Construct a polynomial system representing a segment homotopy H = (1-t) F + t G for t ∈[0,1].
i1 : R = CC[x,y]; |
i2 : S = polySystem {x^2-1, y^2-1}; |
i3 : T = polySystem {x^2+y^2-6, 2*x^2-y}; |
i4 : H := segmentHomotopy(S,T) o4 = {-2} | y2t+x2-5t-1 | {-2} | 2x2t-y2t+y2-yt+t-1 | o4 : PolySystem |
Specialize the continuation parameter:
i5 : specializeContinuationParameter(H,0) o5 = {-2} | x2-1 | {-2} | y2-1 | o5 : PolySystem |
i6 : specializeContinuationParameter(H,1) o6 = {-2} | x2+y2-6 | {-2} | 2x2-y | o6 : PolySystem |
i7 : specializeContinuationParameter(H,2+3*ii) o7 = {-2} | x2+(2+3i)y2-11-15i | {-2} | (4+6i)x2-(1+3i)y2-(2+3i)y+1+3i | o7 : PolySystem |
Substitute 1-t for the continuation parameter to swap the ends of the homotopy.
i8 : t := H.ContinuationParameter o8 = t o8 : CC [x, y, t] 53 |
i9 : H' := substituteContinuationParameter(H,1-t) o9 = {-2} | -y2t+x2+y2+5t-6 | {-2} | -2x2t+y2t+2x2+yt-y-t | o9 : PolySystem |