numericalIrreducibleDecomposition(Ideal) -- constructs a numerical variety defined by the given ideal

• Function: numericalIrreducibleDecomposition

• Usage:

  V = numericalIrreducibleDecomposition I

• Inputs:
  • I, an ideal, contained in the ring of polynomials with complex coefficients
• Optional inputs:
  • Software => ..., default value null, specify internal or external software
• Outputs:
  • V

i1 : R = CC[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : sph = (x^2+y^2+z^2-1); 

i3 : I = ideal {sph*(y-x^2), sph*(z-x^3)};

o3 : Ideal of R

i4 : numericalIrreducibleDecomposition I 

o4 = a "numerical variety" with components in
     dim 1:  (dim=1,deg=3)
     dim 2:  (dim=2,deg=2)

o4 : NumericalVariety