実行例（５）
入力は，主に http://www.cs.bath.ac.uk/~djw42/triangular/examplebank.pdf の Examples from [CMXY09]（https://arxiv.org/pdf/0903.5221.pdf）から選びました．
環境は，Core i5-3210M 2.50GHz/8GB/Ubuntu 14.04/Maxima 5.40.0/SBCL 1.3.20 です．
コントローラー qvpeds の第 4 引数が h1 は Hong タイプ，l は Lazard タイプの処理を表し，%pp はそれぞれの projection set です．
(%i4) [(qvpeds([ex],[a,b,c,x],0,h1,r11,0),
qe(bfpcad(ext('(a*x^2+b*x+c = 0))))),%pp]
Evaluation took 0.2600 seconds (0.2620 elapsed) using 30.789 MB.
(%o4) [[[a < root(a,1),true,root(4*a*c-b^2,1) <= c,true],
[a = root(a,1),b < root(b,1),true,true],
[a = root(a,1),b = root(b,1),c = root(c,1),true],
[a = root(a,1),root(b,1) < b,true,true],
[root(a,1) < a,true,c <= root(4*a*c-b^2,1),true]],
[[a],[b],[c,4*a*c-b^2],[a*x^2+b*x+c]]]
(%i5) [(qvpeds([ex],[a,b,c,x],0,l,r11,0),qe(bfpcad(ext('(a*x^2+b*x+c = 0))))),%pp]
Evaluation took 0.2110 seconds (0.2090 elapsed) using 30.792 MB.
(%o5) [[[a < root(a,1),true,root(4*a*c-b^2,1) <= c,true],
[a = root(a,1),b < root(b,1),true,true],
[a = root(a,1),b = root(b,1),c = root(c,1),true],
[a = root(a,1),root(b,1) < b,true,true],
[root(a,1) < a,true,c <= root(4*a*c-b^2,1),true]],
[[a],[b],[c,4*a*c-b^2],[a*x^2+b*x+c]]]
(%i6) [(qvpeds([all],[c,b,a,x],0,h1,r11,0),
qe(bfpcad(ext('(x^4+a*x^2+b*x+c >= 0))))),%pp]
Evaluation took 2.7640 seconds (2.7610 elapsed) using 665.230 MB.
(%o6) [[[c = root(c,1),b = root(126976*c^3-135*b^4,1),root(a,1) <= a,true],
[root(c,1) < c,b < root(b,1),
root(256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,2)
<= a,true],
[root(c,1) < c,b = root(b,1),
root(256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,1)
<= a,true],
[root(c,1) < c,root(b,1) < b,
root(256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,2)
<= a,true]],
[[c],
[b,256*c^3-27*b^4,1024*c^3-2187*b^4,1024*c^3+3*b^4,4096*c^3+27*b^4,
126976*c^3-135*b^4],
[a,8*a*c-9*b^2-2*a^3,
256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2],
[x^4+a*x^2+b*x+c]]]
(%i7) [(qvpeds([all],[c,b,a,x],0,l,r11,0),
qe(bfpcad(ext('(x^4+a*x^2+b*x+c >= 0))))),%pp]
Evaluation took 0.7110 seconds (0.7090 elapsed) using 174.679 MB.
(%o7) [[[c = root(c,1),b = root(4096*c^3+27*b^4,1),root(a,1) <= a,true],
[root(c,1) < c,b < root(b,1),
root(256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,2)
<= a,true],
[root(c,1) < c,b = root(b,1),
root(256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,1)
<= a,true],
[root(c,1) < c,root(b,1) < b,
root(256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2,2)
<= a,true]],
[[c],[b,256*c^3-27*b^4,4096*c^3+27*b^4],
[256*c^3-128*a^2*c^2+(144*a*b^2+16*a^4)*c-27*b^4-4*a^3*b^2],
[x^4+a*x^2+b*x+c]]]
(%i8) [(qvpeds([all],[d,c,a,b,x],0,h1,r11,0),
qe(bfpcad(ext('(a*x^4+b*x^2+c*x+d >= 0))))),%pp]
Evaluation took 5.4500 seconds (5.4580 elapsed) using 1195.996 MB.
(%o8) [[[d = root(d,1),c = root(c,1),root(a,1) <= a,root(b,1) <= b,true],
[root(d,1) < d,c < root(c,1),root(a,1) <= a,
root(256*a^2*d^3-128*a*b^2*d^2+(144*a*b*c^2+16*b^4)*d-27*a*c^4
-4*b^3*c^2,2)
<= b,true],
[root(d,1) < d,c = root(c,1),root(126976*a*d^3-135*c^4,1) <= a,
root(256*a^2*d^3-128*a*b^2*d^2+(144*a*b*c^2+16*b^4)*d-27*a*c^4
-4*b^3*c^2,1)
<= b,true],
[root(d,1) < d,root(c,1) < c,root(a,1) <= a,
root(256*a^2*d^3-128*a*b^2*d^2+(144*a*b*c^2+16*b^4)*d-27*a*c^4
-4*b^3*c^2,2)
<= b,true]],
[[d],[c],
[a,256*a*d^3-27*c^4,1024*a*d^3-2187*c^4,1024*a*d^3+3*c^4,
4096*a*d^3+27*c^4,126976*a*d^3-135*c^4],
[b,8*a*b*d-9*a*c^2-2*b^3,
256*a^2*d^3-128*a*b^2*d^2+(144*a*b*c^2+16*b^4)*d-27*a*c^4-4*b^3*c^2],
[a*x^4+b*x^2+c*x+d]]]
(%i9) [(qvpeds([all],[d,c,a,b,x],0,l,r11,0),
qe(bfpcad(ext('(a*x^4+b*x^2+c*x+d >= 0))))),%pp]
Evaluation took 1.5370 seconds (1.5370 elapsed) using 368.276 MB.
