globalHeight -- Multiplicative height function

Synopsis

Usage:

globalHeight pt
Inputs:
- pt, a list representing homogeneous coordinates or an instance of the type ProjectivePoint
Outputs:
- the multiplicative height function

Description

This method computes the multiplicative height function given by $(x_0:\dots:x_n)\mapsto \prod_{v}\max_i|x_i|_v ^{d_v/d}$. Over rational numbers the result will be given as a precise value.

i1 : globalHeight {1/1,2/3,5/8}

o1 = 24

o1 : QQ

i2 : PP = Proj(QQ[x,y,z]); pt = PP(1/1,2/3,5/8);

i4 : globalHeight pt

o4 = 24

o4 : QQ

i5 : F = toField(QQ[u]/(u^3-5));

i6 : globalHeight {u,u^2/5,1_F}

o6 = 2.92401773821287

o6 : RR (of precision 53)

Ways to use globalHeight :

globalHeight(List)

For the programmer

The object globalHeight is a method function with options.