In algebraic geometry,                     μ                 is said to be a multiplicative distance function over a field if it satisfies,
                    μ        (        A        B        )        >        1.                        AB is congruent to A'B' iff                     μ        (        A        B        )        =        μ        (                  A          ′                          B          ′                )        .                        AB < A'B' iff                     μ        (        A        B        )        <        μ        (                  A          ′                          B          ′                )        .                                            μ        (        A        B        +        C        D        )        =        μ        (        A        B        )        μ        (        C        D        )        .