(%o9) [[[d = root(d,1),c = root(c,1),root(a,1) <= a,root(b,1) <= b,true],
[root(d,1) < d,c < root(c,1),root(a,1) <= a,
root(256*a^2*d^3-128*a*b^2*d^2+(144*a*b*c^2+16*b^4)*d-27*a*c^4
-4*b^3*c^2,2)
<= b,true],
[root(d,1) < d,c = root(c,1),root(4096*a*d^3+27*c^4,1) <= a,
root(256*a^2*d^3-128*a*b^2*d^2+(144*a*b*c^2+16*b^4)*d-27*a*c^4
-4*b^3*c^2,1)
<= b,true],
[root(d,1) < d,root(c,1) < c,root(a,1) <= a,
root(256*a^2*d^3-128*a*b^2*d^2+(144*a*b*c^2+16*b^4)*d-27*a*c^4
-4*b^3*c^2,2)
<= b,true]],
[[d],[c],[a,256*a*d^3-27*c^4,4096*a*d^3+27*c^4],
[256*a^2*d^3-128*a*b^2*d^2+(144*a*b*c^2+16*b^4)*d-27*a*c^4-4*b^3*c^2],
[a*x^4+b*x^2+c*x+d]]]
(%i10) [(qvpeds([],[x,z,y],0,h1,r11,0),
qe(bfpcad(ext('(z^2+y^2+x^2-1 = 0 and z^3+x*z+y = 0))))),%pp]
Evaluation took 0.2330 seconds (0.2330 elapsed) using 44.868 MB.
(%o10) [[[x = root(x+1,1),z = root(z^6+2*x*z^4+(x^2+1)*z^2+x^2-1,1),
y = root(z^3+x*z+y,1)],
[root(x+1,1) < x and x < root(x-1,1),
z = root(z^6+2*x*z^4+(x^2+1)*z^2+x^2-1,1)
or z = root(z^6+2*x*z^4+(x^2+1)*z^2+x^2-1,2),
y = root(z^3+x*z+y,1)],
[x = root(x-1,1),z = root(z^6+2*x*z^4+(x^2+1)*z^2+x^2-1,1),
y = root(z^3+x*z+y,1)]],
[[x-1,x,x+1,x^2-3,3*x^3-2*x^2-3*x-2,
4*x^5-31*x^4+32*x^3+46*x^2-36*x-31],[z^6+2*x*z^4+(x^2+1)*z^2+x^2-1],
[z^3+x*z+y]]]
(%i11) [(qvpeds([],[x,z,y],0,l,r11,0),
qe(bfpcad(ext('(z^2+y^2+x^2-1 = 0 and z^3+x*z+y = 0))))),%pp]
Evaluation took 0.1250 seconds (0.1300 elapsed) using 22.110 MB.
(%o11) [[[x = root(x+1,1),z = root(z^6+2*x*z^4+(x^2+1)*z^2+x^2-1,1),
y = root(z^3+x*z+y,1)],
[root(x+1,1) < x and x < root(x-1,1),
z = root(z^6+2*x*z^4+(x^2+1)*z^2+x^2-1,1)
or z = root(z^6+2*x*z^4+(x^2+1)*z^2+x^2-1,2),
y = root(z^3+x*z+y,1)],
[x = root(x-1,1),z = root(z^6+2*x*z^4+(x^2+1)*z^2+x^2-1,1),
y = root(z^3+x*z+y,1)]],
[[x-1,x+1,4*x^5-31*x^4+32*x^3+46*x^2-36*x-31],
[z^6+2*x*z^4+(x^2+1)*z^2+x^2-1],[z^3+x*z+y]]]
(%i12) [(qvpeds([],[y,x],0,h1,r11,0),
qe(bfpcad(ext('(y^4-2*y^3+y^2+(-3)*x^2*y+2*x^4 = 0))))),%pp]
Evaluation took 0.1530 seconds (0.1530 elapsed) using 20.637 MB.
(%o12) [[[y = root(y,1),x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,1)],
[root(y,1) < y and y < root(y-1,1),
x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,1)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,2)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,3)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,4)],
[y = root(y-1,1),
x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,1)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,2)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,3)],
[root(y-1,1) < y and y < root(8*y^2-16*y-1,2),
x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,1)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,2)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,3)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,4)],
[y = root(8*y^2-16*y-1,2),
x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,1)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,2)]],
[[y-1,y,8*y^2-16*y-1],[y^4-2*y^3+y^2-3*x^2*y+2*x^4]]]
(%i13) [(qvpeds([],[y,x],0,l,r11,0),
qe(bfpcad(ext('(y^4-2*y^3+y^2+(-3)*x^2*y+2*x^4 = 0))))),%pp]
Evaluation took 0.1170 seconds (0.1170 elapsed) using 20.605 MB.
(%o13) [[[y = root(y,1),x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,1)],
[root(y,1) < y and y < root(y-1,1),
x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,1)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,2)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,3)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,4)],
[y = root(y-1,1),
x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,1)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,2)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,3)],
[root(y-1,1) < y and y < root(8*y^2-16*y-1,2),
x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,1)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,2)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,3)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,4)],
[y = root(8*y^2-16*y-1,2),
x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,1)
or x = root(y^4-2*y^3+y^2-3*x^2*y+2*x^4,2)]],
[[y-1,y,8*y^2-16*y-1],[y^4-2*y^3+y^2-3*x^2*y+2*x^4]]]
(%i14) [(qvpeds([],[y,x],0,h1,r11,0),
qe(bfpcad(ext('(144*y^2+96*x^2*y+9*x^4+105*x^2+70*x-98 = 0
and x*y^2+6*x*y+x^3+9*x = 0))))),%pp]
Evaluation took 0.0780 seconds (0.0780 elapsed) using 9.584 MB.
