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NumericalAlgebraicGeometry :: regeneration(List)

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

Synopsis

Description

Regeneration is a blackbox method that obtains a numerical description of an algebraic variety. Note that Ws are not necessarily irreducible witness sets; use decompose(WitnessSet) to decompose into irreducibles.
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

This function is under development. It may not work well if the input represents a nonreduced scheme.The (temporary) option Output can take two values: Regular (default) and Singular. It specifies whether the algorithm attempts to keep singular points.

See also