isOnImage -- tests whether a point lies on the image of a variety

Synopsis

• Usage:

  isOnImage(W, p)

  isOnImage(F, I, p)

• Inputs:
  • W, a pseudo-witness set, a pseudo-witness set for $F(V(I))$
  • p, a point, a point in the ambient space of $F(V(I))$
  • 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:
  • MaxThreads => ..., default value 1, specifies the maximum number of processor threads
  • Software => ..., default value M2engine, specify software for homotopy continuation
  • Threshold => ..., default value 5, computes a pseudo-witness set for the image of a variety
  • Verbose => ..., default value true, display detailed output
• Outputs:
  • a Boolean value, whether the point $p$ lies on $F(V(I))$

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 : W = pseudoWitnessSet(F, I, Repeats => 2, Verbose => false);

i5 : q = first numericalImageSample(F, I)

o5 = q

o5 : Point

i6 : isOnImage(W, q)

o6 = true

i7 : isOnImage(W, point random(CC^1, CC^#F))

o7 = false

i8 : isOnImage(W, point{{1_CC,0,0,0,0,0}})

o8 = true

See also

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