Interface AbelianGroup<G>

    • Method Summary

      All Methods Instance Methods Abstract Methods 
      Modifier and Type Method Description
      G add​(G that)
      + : G × G → G
      G minus​(G that)
      - : G × G → G
      G opposite()
      For each a in G, there exists an element b in G such that a + b = b + a = 0.
      G ZERO()
      The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.
    • Method Detail

      • add

        G add​(G that)
        + : G × G → G
        Parameters:
        that - the object to be added
        Returns:
        this + that
      • minus

        G minus​(G that)
        - : G × G → G

        The operation "-" is not in the definition of of an additive group but can be deduced. This function is provided for convenience purpose. It is equivalent to

        this.add(that.opposite())
        .
        Parameters:
        that - the object to be subtracted (subtrahend)
        Returns:
        this - that
      • opposite

        G opposite()
        For each a in G, there exists an element b in G such that a + b = b + a = 0. That is, it is the object such as
        this.add(this.opposite()) == this.ZERO
        Returns:
        -this, the additive opposite
        See Also:
        Wikipedia: Additive inverse
      • ZERO

        G ZERO()
        The additive element 0 in the group, such that for all elements a in the group, the equation 0 + a = a + 0 = a holds.
        Returns:
        0, the additive identity