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bertiniSample-bertiniComponentMemberTest.tst.m2
restart loadPackage("Bertini",Reload=>true) peek Bertini ---we will do a sample homotopy R = CC[x,y,z] --F is the defining system of equations F = {(y^2+x^2+z^2-1)*x*z, (y^2+x^2+z^2-1)*y*z} --NV is a numerical variety consisting of 2 components BIC = {RandomSeed=>1} NV = bertiniPosDimSolve(F,BertiniInputConfiguration=>BIC) --W1 is the 1 dimensional component --W2 is the 2 dimensional component W1 = NV#1_0 --z-axis W2 = NV#2_0 W3 = NV#2_1 sample1=bertiniSample(10, W1) sample2=bertiniSample(20, W3--,SHARPENDIGITS =>1e-100 ) assert(#sample1==10) assert(#sample2==20) assert( unique flatten bertiniComponentMemberTest(sample1, NV) === {W1} ) assert( bertiniComponentMemberTest({(1,1,1*ii)}, NV) === {{W3}} --bertiniComponentMemberTest(NV,sample2) -- a problem with precision of bertiniSample ??? ) assert( set flatten bertiniComponentMemberTest({(0,0,1)}, NV) === set {W3,W1} )