# segre(MultirationalMap) -- the composition of a multi-rational map with the Segre embedding of the target

## Synopsis

• Function: segre
• Usage:
segre Phi
• Inputs:
• Phi,
• Outputs:

## Description

 i1 : ZZ/65521[x_0..x_4]; i2 : f = rationalMap({x_3^2-x_2*x_4,x_2*x_3-x_1*x_4,x_1*x_3-x_0*x_4,x_2^2-x_0*x_4,x_1*x_2-x_0*x_3,x_1^2-x_0*x_2},Dominant=>true); o2 : RationalMap (quadratic dominant rational map from PP^4 to hypersurface in PP^5) i3 : g = rationalMap {x_3^2-x_2*x_4,x_2*x_3-x_1*x_4,x_1*x_3-x_0*x_4,x_2^2-x_0*x_4,x_1*x_2-x_0*x_3}; o3 : RationalMap (quadratic rational map from PP^4 to PP^4) i4 : h = rationalMap {-x_3^2+x_2*x_4,2*x_2*x_3-2*x_1*x_4,-3*x_2^2+2*x_1*x_3+x_0*x_4, 2*x_1*x_2-2*x_0*x_3,-x_1^2+x_0*x_2}; o4 : RationalMap (quadratic rational map from PP^4 to PP^4) i5 : Phi = rationalMap {f,g,h}; o5 : MultirationalMap (rational map from PP^4 to hypersurface in PP^5 x PP^4 x PP^4) i6 : time segre Phi; -- used 0.858491 seconds o6 : RationalMap (rational map from PP^4 to PP^149) i7 : describe segre Phi o7 = rational map defined by forms of degree 6 source variety: PP^4 target variety: PP^149 coefficient ring: ZZ/65521