• The function intersectWitnessSets(W1,W2)  applies the diagonal homotopy technique to find a witness set W3  for the intersection of the solution sets represented by the witness sets W1  and W2.

>	with(phc): setPHCloc("C:\\PHCmaple"):

>	S := makeSystem([x,y,z],[],[x^2+y^2+z^2-4]):

>	eS := embed(S,2):

>	sols := solve(eS):

>	W1 := makeWitnessSet(eS, sols):

>	C := makeSystem([x,y,z],[],[9*x^2+9*y^2+(z+1)^2-9]):

>	eC := embed(C,2):

>	sols := solve(eC): printSolutions(eC,sols):

(1) [x = 1.2257+.46996e-1*I, y = -.26918e-1+.80538*I, z = .18498-.27285*I, zz1 = 0., zz2 = 0.]

(2) [x = .13387-.95875e-1*I, y = -.87197-.27648e-3*I, z = .44383+.78500e-1*I, zz1 = 0., zz2 = 0.]

>	W2 := makeWitnessSet(eC, sols):

>	W3 := intersectWitnessSets(W1,W2):

>	printSystem(comp[1]:-system);

(1) 9*x^2+9*y^2+z^2+2*z+.287714760234765*zz1+.957716146226559*I*zz1-8

(2) x^2+y^2+z^2+.657734479394017*zz1-.753249862008804*I*zz1-4

(3) zz1

(4) -.220618184424173*x+.461639293274689*I*x-.639742018307134*y-1.35295644212202*I*y+z+zz1-.294408883451769+.733843356740222*I

>	printSolutions(comp[1]:-system, comp[1]:-points);

(1) [x = 2.1540-.38190*I, y = .42551+1.9332*I, z = -1.7500-.12212e-14*I, zz1 = 0.]

(2) [x = .50842+.82221*I, y = .82221-.50842*I, z = 2.0-.38858e-15*I, zz1 = 0.]

(3) [x = -1.3837-.27074*I, y = -.36754+1.0193*I, z = -1.75-.11102e-15*I, zz1 = 0.]

(4) [x = -1.3704-.86363*I, y = .86363-1.3704*I, z = 2.0+.15543e-14*I, zz1 = 0.]

phc .