Asymptotic critical values test polynomials


In Table 2 of the above paper we test our algorithm for three polynomials s1, s2, s3 in the variables p21, p22, p31 and p32.

These were sent to us in an email and we give them in full Maple format here:

s1:=-4*(47 + 54*p21^4 - 259*p22 + 455*p22^2 - 270*p22^3 + 3*p21^3*(-61 + 126*p22) + p21^2*(251 - 981*p22 + 810*p22^2) + p21*(-169 + 862*p22 - 1305*p22^2 + 540*p22^3) - 252*p31 + 462*p31^2 - 309*p31^3 + 72*p31^4 - 30*p32 + 1107*p31*p32 - 1449*p31^2*p32 + 504*p31^3*p32 + 60*p32^2 - 1575*p31*p32^2 + 1080*p31^2*p32^2 - 30*p32^3 + 720*p31*p32^3)* (-((63 + 216*p21^4 + p21^2*(759 - 864*p22) - 126*p22 + 48*p21^3*(-14 + 9*p22) + 6*p21*(-61 + 93*p22) - 38*p31 + 263*p31^2 - 576*p31^3 + 288*p31^4 + 38*p31*p32 - 336*p31^2*p32 + 576*p31^3*p32)*(9 + 54*p21^4 - 135*p22 + 135*p22^2 + 3*p21^3*(-59 + 90*p22) + p21*(-87 + 570*p22 - 405*p22^2) + 3*p21^2*(67 - 235*p22 + 90*p22^2) - 80*p31 + 260*p31^2 - 243*p31^3 + 72*p31^4 + 275*p31*p32 - 705*p31^2*p32 + 360*p31^3*p32 - 195*p31*p32^2 + 360*p31^2*p32^2)) + 3*(27 - 126*p21 + 243*p21^2 - 216*p21^3 + 72*p21^4 + 35*p31^2 - 104*p31^3 + 96*p31^4)*(47 + 54*p21^4 - 259*p22 + 455*p22^2 - 270*p22^3 + 3*p21^3*(-61 + 126*p22) + p21^2*(251 - 981*p22 + 810*p22^2) + p21*(-169 + 862*p22 - 1305*p22^2 + 540*p22^3) - 252*p31 + 462*p31^2 - 309*p31^3 + 72*p31^4 - 30*p32 + 1107*p31*p32 - 1449*p31^2*p32 + 504*p31^3*p32 + 60*p32^2 - 1575*p31*p32^2 + 1080*p31^2*p32^2 - 30*p32^3 + 720*p31*p32^3)) + ((-3*p21^2 + p21*(3 - 15*p22) + 5*(2 - 3*p22)*p22)^2 + 4*(1 + 3*p21^2 - 15*p22 + 15*p22^2 + p21*(-4 + 15*p22))^2 + (3*p21^2 + p21*(-13 + 15*p22) + 5*(2 - 6*p22 + 3*p22^2))^2 + (-5 + 2*p31 + 5*p32)^2 + (5 - 14*p31 + 6*p31^2 - 35*p32 + 30*p31*p32 + 30*p32^2)^2 + 4*(3*p31^2 + 5*p31*(-2 + 3*p32) + 5*(2 - 5*p32 + 3*p32^2))^2)* (-(63 + 216*p21^4 + p21^2*(759 - 864*p22) - 126*p22 + 48*p21^3*(-14 + 9*p22) + 6*p21*(-61 + 93*p22) - 38*p31 + 263*p31^2 - 576*p31^3 + 288*p31^4 + 38*p31*p32 - 336*p31^2*p32 + 576*p31^3*p32)^2 + 3*(27 - 126*p21 + 243*p21^2 - 216*p21^3 + 72*p21^4 + 35*p31^2 - 104*p31^3 + 96*p31^4)* ((7 - 12*p21)^2*(-1 + p21 + 2*p22)^2 + 4*(4 + 3*p21^2 - 2*p22 + p21*(-7 + 6*p22))^2 + 4*(3*p21^2 - 2*p22 + p21*(-3 + 6*p22))^2 + 16*(-1 + p31 + p32)^2 + (-2 - 19*p31 + 12*p31^2 + 2*p32 + 24*p31*p32)^2 + 16*(1 + 3*p31^2 - p32 + p31*(-4 + 6*p32))^2)) + 4*(9 + 54*p21^4 - 135*p22 + 135*p22^2 + 3*p21^3*(-59 + 90*p22) + p21*(-87 + 570*p22 - 405*p22^2) + 3*p21^2*(67 - 235*p22 + 90*p22^2) - 80*p31 + 260*p31^2 - 243*p31^3 + 72*p31^4 + 275*p31*p32 - 