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

Synopsis

• 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 0.00100037s (cpu); 0.00121583s (thread); 0s (gc)
 -- used 0.160165s (cpu); 0.120404s (thread); 0s (gc)
 -- used 0.179167s (cpu); 0.140255s (thread); 0s (gc)
 -- used 0.168163s (cpu); 0.123648s (thread); 0s (gc)
 -- used 0.142931s (cpu); 0.102861s (thread); 0s (gc)

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

o2 : List

i3 : time assert(oo == multidegree Phi)
 -- used 0.0550126s (cpu); 0.0543396s (thread); 0s (gc)

References

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