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

Function: multidegree
Usage:

multidegree(i,Phi)
Inputs:
- i, an integer
- Phi, a multi-rational map
Outputs:
- an integer, the $i$-th projective degree of Phi

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 0.00154046s (cpu); 0.00146492s (thread); 0s (gc)
 -- used 0.17858s (cpu); 0.137451s (thread); 0s (gc)
 -- used 0.205338s (cpu); 0.160435s (thread); 0s (gc)
 -- used 0.185648s (cpu); 0.141927s (thread); 0s (gc)
 -- used 0.17732s (cpu); 0.130002s (thread); 0s (gc)

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

o2 : List

i3 : time assert(oo == multidegree Phi)
 -- used 0.139187s (cpu); 0.0955153s (thread); 0s (gc)

References

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

See also

multidegree(MultirationalMap) -- projective degrees of a multi-rational map
projectiveDegrees(RationalMap) -- projective degrees of a rational map
degree(MultirationalMap,Option) -- degree of a multi-rational map using a probabilistic approach
MultirationalMap ^* -- inverse image via a multi-rational map

Ways to use this method:

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

The source of this document is in /build/macaulay2-BDMbwf/macaulay2-1.25.11+ds/M2/Macaulay2/packages/MultiprojectiveVarieties.m2:3203:0.