(%o14) [[[y = root(72*y^2-49,1) or y = root(72*y^2-49,2),
x = root(1132535906187264*y^9+2648683072534464*y^8
-11812443576362496*y^7
-144938986561480320*y^6
-169128077155358976*y^5
+764415088047207513*y^4
+4188447484701833676*y^3
+3270406842477283485*y^2
-2768658167053333674*y
+419177363858840230*x
-2534619807825082586,1)]],
[[72*y^2-49],
[1132535906187264*y^9+2648683072534464*y^8-11812443576362496*y^7
-144938986561480320*y^6-169128077155358976*y^5
+764415088047207513*y^4+4188447484701833676*y^3
+3270406842477283485*y^2-2768658167053333674*y
+419177363858840230*x-2534619807825082586]]]
(%i15) [(qvpeds([],[y,x],0,l,r11,0),
qe(bfpcad(ext('(144*y^2+96*x^2*y+9*x^4+105*x^2+70*x-98 = 0
and x*y^2+6*x*y+x^3+9*x = 0))))),%pp]
Evaluation took 0.0780 seconds (0.0800 elapsed) using 9.506 MB.
(%o15) [[[y = root(72*y^2-49,1) or y = root(72*y^2-49,2),
x = root(1132535906187264*y^9+2648683072534464*y^8
-11812443576362496*y^7
-144938986561480320*y^6
-169128077155358976*y^5
+764415088047207513*y^4
+4188447484701833676*y^3
+3270406842477283485*y^2
-2768658167053333674*y
+419177363858840230*x
-2534619807825082586,1)]],
[[72*y^2-49],
[1132535906187264*y^9+2648683072534464*y^8-11812443576362496*y^7
-144938986561480320*y^6-169128077155358976*y^5
+764415088047207513*y^4+4188447484701833676*y^3
+3270406842477283485*y^2-2768658167053333674*y
+419177363858840230*x-2534619807825082586]]]
(%i16) [(qvpeds([ex,ex],[x,y,z,a,b],0,h1,r11,0),
qe(bfpcad(ext('(x-a*b = 0 and y-a*b^2 = 0 and z-a^2 = 0))))),%pp]
Evaluation took 0.4380 seconds (0.4390 elapsed) using 97.523 MB.
(%o16) [[[x < root(x,1),y < root(y,1) or root(y,1) < y,z = root(y^2*z-x^4,1),
true,true],[x = root(x,1),y = root(y,1),root(z,1) <= z,true,true],
[root(x,1) < x,y < root(y,1) or root(y,1) < y,z = root(y^2*z-x^4,1),
true,true]],
[[x],[y],[z,z*y^2-x^4],[a,a*y-x^2,(-a^2)+z,z*y-a*x^2],
[x-a*b,y-b*x,(-a*x)+z*b]]]
(%i17) [(qvpeds([ex,ex],[x,y,z,a,b],0,l,r11,0),
qe(bfpcad(ext('(x-a*b = 0 and y-a*b^2 = 0 and z-a^2 = 0))))),%pp]
Evaluation took 0.4270 seconds (0.4270 elapsed) using 96.663 MB.
(%o17) [[[x < root(x,1),y < root(y,1) or root(y,1) < y,z = root(y^2*z-x^4,1),
true,true],[x = root(x,1),y = root(y,1),root(z,1) <= z,true,true],
[root(x,1) < x,y < root(y,1) or root(y,1) < y,z = root(y^2*z-x^4,1),
true,true]],
[[x],[y],[z,(-x^4)+z*y^2],[a,(-x^2)+y*a,(-a^2)+z,(-a*x^2)+z*y],
[x-a*b,(-b*x)+y,(-a*x)+z*b]]]
(%i18) [(qvpeds([ex,ex,ex],[x,y,z],0,h1,r11,0),
qe(bfpcad(ext('(x^2+y^2+z^2-1 < 0 and x^2+(y+z-2)^2-1 < 0))))),%pp]
Evaluation took 0.3330 seconds (0.3330 elapsed) using 73.647 MB.
(%o18) [[[true,true,true]],
[[x-1,x,x+1,x^4+22*x^2-7],
[y^2+x^2-1,y^4-4*y^3+(x^2+7)*y^2+((-4*x^2)-4)*y+4*x^2],
[z^2+y^2+x^2-1,z^2+(2*y-4)*z+y^2-4*y+x^2+3]]]
(%i19) [(qvpeds([ex,ex,ex],[x,y,z],0,l,r11,0),
qe(bfpcad(ext('(x^2+y^2+z^2-1 < 0 and x^2+(y+z-2)^2-1 < 0))))),%pp]
Evaluation took 0.3160 seconds (0.3170 elapsed) using 65.861 MB.
(%o19) [[[true,true,true]],
[[x-1,x,x+1,x^4+22*x^2-7],
[y^2+x^2-1,y^4-4*y^3+(x^2+7)*y^2+((-4*x^2)-4)*y+4*x^2],
[z^2+y^2+x^2-1,z^2+(2*y-4)*z+y^2-4*y+x^2+3]]]
(%i20) [(qvpeds([ex,all,all],[r,x,y],0,h1,r11,0),
qe(bfpcad(ext('(x-r > 0 and y-r > 0
implies x^2*(1+2*y)^2-y^2*(1+2*x^2) > 0))))),%pp]
Evaluation took 0.9550 seconds (0.9550 elapsed) using 189.163 MB.
(%o20) [[[true,true,true]],
[[r,r+2,2*r+1,4*r+1,2*r^2-1,2*r^2+4*r+1],
[x,x-r,2*x^2-1,2*x^2+1,(2*r^2+4*r+1)*x^2-r^2],
[y-r,(2*x^2-1)*y^2+4*x^2*y+x^2]]]
(%i21) [(qvpeds([ex,all,all],[r,x,y],0,l,r11,0),
qe(bfpcad(ext('(x-r > 0 and y-r > 0
implies x^2*(1+2*y)^2-y^2*(1+2*x^2) > 0))))),%pp]
Evaluation took 0.9320 seconds (0.9330 elapsed) using 175.511 MB.
(%o21) [[[true,true,true]],
[[r,r+2,2*r+1,4*r+1,2*r^2-1,2*r^2+4*r+1],
[x,x-r,2*x^2-1,2*x^2+1,(2*r^2+4*r+1)*x^2-r^2],
[y-r,(2*x^2-1)*y^2+4*x^2*y+x^2]]]
(%i22) [(qvpeds([ex],[a,b,r],0,h1r,r11,0),
qe(bfpcad(ext('(3*a^2*r+3*b^2+(-2)*a*r-a^2-b^2 < 0
and 3*a^2*r+3*b^2*r+(-4)*a*r+r+(-2)*a^2+(-2)*b^2+2*a
> 0 and a-1/2 >= 0 and b > 0 and r > 0
and r-1 < 0))))),%pp]
Evaluation took 2.5190 seconds (2.5200 elapsed) using 659.301 MB.