705*p31^2*p32 + 360*p31^3*p32 - 195*p31*p32^2 + 360*p31^2*p32^2)* ((63 + 216*p21^4 + p21^2*(759 - 864*p22) - 126*p22 + 48*p21^3*(-14 + 9*p22) + 6*p21*(-61 + 93*p22) - 38*p31 + 263*p31^2 - 576*p31^3 + 288*p31^4 + 38*p31*p32 - 336*p31^2*p32 + 576*p31^3*p32)* (47 + 54*p21^4 - 259*p22 + 455*p22^2 - 270*p22^3 + 3*p21^3*(-61 + 126*p22) + p21^2*(251 - 981*p22 + 810*p22^2) + p21*(-169 + 862*p22 - 1305*p22^2 + 540*p22^3) - 252*p31 + 462*p31^2 - 309*p31^3 + 72*p31^4 - 30*p32 + 1107*p31*p32 - 1449*p31^2*p32 + 504*p31^3*p32 + 60*p32^2 - 1575*p31*p32^2 + 1080*p31^2*p32^2 - 30*p32^3 + 720*p31*p32^3) - (9 + 54*p21^4 - 135*p22 + 135*p22^2 + 3*p21^3*(-59 + 90*p22) + p21*(-87 + 570*p22 - 405*p22^2) + 3*p21^2*(67 - 235*p22 + 90*p22^2) - 80*p31 + 260*p31^2 - 243*p31^3 + 72*p31^4 + 275*p31*p32 - 705*p31^2*p32 + 360*p31^3*p32 - 195*p31*p32^2 + 360*p31^2*p32^2)*((7 - 12*p21)^2*(-1 + p21 + 2*p22)^2 + 4*(4 + 3*p21^2 - 2*p22 + p21*(-7 + 6*p22))^2 + 4*(3*p21^2 - 2*p22 + p21*(-3 + 6*p22))^2 + 16*(-1 + p31 + p32)^2 + (-2 - 19*p31 + 12*p31^2 + 2*p32 + 24*p31*p32)^2 + 16*(1 + 3*p31^2 - p32 + p31*(-4 + 6*p32))^2)) + 4*(9 + 54*p21^4 - 135*p22 + 135*p22^2 + 3*p21^3*(-59 + 90*p22) + p21*(-87 + 570*p22 - 405*p22^2) + 3*p21^2*(67 - 235*p22 + 90*p22^2) - 80*p31 + 260*p31^2 - 243*p31^3 + 72*p31^4 + 275*p31*p32 - 705*p31^2*p32 + 360*p31^3*p32 - 195*p31*p32^2 + 360*p31^2*p32^2)* ((63 + 216*p21^4 + p21^2*(759 - 864*p22) - 126*p22 + 48*p21^3*(-14 + 9*p22) + 6*p21*(-61 + 93*p22) - 38*p31 + 263*p31^2 - 576*p31^3 + 288*p31^4 + 38*p31*p32 - 336*p31^2*p32 + 576*p31^3*p32)* (47 + 54*p21^4 - 259*p22 + 455*p22^2 - 270*p22^3 + 3*p21^3*(-61 + 126*p22) + p21^2*(251 - 981*p22 + 810*p22^2) + p21*(-169 + 862*p22 - 1305*p22^2 + 540*p22^3) - 252*p31 + 462*p31^2 - 309*p31^3 + 72*p31^4 - 30*p32 + 1107*p31*p32 - 1449*p31^2*p32 + 504*p31^3*p32 + 60*p32^2 - 1575*p31*p32^2 + 1080*p31^2*p32^2 - 30*p32^3 + 720*p31*p32^3) - (9 + 54*p21^4 - 135*p22 + 135*p22^2 + 3*p21^3*(-59 + 90*p22) + p21*(-87 + 570*p22 - 405*p22^2) + 3*p21^2*(67 - 235*p22 + 90*p22^2) - 80*p31 + 260*p31^2 - 243*p31^3 + 72*p31^4 + 275*p31*p32 - 705*p31^2*p32 + 360*p31^3*p32 - 195*p31*p32^2 + 360*p31^2*p32^2)*((7 - 12*p21)^2*(-1 + p21 + 2*p22)^2 + 4*(4 + 3*p21^2 - 2*p22 + p21*(-7 + 6*p22))^2 + 4*(3*p21^2 - 2*p22 + p21*(-3 + 6*p22))^2 + 16*(-1 + p31 + p32)^2 + (-2 - 19*p31 + 12*p31^2 + 2*p32 + 24*p31*p32)^2 + 16*(1 + 3*p31^2 - p32 + p31*(-4 + 6*p32))^2)):

s1:=expand(s1):

s2:=expand(subs({p32=p32+1, p21=p21+1}, s1)):

s2:=s2/content(s2):

s3:=expand(subs({p21=p21-p22, p31=p31-p32}, s2)):