Package edu.jas.structure

Interface MonoidElem<C extends MonoidElem<C>>

    • Method Detail

      • isONE

        boolean isONE()
        Test if this is one.
        Returns:
        true if this is 1, else false.

      • isUnit

        boolean isUnit()
        Test if this is a unit. I.e. there exists x with this.multiply(x).isONE() == true.
        Returns:
        true if this is a unit, else false.

      • multiply

        C multiply​(C S)
        Multiply this with S.
        Parameters:
        S -
        Returns:
        this * S.

      • divide

        C divide​(C S)
        Divide this by S.
        Parameters:
        S -
        Returns:
        this / S.

      • remainder

        C remainder​(C S)
        Remainder after division of this by S.
        Parameters:
        S -
        Returns:
        this - (this / S) * S.

      • quotientRemainder

        default C[] quotientRemainder​(C S)
        Quotient and remainder by division of this by S.
        Parameters:
        S -
        Returns:
        [this/S, this - (this/S)*S].

      • rightDivide

        default C rightDivide​(C a)
        Right division. Returns commutative divide if not overwritten.
        Parameters:
        a - element.
        Returns:
        right, with a * right = this

      • leftDivide

        default C leftDivide​(C a)
        Left division. Returns commutative divide if not overwritten.
        Parameters:
        a - element.
        Returns:
        left, with left * a = this

      • rightRemainder

        default C rightRemainder​(C a)
        Right remainder. Returns commutative remainder if not overwritten.
        Parameters:
        a - element.
        Returns:
        r = this - a * (1/right), where a * right = this.

      • leftRemainder

        default C leftRemainder​(C a)
        Left remainder. Returns commutative remainder if not overwritten.
        Parameters:
        a - element.
        Returns:
        r = this - (1/left) * a, where left * a = this.

      • twosidedDivide

        default C[] twosidedDivide​(C a)
        Two-sided division. Returns commutative divide if not overwritten.
        Parameters:
        a - element.
        Returns:
        [left,right], with left * a * right = this

      • twosidedRemainder

        default C twosidedRemainder​(C a)
        Two-sided remainder. Returns commutative remainder if not overwritten.
        Parameters:
        a - element.
        Returns:
        r = this - (a/left) * a * (a/right), where left * a * right = this.

      • inverse

        C inverse()
        Inverse of this. Some implementing classes will throw NotInvertibleException if the element is not invertible.
        Returns:
        x with this * x = 1, if it exists.

      • power

        default C power​(long n)
        Power of this to the n-th.
        Parameters:
        n - integer exponent.
        Returns:
        a**n, with a**0 = 1 and a**{-n} = {1/a}**n. Java 8 only