i1 : R = ring PP_(ZZ/65521)^{2,1};
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i2 : f = rationalMap for i to 3 list random({1,1},R);
o2 : MultihomogeneousRationalMap (rational map from PP^2 x PP^1 to PP^3)
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i3 : g = rationalMap(for i to 4 list random({0,1},R),Dominant=>true);
o3 : MultihomogeneousRationalMap (dominant rational map from PP^2 x PP^1 to curve in PP^4)
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i4 : h = rationalMap for i to 2 list random({1,0},R);
o4 : MultihomogeneousRationalMap (rational map from PP^2 x PP^1 to PP^2)
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i5 : Phi = multirationalMap {f,g,h}
o5 = Phi
o5 : MultirationalMap (rational map from PP^2 x PP^1 to 6-dimensional subvariety of PP^3 x PP^4 x PP^2)
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i6 : describe Phi -- long description
o6 = multi-rational map consisting of 3 rational maps
source variety: PP^2 x PP^1
target variety: 6-dimensional subvariety of PP^3 x PP^4 x PP^2 cut out by 3 hypersurfaces of multi-degree (0,1,0)
base locus: empty subscheme of PP^2 x PP^1
dominance: false
image: threefold in PP^3 x PP^4 x PP^2 cut out by 14 hypersurfaces of multi-degrees (0,1,0)^3 (1,0,2)^4 (1,1,1)^6 (1,3,0)^1
multidegree: {3, 6, 12, 24}
degree: 1
degree sequence (map 1/3): [(1,1)]
degree sequence (map 2/3): [(0,1)]
degree sequence (map 3/3): [(1,0)]
coefficient ring: ZZ/65521
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i7 : ? Phi -- short description
o7 = multi-rational map consisting of 3 rational maps
source variety: PP^2 x PP^1
target variety: 6-dimensional subvariety of PP^3 x PP^4 x PP^2 cut out by 3 hypersurfaces of multi-degree (0,1,0)
base locus: empty subscheme of PP^2 x PP^1
dominance: false
image: threefold in PP^3 x PP^4 x PP^2 cut out by 14 hypersurfaces of multi-degrees (0,1,0)^3 (1,0,2)^4 (1,1,1)^6 (1,3,0)^1
multidegree: {3, 6, 12, 24}
degree: 1
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i8 : X = projectiveVariety R;
o8 : ProjectiveVariety, PP^2 x PP^1
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i9 : Phi;
o9 : MultirationalMap (morphism from X to 6-dimensional subvariety of PP^3 x PP^4 x PP^2)
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i10 : Y = target Phi;
o10 : ProjectiveVariety, 6-dimensional subvariety of PP^3 x PP^4 x PP^2
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i11 : Phi;
o11 : MultirationalMap (morphism from X to Y)
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i12 : Z = (image multirationalMap {f,g}) ** target h;
o12 : ProjectiveVariety, 5-dimensional subvariety of PP^3 x PP^4 x PP^2
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i13 : Psi = multirationalMap({f,g,h},Z)
o13 = Psi
o13 : MultirationalMap (rational map from X to Z)
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i14 : assert(image Psi == image Phi)
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