next | previous | forward | backward | up | index | toc

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

## Synopsis

• Function: isIsomorphism
• Usage:
isIsomorphism Phi
• Inputs:
• Phi,
• Outputs:
• , whether Phi is an isomorphism

## 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 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))