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) |
The object globalHeight is a method function with options.