• The function decompose(W)  decomposes the pure-dimensional solution component represented by the (filtered) witness set W  into irreducible components.
• The irreducible components are represented by the witness sets in the returned list L .
• The witness set W is expected to be pure-dimensional and filtered (one can remove the junk points using filter )

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

Warning, the assigned name factor now has a global binding

Warning, the protected name solve has been redefined and unprotected

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

(1) [x = -15.519-3.3181*I, y = -3.3230+15.496*I, z = .50+.14960e-15*I, zz1 = .10614e-15-.15267e-14*I]

(2) [x = -18.412+5.1850*I, y = 5.1921+18.387*I, z = 1.0-.14980e-15*I, zz1 = -.74654e-15-.16886e-14*I]

(3) [x = -.18141+.25754e-1*I, y = -.84722-.55146e-2*I, z = .50+.10063e-17*I, zz1 = .51769e-17-.76397e-17*I]

(4) [x = .27214+.70690e-1*I, y = -.96506+.19934e-1*I, z = 1.0+.58146e-16*I, zz1 = -.42452e-16+.17505e-16*I]

>	irr1 := decompose(dim1): nops(irr1);

>	printSolutions(irr1[1]:-system,irr1[1]:-points);

(1) [x = -15.519-3.3181*I, y = -3.3230+15.496*I, z = .50+.14960e-15*I, zz1 = .10614e-15-.15267e-14*I]

(2) [x = -.18141+.25754e-1*I, y = -.84722-.55146e-2*I, z = .50+.10063e-17*I, zz1 = .51769e-17-.76397e-17*I]

>	printSolutions(irr1[2]:-system,irr1[2]:-points);

(1) [x = -18.412+5.1850*I, y = 5.1921+18.387*I, z = 1.0-.14980e-15*I, zz1 = -.74654e-15-.16886e-14*I]

(2) [x = .27214+.70690e-1*I, y = -.96506+.19934e-1*I, z = 1.0+.58146e-16*I, zz1 = -.42452e-16+.17505e-16*I]

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