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MultiprojectiveVarieties :: graph(MultirationalMap)

graph(MultirationalMap) -- the graph of a multi-rational map

Synopsis

Description

The equalities (first graph Phi) * Phi == last graph Phi and (first graph Phi)^-1 * (last graph Phi) == Phi are always satisfied.

i1 : ZZ/333331[x_0..x_4];
i2 : Phi = multirationalMap {rationalMap(minors(2,matrix{{x_0..x_3},{x_1..x_4}}),Dominant=>true)}

o2 = Phi

o2 : MultirationalMap (dominant rational map from PP^4 to hypersurface in PP^5)
i3 : time (Phi1,Phi2) = graph Phi
     -- used 0.303552 seconds

o3 = (Phi1, Phi2)

o3 : Sequence
i4 : Phi1;

o4 : MultirationalMap (birational map from 4-dimensional subvariety of PP^4 x PP^5 to PP^4)
i5 : Phi2;

o5 : MultirationalMap (dominant rational map from 4-dimensional subvariety of PP^4 x PP^5 to hypersurface in PP^5)
i6 : time (Phi21,Phi22) = graph Phi2
     -- used 0.882578 seconds

o6 = (Phi21, Phi22)

o6 : Sequence
i7 : Phi21;

o7 : MultirationalMap (birational map from 4-dimensional subvariety of PP^4 x PP^5 x PP^5 to 4-dimensional subvariety of PP^4 x PP^5)
i8 : Phi22;

o8 : MultirationalMap (dominant rational map from 4-dimensional subvariety of PP^4 x PP^5 x PP^5 to hypersurface in PP^5)
i9 : time (Phi211,Phi212) = graph Phi21
     -- used 6.65398 seconds

o9 = (Phi211, Phi212)

o9 : Sequence
i10 : Phi211;

o10 : MultirationalMap (birational map from 4-dimensional subvariety of PP^4 x PP^5 x PP^5 x PP^4 x PP^5 to 4-dimensional subvariety of PP^4 x PP^5 x PP^5)
i11 : Phi212;

o11 : MultirationalMap (birational map from 4-dimensional subvariety of PP^4 x PP^5 x PP^5 x PP^4 x PP^5 to 4-dimensional subvariety of PP^4 x PP^5)
i12 : assert(
      source Phi1 == source Phi2 and target Phi1 == source Phi and target Phi2 == target Phi and
      source Phi21 == source Phi22 and target Phi21 == source Phi2 and target Phi22 == target Phi2 and 
      source Phi211 == source Phi212 and target Phi211 == source Phi21 and target Phi212 == target Phi21)
i13 : assert(Phi1 * Phi == Phi2 and Phi21 * Phi2 == Phi22 and Phi211 * Phi21 == Phi212)

See also