In algebraic geometry, ${\displaystyle \mu }$ is said to be a multiplicative distance function over a field if it satisfies^[1]

• ${\displaystyle \mu (AB)>1.\,}$
• AB is congruent to A'B' iff ${\displaystyle \mu (AB)=\mu (A'B').\,}$
• AB < A'B' iff ${\displaystyle \mu (AB)<\mu (A'B').\,}$
• ${\displaystyle \mu (AB+CD)=\mu (AB)\mu (CD).\,}$

See also

• Algebraic geometry
• Hyperbolic geometry
• Poincaré disc model
• Hilbert's arithmetic of ends

References