isIsomorphism(MultirationalMap) -- whether a birational map is an isomorphism

i1 : -- map defined by the quadrics through a twisted cubic curve
     ZZ/33331[a..d]; f = rationalMap {c^2-b*d,b*c-a*d,b^2-a*c};

o2 : RationalMap (quadratic rational map from PP^3 to PP^2)

i3 : Phi = rationalMap {f,f};

o3 : MultirationalMap (rational map from PP^3 to PP^2 x PP^2)

i4 : time isIsomorphism Phi
 -- used 0.00040967s (cpu); 8.49e-06s (thread); 0s (gc)

o4 = false

i5 : Psi = first graph Phi;

o5 : MultirationalMap (birational map from threefold in PP^3 x PP^2 x PP^2 to PP^3)

i6 : time isIsomorphism Psi
 -- used 0.515351s (cpu); 0.301114s (thread); 0s (gc)

o6 = false

i7 : Eta = first graph Psi;

o7 : MultirationalMap (birational map from threefold in PP^3 x PP^2 x PP^2 x PP^3 to threefold in PP^3 x PP^2 x PP^2)

i8 : time isIsomorphism Eta
 -- used 2.23565s (cpu); 1.34328s (thread); 0s (gc)

o8 = true

i9 : assert(o8 and (not o6) and (not o4))