# MultirationalMap || MultirationalMap -- product of multi-rational maps

## Synopsis

• Operator: ||
• Usage:
Phi || Psi
• Inputs:
• Phi, , $\Phi:X \dashrightarrow Y$
• Psi, , $\Psi:Z \dashrightarrow W$
• Outputs:
• , the rational map $\Phi\times\Psi:X\times Z \dashrightarrow Y\times W$ defined by $\Phi\times\Psi(p,q) = (\Phi(p),\Psi(q))$

## Description

 i1 : Phi = rationalMap({veronese(1,4,ZZ/33331)},Dominant=>true); o1 : MultirationalMap (dominant rational map from PP^1 to curve in PP^4) i2 : Psi = last graph rationalMap PP_(ZZ/33331)^(1,3); o2 : MultirationalMap (rational map from threefold in PP^3 x PP^2 to PP^2) i3 : (X,Y,Z,W) = (source Phi,target Phi,source Psi,target Psi); i4 : Eta = Phi || Psi; o4 : MultirationalMap (rational map from X x Z to Y x W) i5 : Psi || Eta; o5 : MultirationalMap (rational map from Z x X x Z to W x Y x W) i6 : Psi || Eta || Phi; o6 : MultirationalMap (rational map from Z x X x Z x X to W x Y x W x Y) i7 : assert(oo == (Psi || Eta) || Phi and (Psi || Eta) || Phi == Psi || (Eta || Phi))