PHCmaple.test

libname := ".", libname:
with(phc): setPHCloc("."):
# Cascade
printf("Testing...\n"):
printf("cascade...\n"):
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]): d := 1:
embsys := embed(sys,d):
embsols := solve(embsys):
comps := cascade(embsys,embsols):

# Filter
printf("filter...\n"):
filter(comps[d+1], comps[d]):
 
# Decompose
printf("decompose...\n"):
topcomps := decompose(comps[d+1]):

# Refine
printf("refine...\n"):
sys := makeSystem([x,y],[],[x^2+y^2-1, x+y]):
sols := solve(sys): 
refsols := refine(sols,sys,
digits=32,residual_tol=1e-50,error_tol=1e-51,singular_tol=1e-52,max_iterations=5):

# Positive-dimensional solutions
printf("embed,solve...\n"):
sys := makeSystem([x,y,z],[],[x^2+y^2+z^2+1, 4*z^2-1, 2*z-1]):
s := embed(sys,1):
sols := solve(s): 
 
# Factor
printf("factor...\n"):
p := x^2-y^2:
factor(p):

# Deflation
printf("deflation...\n"):
T := makeSystem([x,y],[],[x^2+y-3, x+0.125*y^2-1.5]):
sols := solve(T):
l := deflationStep(sols,T):
DT := l[2]["deflated system"]: 
eqns := map(p->p=0,DT:-polys[nops(T:-polys)+1..nops(DT:-polys)]):
DTmu := subsVariables(DT,[seq(lambda[i]=mu[i],i=1..l[2]["corank"])]): 
g := deflationStep(l[2]["points"],DTmu)[1]: 

# Equation-by-equation
printf("equbyequ...\n"):
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):
 
# Intersection
printf("intersect...\n"):
S := makeSystem([x,y,z],[],[x^2+y^2+z^2-4]):
eS := embed(S,2):
sols := solve(eS):
wS := 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): 
wC := makeWitnessSet(eC, sols):
comp := intersectWitnessSets(wC,wS):

# Bertini
printf("solve(Bertini)...\n"):
setPHCloc(".", phc="Bertini"):
sys := makeSystem([x,y],[],[x^2+y^2-1, x+y]):
sols := solve(sys):