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bertiniPosDimSolve.tst.m2
needsPackage "Bertini" --To solve a positive dimensional system use the bertiniPosDimSolve command -- the input is a list of equations -- the outpt is a numerical variety R=QQ[x,y,z] outHyper=bertiniPosDimSolve( {(z+2)*x*(x^2+y^2-1),(y-1)*(2+y)*(x^2+y^2-1),(2+y)*(x-3)*(x^2+y^2-1)}) numDecomp=for i from 0 to 2 list apply(outHyper#i,degree) assert(member({1},numDecomp)) assert(member({1,1},numDecomp)) assert(member({2},numDecomp)) -- testing that dim and deg of witness sets is correct R=CC[x,y,z,w,a] F={(x+1)*z,(x+1)*y,(x+1)*w,(x+1)*a*(a+1)} comps = components bertiniPosDimSolve F assert( comps / dim == {1,1,4} and comps / degree == {1,1,1} ) --TODO: We need a test to check if it produces correct slices --TODO: We need to check if the witness sets work with the other stuff in NumericalAlgebraicGeometry. -- affine R = CC[x,y,z,t] I = ideal(x + 3, y+1) nv = bertiniPosDimSolve(I_*, Verbose => true) w = first components nv assert all(points w, p->norm evaluate(polySystem slice w,p) < 0.0001) R = CC[x,y,z,t] I = ideal(x + 3, y+1, z, t-0.5*ii) nv = bertiniPosDimSolve(I_*, Verbose => true) w = first components nv assert(slice w == {}) -- projective R = CC[x,y,z,t] I = ideal(x + z, y+z) nv = bertiniPosDimSolve(I_*, Verbose => true, IsProjective=>1) w = first components nv assert all(points w, p->norm evaluate(polySystem slice w,p) < 0.0001) I = ideal(x + z, y+x, z) nv = bertiniPosDimSolve(I_*, Verbose => true, IsProjective=>1) w = first components nv assert(slice w == {})