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multidegree(ZZ,MultirationalMap) -- i-th projective degree of a multi-rational map using a probabilistic approach

Description

This is calculated by means of the inverse image of an appropriate random subvariety of the target.

i1 : Phi = last graph rationalMap PP_(ZZ/300007)^(1,4);

o1 : MultirationalMap (rational map from 4-dimensional subvariety of PP^4 x PP^5 to PP^5)
i2 : for i in {4,3,2,1,0} list time multidegree(i,Phi)
 -- used 0.00410901s (cpu); 0.00130137s (thread); 0s (gc)
 -- used 0.303432s (cpu); 0.15419s (thread); 0s (gc)
 -- used 0.23549s (cpu); 0.171747s (thread); 0s (gc)
 -- used 0.222841s (cpu); 0.139569s (thread); 0s (gc)
 -- used 0.192455s (cpu); 0.116093s (thread); 0s (gc)

o2 = {51, 28, 14, 6, 2}

o2 : List
i3 : time assert(oo == multidegree Phi)
 -- used 0.141073s (cpu); 0.0760419s (thread); 0s (gc)

References

ArXiv preprint: Computations with rational maps between multi-projective varieties.

See also

Ways to use this method:


The source of this document is in /build/reproducible-path/macaulay2-1.25.05+ds/M2/Macaulay2/packages/MultiprojectiveVarieties.m2:3203:0.