• The function embed(S,d)  uses PHCpack to create an embedded system for the polynomial system S  taking into account the expected dimension of the solution. The slack variables are given names that start with zz.
• The constructed embedded system is 0-dimensional provided d  is correct. It can be solved using phc[solve] .

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

>	S := makeSystem([x,y,z], [], [x^2+y^2+z^2-4, x^2+y^2+z^2+6*z+5]):

>	R := embed(S,1):

>	R:-vars; R:-slacks; R:-polys;

>	printSolutions(R,solve(R)):

(1) [x = .963326949372258+.352976981481303e-1*I, y = .908101971236005-.374442793364052e-1*I, z = -1.50000000000000-.185905325060273e-17*I, zz1 = 0.+0.*I]

(2) [x = 155856.106073420-3045.70563603234*I, y = -6286.96293100190+347327.819587514*I, z = 310464.717096544+8562.43230503281*I, zz1 = -1.67423531232313-.461794678339994e-1*I]

(3) [x = -1.05534156291319+.571602916817716*I, y = -1.11952071523771-.538834438156918*I, z = -1.50000000000000+.200844531654971e-16*I, zz1 = 0.+0.*I]

(4) [x = 1295.28329951832+355294.434510200*I, y = -14980.4904238393-7443.51281973382*I, z = -355060.793290178+1610.20924607912*I, zz1 = 3.66633041358933-.166364482826447e-1*I]

>

phc , phc[solve] , phc[cascade] .