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



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 0.00399884s (cpu); 0.00127258s (thread); 0s (gc)
 -- used 0.288515s (cpu); 0.197103s (thread); 0s (gc)
 -- used 0.294612s (cpu); 0.200776s (thread); 0s (gc)
 -- used 0.180017s (cpu); 0.181527s (thread); 0s (gc)
 -- used 0.249981s (cpu); 0.157321s (thread); 0s (gc)

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

o2 : List
i3 : time assert(oo == multidegree Phi)
 -- used 0.245141s (cpu); 0.141714s (thread); 0s (gc)


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

See also

Ways to use this method: