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 ) .