• The function filter(H,W)  detects the junk points in the witness set W , i.e. the ones that lie on the higher-dimensional solution component represented by H .
• The retuned witness set C  consists of the good point of W .
• The optional parameters residual_tol  and wit_set_tol  let the user to tune the tolerances.

>	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]):

>	embsys := embed(sys,1):

>	embsols := solve(embsys):

>	comps := cascade(embsys,embsols):

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

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

(1) [x = 0, y = 0, z = 2.0]

(2) [x = 0, y = 0, z = 0]

(3) [x = -.923027707251813+.593279148760967*I, y = .923027707251813+.593279148760967*I, z = 1.0+.481482486096809e-34*I]

(4) [x = -.799365442876975+.513794814362604*I, y = .799365442876975+.513794814362604*I, z = .50-.137297740176043e-33*I]

(5) [x = .923027707251812-.593279148760966*I, y = -.923027707251812-.593279148760966*I, z = 1.0+.188079096131566e-36*I]

(6) [x = .799365442876975-.513794814362604*I, y = -.799365442876976-.513794814362604*I, z = .50+.700649232162409e-45*I]

>	dim0f := filter(dim1, dim0):

>	printSolutions(dim0f:-system,dim0f:-points);

(1) [x = 0, y = 0, z = 2.0]

(2) [x = 0, y = 0, z = 0]

phc , phc[embed] , phc[cascade] .