isMorphism(MultirationalMap) -- whether a multi-rational map is a morphism

i1 : ZZ/300007[a..e], f = first graph rationalMap ideal(c^2-b*d,b*c-a*d,b^2-a*c,e), g = rationalMap submatrix(matrix f,{0..2});

i2 : Phi = rationalMap {f,g};

o2 : MultirationalMap (rational map from 4-dimensional subvariety of PP^4 x PP^7 to PP^4 x PP^2)

i3 : time isMorphism Phi
 -- used 0.551965s (cpu); 0.337797s (thread); 0s (gc)

o3 = false

i4 : time Psi = first graph Phi;
 -- used 0.146346s (cpu); 0.147434s (thread); 0s (gc)

o4 : MultirationalMap (birational map from 4-dimensional subvariety of PP^4 x PP^7 x PP^4 x PP^2 to 4-dimensional subvariety of PP^4 x PP^7)

i5 : time isMorphism Psi
 -- used 6.15945s (cpu); 5.36353s (thread); 0s (gc)

o5 = true

i6 : assert((not o3) and o5)