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) Temporary directory for input and output files:/var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-74594-0/1 The version of Bertini you have installed on your computer was used for this run. Bertini is under ongoing development by D. Bates, J. Hauenstein, A. Sommese, and C. Wampler. o3 = NV o3 : NumericalVariety |
i4 : W = NV#1_0 --z-axis o4 = W o4 : WitnessSet |
i5 : bertiniSample(4, W) Temporary directory for input and output files:/var/folders/j_/gx42s4z576z_vj47_ym0j5xm0000gn/T/M2-74594-0/2 The version of Bertini you have installed on your computer was used for this run. Bertini is under ongoing development by D. Bates, J. Hauenstein, A. Sommese, and C. Wampler. o5 = {{4.41976e-20+1.80005e-20*ii, 1.8687e-21+3.61538e-20*ii, ------------------------------------------------------------------------ -.0423553+.236583*ii}, {1.11808e-19+1.93797e-19*ii, ------------------------------------------------------------------------ 1.65165e-193-8.33116e-194*ii, .007043+.84133*ii}, ------------------------------------------------------------------------ {-2.44197e-19-6.00744e-19*ii, -1.18682e-114+7.46723e-114*ii, ------------------------------------------------------------------------ -1.65149+.214192*ii}, {2.43395e-19+1.46333e-19*ii, ------------------------------------------------------------------------ 3.28446e-276+2.07753e-275*ii, -.068132+1.02949*ii}} o5 : List |