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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 describtion of an algebraic variety. Note that Ws are not necessarily irreducible witness sets; use decompose(WitnessSet) to decompose into irreducibles.
i1 : setRandomSeed 7

o1 = 7
i2 : R = CC[x,y]

o2 = R

o2 : PolynomialRing
i3 : F = {x^2+y^2-1, x*y};
i4 : regeneration F 

o4 = {[dim=0,deg=4]}

o4 : List
i5 : R = CC[x,y,z]

o5 = R

o5 : PolynomialRing
i6 : sph = (x^2+y^2+z^2-1); 
i7 : I = ideal {sph*(x-0.5)*(y-x^2), sph*(y-0.5)*(z-x^3), sph*(z-0.5)*(z-x^3)*(y-x^3)};

o7 : Ideal of R
i8 : cs = regeneration I_*

o8 = {[dim=0,deg=3], [dim=1,deg=8], [dim=2,deg=2]}

o8 : List

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