal_upto_scalar(self, other: object) -> bool:
        """Check if other is a monomial equivalent to self up to scalar multiple.

        Args:
            other: Another Monomial to compare.

        Returns: