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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)
Temporary directory for input and output files:/var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-66077-0/0

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/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-66077-0/1

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.


o5 = {{2.87208e-318+2.93501e-318*ii, 6.67432e-21-1.12604e-20*ii,
     ------------------------------------------------------------------------
     .513657-.94029*ii}, {2.25077e-315-1.17713e-315*ii,
     ------------------------------------------------------------------------
     4.95972e-20+1.08459e-19*ii, .285085-.0441893*ii},
     ------------------------------------------------------------------------
     {-1.77751e-272-3.3852e-272*ii, 3.83315e-20-2.38351e-19*ii,
     ------------------------------------------------------------------------
     .0479183-.411661*ii}, {6.49578e-316+1.57193e-315*ii,
     ------------------------------------------------------------------------
     -4.92392e-21-2.31591e-21*ii, .121787-.719758*ii}}

o5 : List

Ways to use bertiniSample :