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MultiprojectiveVarieties :: isIsomorphism(MultirationalMap)

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

Synopsis

Description

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 6.168e-6 seconds

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 0.238736 seconds

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 0.927329 seconds

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

See also