(%o22) [[[root(2*a-1,1) <= a and a < root(3*a-2,1),
root(b,1) < b and b < root(b^2+a^2-a,2),true],
[a = root(3*a-2,1),root(b,1) < b and b <= root(b^2+a^2-a,2),true],
[root(3*a-2,1) < a and a < root(a-1,1),
root(b,1) < b and b < root(6*b^4+(9*a^2-12*a+2)*b^2+3*a^4-6*a^3
+3*a^2,4),true],
[a = root(a-1,1),
root(b,1) < b and b < root(6*b^4+(9*a^2-12*a+2)*b^2+3*a^4-6*a^3
+3*a^2,3),true],
[root(a-1,1) < a and a < root(9*a^4-72*a^3+108*a^2-48*a+4,3),
root(6*b^4+(9*a^2-12*a+2)*b^2+3*a^4-6*a^3+3*a^2,3) < b
and b < root(6*b^4+(9*a^2-12*a+2)*b^2+3*a^4-6*a^3+3*a^2,4),true]],
[[9*a^4-72*a^3+108*a^2-48*a+4,9*a^2-12*a+2,3*a-1,3*a-2,2*a-1,a,a-1],
[6*b^4+(9*a^2-12*a+2)*b^2+3*a^4-6*a^3+3*a^2,3*b^2+3*a^2-4*a+1,
2*b^2-a^2,b^2+a^2-a,b^2+a^2-2*a+1,b],
[(3*b^2+3*a^2-4*a+1)*r-2*b^2-2*a^2+2*a,(3*a^2-2*a)*r+2*b^2-a^2,r,
r-1]]]
(%i23) [(qvpeds([ex],[a,b,r],0,l,r11,0),
qe(bfpcad(ext('(3*a^2*r+3*b^2+(-2)*a*r-a^2-b^2 < 0
and 3*a^2*r+3*b^2*r+(-4)*a*r+r+(-2)*a^2+(-2)*b^2+2*a
> 0 and a-1/2 >= 0 and b > 0 and r > 0
and r-1 < 0))))),%pp]
Evaluation took 2.1620 seconds (2.1620 elapsed) using 514.650 MB.
(%o23) [[[root(2*a-1,1) <= a and a < root(3*a-2,1),
root(b,1) < b and b < root(b^2+a^2-a,2),true],
[a = root(3*a-2,1),root(b,1) < b and b < root(2*b^2-a^2,2),true],
[root(3*a-2,1) < a and a < root(a-1,1),
root(b,1) < b and b < root(6*b^4+(9*a^2-12*a+2)*b^2+3*a^4-6*a^3
+3*a^2,4),true],
[a = root(a-1,1),
root(6*b^4+(9*a^2-12*a+2)*b^2+3*a^4-6*a^3+3*a^2,2) < b
and b < root(6*b^4+(9*a^2-12*a+2)*b^2+3*a^4-6*a^3+3*a^2,3),true],
[root(a-1,1) < a and a < root(9*a^4-72*a^3+108*a^2-48*a+4,3),
root(6*b^4+(9*a^2-12*a+2)*b^2+3*a^4-6*a^3+3*a^2,3) < b
and b < root(6*b^4+(9*a^2-12*a+2)*b^2+3*a^4-6*a^3+3*a^2,4),true]],
[[a-1,a,2*a-1,3*a-2,3*a-1,9*a^4-72*a^3+108*a^2-48*a+4],
[b,b^2+a^2-2*a+1,b^2+a^2-a,2*b^2-a^2,3*b^2+3*a^2-4*a+1,
6*b^4+(9*a^2-12*a+2)*b^2+3*a^4-6*a^3+3*a^2],
[r-1,r,(3*a^2-2*a)*r+2*b^2-a^2,
(3*b^2+3*a^2-4*a+1)*r-2*b^2-2*a^2+2*a]]]
(%i24) [(qvpeds([all,all,all,ex],[y,x,a,b,c,z],0,h1,r11,0),
qe(bfpcad(ext('(a > 0 and a*z^2+b*z+c # 0
implies a*x^2+b*x+c-y > 0))))),%pp]
Evaluation took 3.0010 seconds (3.0030 elapsed) using 622.586 MB.
(%o24) [[[y <= root(y,1),true,true,true,true,true]],
[[y],[x],[a,(-x^2*a)+y],
[b,(-x*b)-x^2*a+y,(-b^2)-4*x*a*b-4*x^2*a^2+4*y*a],
[c,4*a*c-b^2,(-c)-x*b-x^2*a+y],[a*z^2+b*z+c]]]
(%i25) [(qvpeds([all,all,all,ex],[y,x,a,b,c,z],0,l,r11,0),
qe(bfpcad(ext('(a > 0 and a*z^2+b*z+c # 0
implies a*x^2+b*x+c-y > 0))))),%pp]
Evaluation took 2.9450 seconds (2.9450 elapsed) using 598.900 MB.
(%o25) [[[y <= root(y,1),true,true,true,true,true]],
[[y],[x],[a,(-x^2*a)+y],
[b,(-x*b)-x^2*a+y,(-b^2)-4*x*a*b-4*x^2*a^2+4*y*a],
[c,4*a*c-b^2,(-c)-x*b-x^2*a+y],[a*z^2+b*z+c]]]
(%i26) [(qvpeds([all,all],[b,a,c,x,y],0,h1r,r11,0),
qe(bfpcad(ext('(0 < a and 0 < b
and ((x-c)^2/a^2+y^2/b^2 = 1
implies x^2+y^2 <= 1)))))),%pp]
Evaluation took 76.6110 seconds (76.6430 elapsed) using 15531.535 MB.
