# MultirationalMap MultiprojectiveVariety -- direct image via a multi-rational map

## Synopsis

• Operator: SPACE
• Usage:
Phi X
• Inputs:
• Phi,
• X, , a subvariety of the source of Phi
• Outputs:
• , the (closure of the) direct image of X via Phi

## Description

 i1 : ZZ/65521[x_0..x_4]; i2 : f = last graph rationalMap {x_2^2-x_1*x_3, x_1*x_2-x_0*x_3, x_1^2-x_0*x_2, x_0*x_4, x_1*x_4, x_2*x_4, x_3*x_4, x_4^2}; o2 : MultihomogeneousRationalMap (rational map from 4-dimensional subvariety of PP^4 x PP^7 to PP^7) i3 : Phi = rationalMap {f,f}; o3 : MultirationalMap (rational map from 4-dimensional subvariety of PP^4 x PP^7 to PP^7 x PP^7) i4 : Z = source Phi; o4 : ProjectiveVariety, 4-dimensional subvariety of PP^4 x PP^7 i5 : time Phi Z; -- used 0.132341 seconds o5 : ProjectiveVariety, 4-dimensional subvariety of PP^7 x PP^7 i6 : dim oo, degree oo, degrees oo o6 = (4, 80, {({2, 0}, 5), ({0, 2}, 5), ({1, 1}, 33)}) o6 : Sequence i7 : time Phi (point Z + point Z + point Z) -- used 1.80619 seconds o7 = 0-dimensional subvariety of PP^7 x PP^7 cut out by 22 hypersurfaces of multi-degrees (0,1)^5 (1,0)^5 (2,0)^3 (1,1)^6 (0,2)^3 o7 : ProjectiveVariety, 0-dimensional subvariety of PP^7 x PP^7 i8 : dim oo, degree oo, degrees oo o8 = (0, 3, {({0, 1}, 5), ({1, 0}, 5), ({2, 0}, 3), ({1, 1}, 6), ({0, 2}, ------------------------------------------------------------------------ 3)}) o8 : Sequence