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

Synopsis

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 0.00132407s (cpu); 0.00145756s (thread); 0s (gc)
 -- used 0.174914s (cpu); 0.101662s (thread); 0s (gc)
 -- used 0.196399s (cpu); 0.153325s (thread); 0s (gc)
 -- used 0.0838806s (cpu); 0.0864722s (thread); 0s (gc)
 -- used 0.147316s (cpu); 0.0844356s (thread); 0s (gc)

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

o2 : List
i3 : time assert(oo == multidegree Phi)
 -- used 0.15608s (cpu); 0.085233s (thread); 0s (gc)

References

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

See also

Ways to use this method: