Writes the witness set to a temporary file
Invokes Bertini’s solver with option TRACKTYPE: 2. To sample, Bertini moves the hyperplannes defined in the WitnessSet W within the space until the desired points are sampled.
Stores output of Bertini in temporary file
Parses and outputs the solutions
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 |