• The function eqnbyeqn(S)  applies the equation-by-equation solver of PHCpack to find a list witness sets C  for the component of the solution to the original system set in each dimension .
• This is an alternative to cascade  of homotopies.  

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

>	sys := makeSystem([x,y,z],[],[x^2+y^2+(z-1)^2-1, (z-0.5)*(z-1)*y,(z-0.5)*(z-1)*x]):

>	comps := eqnbyeqn(sys):

>	dim0 := comps[1]: dim1 :=comps[2]:

>	printSolutions(dim0:-system,dim0:-points);

(1) [x = .34694e-17-.13878e-16*I, y = -.16653e-15-.55511e-16*I, z = .13878e-16-.11102e-15*I]

(2) [x = -.13878e-16+.13878e-16*I, y = -.83267e-16-.11102e-15*I, z = 2.0-.11102e-15*I]

>	printSolutions(dim1:-system,dim1:-points);

(1) [x = .15070+.65651*I, y = 1.0801-.91596e-1*I, z = .50+.83267e-16*I, zz1 = 0.]

(2) [x = -.26247+.93573*I, y = -1.3563-.18109*I, z = 1.0, zz1 = 0.]

(3) [x = .15070+.65651*I, y = 1.0801-.91596e-1*I, z = .50-.55511e-16*I, zz1 = 0.]

(4) [x = .12899+.56639*I, y = -1.0292+.70986e-1*I, z = .50, zz1 = 0.]

phc , phc[cascade] .