(%o26) [[[root(b,1) < b and b < root(b-1,1),
root(a,1) < a and a < root(b^2-a,1),
root(b^2*c^2+b^4+((-a^2)-1)*b^2+a^2,1) <= c
and c <= root(b^2*c^2+b^4+((-a^2)-1)*b^2+a^2,2),true,true],
[root(b,1) < b and b < root(b-1,1),
root(b^2-a,1) <= a and a < root(a-1,1),
root(c-a+1,1) <= c and c <= root(c+a-1,1),true,true],
[root(b,1) < b and b < root(b-1,1),a = root(a-1,1),c = root(c,1),
true,true],
[b = root(b-1,1),root(a,1) < a and a <= root(a-1,1),c = root(c,1),
true,true]],
[[b+1,b,b-1],
[(2*a+1)*b^2+a^2,(2*a-1)*b^2-a^2,b^2+a,b^2-a,b+a,b-a,a+1,a,a-1],
[b^2*c^2+b^4+((-a^2)-1)*b^2+a^2,b^2*c^2-a^2*b^2+a^2,c+a+1,c+a-1,
c-a+1,c-a-1,c],
[(b^2-a^2)*x^2-2*b^2*c*x+b^2*c^2-a^2*b^2+a^2,x-c+a,x-c-a,x+1,x-1],
[a^2*y^2+b^2*x^2-2*b^2*c*x+b^2*c^2-a^2*b^2,y^2+x^2-1]]]
(%i27) [(qvpeds([all,all],[b,a,c,x,y],0,l,r11,0),
qe(bfpcad(ext('(0 < a and 0 < b
and ((x-c)^2/a^2+y^2/b^2 = 1
implies x^2+y^2 <= 1)))))),%pp]
Evaluation took 62.6640 seconds (62.6860 elapsed) using 11842.095 MB.
(%o27) [[[root(b,1) < b and b < root(b-1,1),
root(a,1) < a and a <= root(b^2-a,1),
root(b^2*c^2+b^4+((-a^2)-1)*b^2+a^2,1) <= c
and c <= root(b^2*c^2+b^4+((-a^2)-1)*b^2+a^2,2),true,true],
[root(b,1) < b and b < root(b-1,1),
root(b^2-a,1) < a and a < root(a-1,1),
root(c-a+1,1) <= c and c <= root(c+a-1,1),true,true],
[root(b,1) < b and b < root(b-1,1),a = root(a-1,1),c = root(c+a-1,1),
true,true],
[b = root(b-1,1),root(a,1) < a and a <= root((2*a-1)*b^2-a^2,1),
c = root(b^2*c^2+b^4+((-a^2)-1)*b^2+a^2,1),true,true]],
[[b-1,b,b+1],
[a-1,a,a+1,b-a,b+a,b^2-a,b^2+a,(2*a-1)*b^2-a^2,(2*a+1)*b^2+a^2],
[c-a-1,c-a+1,c+a-1,c+a+1,b^2*c^2-a^2*b^2+a^2,
b^2*c^2+b^4+((-a^2)-1)*b^2+a^2],
[x-1,x+1,x-c-a,x-c+a,(b^2-a^2)*x^2-2*b^2*c*x+b^2*c^2-a^2*b^2+a^2],
[y^2+x^2-1,a^2*y^2+b^2*x^2-2*b^2*c*x+b^2*c^2-a^2*b^2]]]
(%i28) [(qvpeds([ex,all,all],[d,c,a,b],0,h1r,r11,0),
qe(bfpcad(ext('((a-d = 0 and b-c = 0 or a-c = 0 and b-1 = 0)
implies a^2-b = 0))))),%pp]
Evaluation took 9.7020 seconds (9.7060 elapsed) using 1360.997 MB.
(%o28) [[[d = root(d+1,1) or d = root(d-1,1),true,true,true]],
[[d+1,d,d-1],[(-c)+d^2,(-c)+d,c+1,c,c-1],
[(-a)+d,(-a^2)+c,(-a)+c,a+1,a-1],[(-b)+c,b-a^2,b-1]]]
(%i29) [(qvpeds([ex,all,all],[d,c,a,b],0,l,r11,0),
qe(bfpcad(ext('((a-d = 0 and b-c = 0 or a-c = 0 and b-1 = 0)
implies a^2-b = 0))))),%pp]
Evaluation took 9.5980 seconds (9.6010 elapsed) using 1325.779 MB.
(%o29) [[[d = root(d+1,1) or d = root(d-1,1),true,true,true]],
[[d-1,d,d+1],[c-1,c,c+1,(-c)+d,(-c)+d^2],
[a-1,a+1,(-a)+c,(-a^2)+c,(-a)+d],[b-1,b-a^2,(-b)+c]]]
(%i30) [(qvpeds([ex,ex,ex],[b,a,x,y,z],0,h1,r11,0),
qe(bfpcad(ext('(x+y+z = 0 and x*y+y*z+z*x-a = 0 and x*y*z-b = 0))))),
%pp]
Evaluation took 1.1200 seconds (1.1250 elapsed) using 273.509 MB.
(%o30) [[[true,a <= root(27*b^2+4*a^3,1),true,true,true]],
[[b],[a,4*a^3+27*b^2],[3*x^2+4*a,x^3+a*x-b],[y^2+x*y+x^2+a],[y+x+z]]]
(%i31) [(qvpeds([ex,ex,ex],[b,a,x,y,z],0,l,r11,0),
qe(bfpcad(ext('(x+y+z = 0 and x*y+y*z+z*x-a = 0 and x*y*z-b = 0))))),
%pp]
Evaluation took 0.7980 seconds (0.7980 elapsed) using 145.864 MB.
(%o31) [[[true,a <= root(27*b^2+4*a^3,1),true,true,true]],
[[b],[a,4*a^3+27*b^2],[3*x^2+4*a,x^3+a*x-b],[y^2+x*y+x^2+a],[y+x+z]]]
(%i32) [(qvpeds([ex,ex,ex],[a,b,c,x,y,z],0,h1r,r11,0),
qe(bfpcad(ext('(x+y+z = a and x*y+y*z+z*x = b and x*y*z = c))))),%pp]
Evaluation took 0.7660 seconds (0.7660 elapsed) using 184.901 MB.
