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Bertini :: bertiniSample

bertiniSample -- sample points from an irreducible component of a variety

Synopsis

Description

Samples points from an irreducible component of a variety using Bertini. The irreducible component needs to be in its numerical form as a WitnessSet. The method bertiniPosDimSolve can be used to generate a witness set for the component.

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

o1 = R

o1 : PolynomialRing
i2 : F = { (y^2+x^2+z^2-1)*x, (y^2+x^2+z^2-1)*y }

       3      2      2       2     3      2
o2 = {x  + x*y  + x*z  - x, x y + y  + y*z  - y}

o2 : List
i3 : NV = bertiniPosDimSolve(F)

o3 = NV

o3 : NumericalVariety
i4 : W = NV#1_0 --z-axis

o4 = W

o4 : WitnessSet
i5 : bertiniSample(4, W)

o5 = {{0, 0, -.465556-.605586*ii}, {-1.82159e-318+3.7247e-317*ii,
     ------------------------------------------------------------------------
     4.94066e-324-9.88131e-324*ii, -.79065-.430166*ii},
     ------------------------------------------------------------------------
     {4.94642e-277-1.85732e-276*ii, 5.17729e-277+1.37882e-277*ii,
     ------------------------------------------------------------------------
     .780913+.714707*ii}, {-2.96439e-323+3.55727e-322*ii,
     ------------------------------------------------------------------------
     1.42291e-321+1.28457e-322*ii, .552555-.359719*ii}}

o5 : List

Ways to use bertiniSample :