numericalImageDegree -- computes the degree of the image of a variety

Synopsis

• Usage:

  numericalImageDegree W

  numericalImageDegree(F, I)

• Inputs:
  • W, a pseudo-witness set, a pseudo-witness set for $F(V(I))$
  • F, a matrix, or list, or ring map, specifying a map
  • I, an ideal, which is prime, specifying a source variety $V(I)$
• Optional inputs:
  • DoRefinements => ..., default value false, computes a pseudo-witness set for the image of a variety
  • DoTraceTest => ..., default value true, computes a pseudo-witness set for the image of a variety
  • MaxAttempts => ..., default value 5, computes a pseudo-witness set for the image of a variety
  • MaxPoints => ..., default value infinity, computes a pseudo-witness set for the image of a variety
  • MaxThreads => ..., default value 1, specifies the maximum number of processor threads
  • Repeats => ..., default value 3, computes a pseudo-witness set for the image of a variety
  • Software => ..., default value M2engine, specify software for homotopy continuation
  • Threshold => ..., default value 5, computes a pseudo-witness set for the image of a variety
  • TraceThreshold => ..., default value .00001, computes a pseudo-witness set for the image of a variety
  • Verbose => ..., default value true, display detailed output
• Outputs:
  • an integer, the degree of $F(V(I))$

Description

i1 : R = CC[x_(1,1)..x_(2,4)]; I = ideal 0_R;

o2 : Ideal of R

i3 : F = (minors(2, genericMatrix(R, 2, 4)))_*;

i4 : numericalImageDegree(F, I, Repeats => 2, Verbose => false)

o4 = 2

See also

• pseudoWitnessSet -- computes a pseudo-witness set for the image of a variety
• PseudoWitnessSet -- the class of all pseudo-witness sets