(%o32) [[[true,b < root(3*b-a^2,1),
root(27*c^2-18*a*b*c+4*a^3*c+4*b^3-a^2*b^2,1) <= c
and c <= root(27*c^2-18*a*b*c+4*a^3*c+4*b^3-a^2*b^2,2),true,true,
true],
[true,b = root(3*b-a^2,1),
c = root(27*c^2-18*a*b*c+4*a^3*c+4*b^3-a^2*b^2,1),true,true,true]],
[[],[3*b-a^2],[27*c^2-18*a*b*c+4*a^3*c+4*b^3-a^2*b^2],
[x^3-a*x^2+b*x-c,3*x^2-2*a*x+4*b-a^2],[y^2+x*y-a*y+x^2-a*x+b],
[z+y+x-a]]]
(%i33) [(qvpeds([ex,ex,ex],[a,b,c,x,y,z],0,l,r11,0),
qe(bfpcad(ext('(x+y+z = a and x*y+y*z+z*x = b and x*y*z = c))))),%pp]
Evaluation took 0.6550 seconds (0.6560 elapsed) using 140.720 MB.
(%o33) [[[true,b < root(3*b-a^2,1),
root(27*c^2-18*a*b*c+4*a^3*c+4*b^3-a^2*b^2,1) <= c
and c <= root(27*c^2-18*a*b*c+4*a^3*c+4*b^3-a^2*b^2,2),true,true,
true],
[true,b = root(3*b-a^2,1),
c = root(27*c^2-18*a*b*c+4*a^3*c+4*b^3-a^2*b^2,1),true,true,true]],
[[],[3*b-a^2],[27*c^2-18*a*b*c+4*a^3*c+4*b^3-a^2*b^2],
[3*x^2-2*a*x+4*b-a^2,x^3-a*x^2+b*x-c],[y^2+x*y-a*y+x^2-a*x+b],
[z+y+x-a]]]
(%i34) [(qvpeds([ex,ex,ex],[t,x,y],0,h1r,r11,0),
qe(bfpcad(ext('((17/16)*t-6 >= 0 and (17/16)*t-10 <= 0
and x-(17/16)*t+1 >= 0
and x-(17/16)*t-1 <= 0
and y-(17/16)*t+9 >= 0
and y-(17/16)*t+7 <= 0
and (x-t)^2+y^2-1 <= 0))))),%pp]
Evaluation took 3.1300 seconds (3.1330 elapsed) using 890.252 MB.
(%o34) [[[true,true,true]],
[[145*t^2-1920*t+6272,145*t^2-2464*t+10368,17*t-96,17*t-112,17*t-128,
17*t-144,17*t-160,t+32,t,t-32],
[256*x^2-512*t*x+545*t^2-3808*t+12288,
256*x^2-512*t*x+545*t^2-4896*t+20480,16*x-17*t+16,16*x-17*t-16,
x-t+1,x-t-1],[y^2+x^2-2*t*x+t^2-1,16*y-17*t+144,16*y-17*t+112]]]
(%i35) [(qvpeds([ex,ex,ex],[t,x,y],0,l,r11,0),
qe(bfpcad(ext('((17/16)*t-6 >= 0 and (17/16)*t-10 <= 0
and x-(17/16)*t+1 >= 0
and x-(17/16)*t-1 <= 0
and y-(17/16)*t+9 >= 0
and y-(17/16)*t+7 <= 0
and (x-t)^2+y^2-1 <= 0))))),%pp]
Evaluation took 1.5770 seconds (1.5780 elapsed) using 246.028 MB.
(%o35) [[[true,true,true]],
[[t-32,t,t+32,17*t-160,17*t-144,17*t-128,17*t-112,17*t-96,
145*t^2-2464*t+10368,145*t^2-1920*t+6272],
[x-t-1,x-t+1,16*x-17*t-16,16*x-17*t+16,
256*x^2-512*t*x+545*t^2-4896*t+20480,
256*x^2-512*t*x+545*t^2-3808*t+12288],
[16*y-17*t+112,16*y-17*t+144,y^2+x^2-2*t*x+t^2-1]]]
(%i36) [fpprec,%ez,ratepsilon]:[48,1.0b-12,1.0b-48]
Evaluation took 0.0010 seconds (0.0000 elapsed) using 0 bytes.
(%o36) [48,1.0b-12,1.0b-48]
(%i37) f0:x < 0 and 50000*(x^2+y^2)-49719 < 0
implies 360000+720000*x+720000*x^2+480000*x^3+240000*x^4+96000*x^5
+32200*x^6+9200*x^7+2225*x^8+450*x^9+75*x^10+10*x^11
+x^12+(-3000)*x^4*y^2+1200*x^5*y^2+2100*x^6*y^2
+1000*x^7*y^2+275*x^8*y^2+50*x^9*y^2+6*x^10*y^2
+3000*x^2*y^4+(-6000)*x^3*y^4+(-2250)*x^4*y^4
+300*x^5*y^4+350*x^6*y^4+100*x^7*y^4+15*x^8*y^4
+(-200)*y^6+2000*x*y^6+(-1900)*x^2*y^6+(-600)*x^3*y^6
+150*x^4*y^6+100*x^5*y^6+20*x^6*y^6+225*y^8
+(-350)*x*y^8+(-25)*x^2*y^8+50*x^3*y^8+15*x^4*y^8
+(-25)*y^10+10*x*y^10+6*x^2*y^10+y^12-360000
< 0
Evaluation took 0.0290 seconds (0.0300 elapsed) using 3.558 MB.
(%i38) [(qvpeds([all,all],[x,y],0,h1,r11,0),qe(bfpcad(ext(f0)))),%pp]
Evaluation took 10.0710 seconds (10.0740 elapsed) using 2590.940 MB.
