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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 : Phi = rationalMap(PP_(ZZ/333331)^(1,4),Dominant=>true)

o1 = Phi

o1 : MultirationalMap (dominant rational map from PP^4 to hypersurface in PP^5)
i2 : time (Phi1,Phi2) = graph Phi
     -- used 0.0522304 seconds

o2 = (Phi1, Phi2)

o2 : Sequence
i3 : Phi1;

o3 : MultirationalMap (birational map from 4-dimensional subvariety of PP^4 x PP^5 to PP^4)
i4 : Phi2;

o4 : MultirationalMap (dominant rational map from 4-dimensional subvariety of PP^4 x PP^5 to hypersurface in PP^5)
i5 : time (Phi21,Phi22) = graph Phi2
     -- used 0.0716642 seconds

o5 = (Phi21, Phi22)

o5 : Sequence
i6 : Phi21;

o6 : 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)
i7 : Phi22;

o7 : MultirationalMap (dominant rational map from 4-dimensional subvariety of PP^4 x PP^5 x PP^5 to hypersurface in PP^5)
i8 : time (Phi211,Phi212) = graph Phi21
     -- used 0.243379 seconds

o8 = (Phi211, Phi212)

o8 : Sequence
i9 : Phi211;

o9 : 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)
i10 : Phi212;

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)
i11 : 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)
i12 : assert(Phi1 * Phi == Phi2 and Phi21 * Phi2 == Phi22 and Phi211 * Phi21 == Phi212)

See also