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_bertini__Pos__Dim__Solve.out
-- -*- M2-comint -*- hash: 1503209601929851452 i1 : R = QQ[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 : S = bertiniPosDimSolve F o3 = S o3 : NumericalVariety i4 : S#1_0#Points -- 1_0 chooses the first witness set in dimension 1 o4 = {{2.64468e-59+1.83949e-59*ii, -1.0877e-60+3.37583e-59*ii, .261246+.146018*ii}} o4 : VerticalList i5 : S#1 --first specify dimension o5 = {(dim=1,deg=1)} o5 : List i6 : peek oo_0 --then list position o6 = WitnessSet{cache => CacheTable{...3...} } Equations => {-3} | x3+xy2+xz2-x | {-3} | x2y+y3+yz2-y | Points => {{2.64468e-59+1.83949e-59*ii, -1.0877e-60+3.37583e-59*ii, .261246+.146018*ii}} Slice => | .073883+1.51329ii 1.3836+.186588ii -2.02193+.757676ii .638855+.0972991ii | i7 : PD=primaryDecomposition( ideal F) 2 2 2 o7 = {ideal(x + y + z - 1), ideal (y, x)} o7 : List i8 : dim PD_0 o8 = 2 i9 : degree PD_0 o9 = 2 i10 : dim PD_1 o10 = 1 i11 : degree PD_1 o11 = 1 i12 :