(%o38) [[[true,true]],
[[x,6*x^2+10*x-25,28*x^2-68*x-17,50000*x^2-49719,
x^5+5*x^4+25*x^3+100*x^2+300*x+600,
28*x^6-204*x^5-101*x^4-190*x^3+5269*x^2-5710*x+1875,
1088*x^6-7552*x^5+12736*x^4-3600*x^3+21000*x^2-41240*x+14039,
200000000000000000000000000000000*x^6
+599438000000000000000000000000000*x^5
+1225000789610000000000000000000000*x^4
+2442297336707065300000000000000000*x^3
+3754710227977240336626750000000000*x^2
+3758510381317956468954765766500000*x-5402844825834997735210773,
1088*x^12-15104*x^11+59904*x^10-3344*x^9+112936*x^8-298200*x^7
-6467281*x^6+17310870*x^5-5750825*x^4+6290450*x^3
-14463075*x^2+6471500*x-580150,
120832*x^12-989184*x^11+1965568*x^10+1699840*x^9+3373952*x^8
-10134400*x^7-57194464*x^6+73892480*x^5-12046600*x^4
-5395400*x^3-126535850*x^2+56676900*x-290075,
120832*x^19-1648640*x^18+5940736*x^17+8692736*x^16-23252608*x^15
-246864000*x^14-1190564192*x^13-3079579840*x^12
+12973976600*x^11+1232865000*x^10-84076534050*x^9
-209944983400*x^8+39826614875*x^7+1457720531250*x^6
+2010504800625*x^5+25224378750*x^4-957912804375*x^3
-949924375000*x^2+750565675000*x-43511250000,
4571136*x^19+2818048*x^18-25075712*x^17+34385920*x^16+930661376*x^15
+3433646080*x^14+8198400*x^13-47876089600*x^12
-184510347200*x^11-302452144000*x^10+194216259600*x^9
+2048648030000*x^8+4813290745000*x^7+5892848620000*x^6
+2971088911875*x^5-473950680000*x^4-1572986706250*x^3
+258053312500*x^2+440250359375*x+1631671875,
4571136*x^28+4227072*x^27-51011584*x^26+208793600*x^25
+4487152640*x^24+21158707200*x^23-2748128000*x^22
-513743699200*x^21-1859278084800*x^20
+11836781184000*x^19+177227571163600*x^18
+1147497743010000*x^17+5032673524115000*x^16
+16422964823940000*x^15+40583034110816875*x^14
+73030624007188750*x^13+78801621529646875*x^12
-18223494396843750*x^11-288264068603906250*x^10
-681410411614046875*x^9-946722681541984375*x^8
-792370510167421875*x^7-273080203974921875*x^6
+181512821587890625*x^5+197555235933593750*x^4
-7722981467968750*x^3-126478640906250000*x^2
-6832921593750000*x-1599038437500000,
855113728*x^28+21377843200*x^27+283256422400*x^26+2608096870400*x^25
+18521228902400*x^24+106982744064000*x^23
+518383694233600*x^22+2147375910912000*x^21
+7692855189760000*x^20+23980542444800000*x^19
+65142992800320000*x^18+153700917730560000*x^17
+311998085014880000*x^16+534257219535200000*x^15
+740482905349000000*x^14+746555405314000000*x^13
+321582900808375000*x^12-619086555599625000*x^11
-1781201761577531250*x^10-2496929229230000000*x^9
-2168728237020312500*x^8-905392388410156250*x^7
+397713892669921875*x^6+915322655607031250*x^5
+609971037097656250*x^4+165439917011718750*x^3
-20690934755859375*x^2+38769456621093750*x
-1019794921875],
[50000*y^2+50000*x^2-49719,
y^12+(6*x^2+10*x-25)*y^10+(15*x^4+50*x^3-25*x^2-350*x+225)*y^8
+(20*x^6+100*x^5+150*x^4-600*x^3-1900*x^2+2000*x-200)*y^6
+(15*x^8+100*x^7+350*x^6+300*x^5-2250*x^4-6000*x^3+3000*x^2)*y^4
+(6*x^10+50*x^9+275*x^8+1000*x^7+2100*x^6+1200*x^5-3000*x^4)*y^2
+x^12+10*x^11+75*x^10+450*x^9+2225*x^8+9200*x^7+32200*x^6
+96000*x^5+240000*x^4+480000*x^3+720000*x^2+720000*x]]]
(%i39) [(qvpeds([all,all],[x,y],0,l,r11,0),qe(bfpcad(ext(f0)))),%pp]
Evaluation took 1.6160 seconds (1.6180 elapsed) using 603.005 MB.
(%o39) [[[true,true]],
[[x,50000*x^2-49719,x^5+5*x^4+25*x^3+100*x^2+300*x+600,
200000000000000000000000000000000*x^6
+599438000000000000000000000000000*x^5
+1225000789610000000000000000000000*x^4
+2442297336707065300000000000000000*x^3
+3754710227977240336626750000000000*x^2
+3758510381317956468954765766500000*x-5402844825834997735210773,
855113728*x^28+21377843200*x^27+283256422400*x^26+2608096870400*x^25
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-1781201761577531250*x^10-2496929229230000000*x^9
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+397713892669921875*x^6+915322655607031250*x^5
+609971037097656250*x^4+165439917011718750*x^3
-20690934755859375*x^2+38769456621093750*x
-1019794921875],
[50000*y^2+50000*x^2-49719,
y^12+(6*x^2+10*x-25)*y^10+(15*x^4+50*x^3-25*x^2-350*x+225)*y^8
+(20*x^6+100*x^5+150*x^4-600*x^3-1900*x^2+2000*x-200)*y^6
+(15*x^8+100*x^7+350*x^6+300*x^5-2250*x^4-6000*x^3+3000*x^2)*y^4
+(6*x^10+50*x^9+275*x^8+1000*x^7+2100*x^6+1200*x^5-3000*x^4)*y^2
+x^12+10*x^11+75*x^10+450*x^9+2225*x^8+9200*x^7+32200*x^6
+96000*x^5+240000*x^4+480000*x^3+720000*x^2+720000*x]]]
以下の出力は長い為，省略しました．
(%i40) [fpprec,%ez,ratepsilon]: [32,1.0b-6,1.0b-32];
Evaluation took 0.0000 seconds (0.0000 elapsed) using 0 bytes.
