Used to construct a witness set for a component of the variety V(E). An affine chart is specified by the matrix of the coefficients of the (normalized) linear equation defining the chart: e.g., ax+by+cz=1 is encoded as [a,b,c].
It is expected that the, V(E) and the plane V(S) defined by S are of complementary dimensions and that P is contained in the intersection of V(E+C) and V(S).
i1 : R = CC[x,y,z] o1 = R o1 : PolynomialRing |
i2 : w = projectiveWitnessSet( ideal(x^2+y^2+2*z^2), matrix{{0,0,1}}, matrix{{1,-1,0}}, {point {{0.999999*ii,0.999999*ii,1.}}, point {{ -1.000001*ii,-1.000001*ii,1.}}} ) o2 = w o2 : WitnessSet |
i3 : peek w o3 = WitnessSet{AffineChart => | 0 0 1 | } IsIrreducible => null Points => {{.999999*ii, .999999*ii, 1}} {{-ii, -ii, 1} } Slice => | 1 -1 0 | 2 2 2 Equations => ideal(x + y + 2z ) |
The object projectiveWitnessSet is a method function.