This method produces a Homotopy (1-t) S+ t \gamma T, t\in[0,1].
i1 : R = QQ[x,y] o1 = R o1 : PolynomialRing |
i2 : T = {random(3,R)-1, random(2,R)-2} 9 3 1 2 9 2 1 3 2 3 3 2 o2 = {-x + -x y + -x*y + -y - 1, x + -x*y + -y - 2} 2 2 4 2 4 2 o2 : List |
i3 : (S,solsS) = totalDegreeStartSystem T 3 2 o3 = ({x - 1, y - 1}, {{1, -1}, {-.5-.866025*ii, -1}, {-.5+.866025*ii, -1}, {-.5-.866025*ii, 1}, {1, 1}, {-.5+.866025*ii, 1}}) o3 : Sequence |
i4 : H = segmentHomotopy(S,T,gamma=>1+ii) o4 = GateHomotopy{...11...} o4 : GateHomotopy |
i5 : evaluateH(H,transpose matrix first solsS,0) o5 = | 0 | | -2.44929e-16ii | 2 1 o5 : Matrix CC <--- CC 53 53 |
The object segmentHomotopy is a method function with options.