regeneration(List) -- solve a system of polynomial equations with regeneration method

Synopsis

• Function: regeneration

• Usage:

  Ws = regeneration F

• Inputs:
  • F, a list, contains polynomials with complex coefficients
• Optional inputs:
  • Output => ..., default value Singular
  • Software => ..., default value null, specify internal or external software
• Outputs:
  • Ws, a list, contains witness sets for equidimensional components of the variety {x|F(x)=0}

Description

i1 : R = CC[x,y]

o1 = R

o1 : PolynomialRing

i2 : F = {x^2+y^2-1, x*y};

i3 : regeneration F 

o3 = a "numerical variety" with components in
     dim 0:  [dim=0,deg=4]-*may be reducible*-

o3 : NumericalVariety

i4 : R = CC[x,y,z]

o4 = R

o4 : PolynomialRing

i5 : sph = (x^2+y^2+z^2-1); 

i6 : regeneration {sph*(x-1)*(y-x^2), sph*(y-2)*(z-x^3)}

o6 = a "numerical variety" with components in
     dim 1:  [dim=1,deg=7]-*may be reducible*-
     dim 2:  [dim=2,deg=2]-*may be reducible*-

o6 : NumericalVariety

Caveat

See also

• decompose(WitnessSet)