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

## Synopsis

• Function: graph
• Usage:
graph Phi
• Inputs:
• Phi,
• Optional inputs:
• Outputs:
• , the first projection from the graph of Phi
• , the second projection from the graph of Phi

## 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)