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

## Synopsis

• Function: multidegree
• Usage:
multidegree(i,Phi)
• Inputs:
• 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 0.00211317 seconds -- used 0.808295 seconds -- used 0.739444 seconds -- used 0.67732 seconds -- used 0.516047 seconds o2 = {51, 28, 14, 6, 2} o2 : List i3 : time assert(oo == multidegree Phi) -- used 0.176345 seconds

## References

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