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RationalPoints2 > rationalPoints > globalHeight

globalHeight -- Multiplicative height function

Synopsis

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 :

For the programmer

The object globalHeight is a method function with options.