(%o40) [32,1.0b-6,1.0b-32]
(%i41) [(qvpeds ([],[x,y,z],0,h1,r11,0 ),
qe( bfpcad(ext( '( (y-1)*z^4+x*z^3+x*(1-y)*z^2+(y-x-1)*z+y=0 ) ))),%pp)];
Evaluation took 163.0310 seconds (163.1330 elapsed) using 57799.604 MB.
(%o41) [[[x-6,x,x+1,x+2,3*x+8,8*x+3,4*x^2-27,2*x^3-8*x-9,2*x^3-24*x^2+72*x+27,
8*x^3+7*x^2-42*x-36,x^4+38*x^3+18*x^2-156*x-108,
2*x^4+47*x^3-124*x-72,4*x^4+x^3-16*x^2-22*x-6,
4*x^4+21*x^3-4*x^2-36*x-18,5*x^4+26*x^3-9*x^2-54*x-27,
8*x^4+96*x^3-416*x^2+201*x+282,16*x^4-95*x^3+24*x^2+704*x+512,
16*x^4+4*x^3-128*x^2-144*x+229,44*x^4+52*x^3-391*x^2-318*x+303,
4*x^5-88*x^4+645*x^3-1854*x^2+1920*x-1024,
8*x^5+281*x^4+146*x^3-1806*x^2-1404*x+363,
15*x^5+278*x^4-30*x^3-1171*x^2-972*x-142,x^6-4*x^5+7*x^3-x^2-3*x+1,
x^6+46*x^5+142*x^4-74*x^3-426*x^2-342*x-81,
x^6+78*x^5+556*x^4-208*x^3-1898*x^2-1608*x-405,
16*x^6+4*x^5-128*x^4-272*x^3+85*x^2+485*x+256,
192*x^9+1952*x^8-7786*x^7-18888*x^6+41108*x^5+45845*x^4+11523*x^3
-47238*x^2-78912*x-104832,
x^10-36*x^9+540*x^8-4212*x^7+16875*x^6-23679*x^5-43659*x^4+114669*x^3
+96228*x^2-58320*x-46656,
4*x^11-24*x^10-640*x^9+8377*x^8-38996*x^7+57424*x^6+130396*x^5
-397672*x^4-88296*x^3+476802*x^2+291240*x+52488,
2304*x^11-68736*x^10+753424*x^9-2747520*x^8-12830688*x^7
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-1352650752*x^2-339738624*x+905969664,
192*x^13-1408*x^12-7536*x^11+72256*x^10-85432*x^9-418072*x^8
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-1186326*x^2-1959552*x-373248,
16*x^15-640*x^14+11060*x^13-106516*x^12+610680*x^11-1996383*x^10
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-944784,
4096*x^19-76032*x^18-122880*x^17+10690448*x^16-84608248*x^15
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4096*x^20-163840*x^19+2852864*x^18-27393408*x^17+149542144*x^16
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1024*x^25-36864*x^24+258048*x^23+9652320*x^22-275282941*x^21
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-55109356535808*x^5+147054424817664*x^4+90730087317504*x^3
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63488*x^29-3822208*x^28+101436112*x^27-1558519760*x^26
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-650077067955*x^22-1132725702993*x^21+8060985767681*x^20
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7936*x^36-758304*x^35+33419327*x^34-901346428*x^33+16631964287*x^32
-222094789346*x^31+2209871734238*x^30-16568887999552*x^29
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-226468951385702400*x^2+292162779488452608*x
+68475651442606080],
[y-1,y,y-x-1,8*y^2-16*y+3*x+8,
(4*x^3-16*x-18)*y^4+((-16*x^3)-14*x^2+84*x+72)*y^3
+(x^4+38*x^3+18*x^2-156*x-108)*y^2
+((-2*x^4)-47*x^3+124*x+72)*y+4*x^4+21*x^3-4*x^2
-36*x-18,
(16*x^4+4*x^3-128*x^2-144*x+229)*y^6
+((-88*x^4)-104*x^3+782*x^2+636*x-606)*y^5
+(8*x^5+281*x^4+146*x^3-1806*x^2-1404*x+363)*y^4
+((-30*x^5)-556*x^4+60*x^3+2342*x^2+1944*x+284)*y^3
+(x^6+78*x^5+556*x^4-208*x^3-1898*x^2-1608*x-405)*y^2
+((-2*x^6)-92*x^5-284*x^4+148*x^3+852*x^2+684*x+162)*y+5*x^6+36*x^5
+48*x^4-46*x^3-144*x^2-108*x-27],
[(y-1)*z^4+x*z^3+((-x*y)+x)*z^2+(y-x-1)*z+y]]]
(%i42) [(qvpeds ([],[x,y,z],0,l,r11,0 ),
qe( bfpcad(ext( '( (y-1)*z^4+x*z^3+x*(1-y)*z^2+(y-x-1)*z+y=0 ) ))),%pp)];
Evaluation took 8.0460 seconds (8.0510 elapsed) using 3347.636 MB.
(%o42) [[[x,x+1,4*x^2-27,5*x^4+26*x^3-9*x^2-54*x-27,
16*x^4-95*x^3+24*x^2+704*x+512,16*x^4+4*x^3-128*x^2-144*x+229,
x^6-4*x^5+7*x^3-x^2-3*x+1,
x^10-36*x^9+540*x^8-4212*x^7+16875*x^6-23679*x^5-43659*x^4+114669*x^3
+96228*x^2-58320*x-46656],
[y-1,y,
(16*x^4+4*x^3-128*x^2-144*x+229)*y^6
+((-88*x^4)-104*x^3+782*x^2+636*x-606)*y^5
+(8*x^5+281*x^4+146*x^3-1806*x^2-1404*x+363)*y^4
+((-30*x^5)-556*x^4+60*x^3+2342*x^2+1944*x+284)*y^3
+(x^6+78*x^5+556*x^4-208*x^3-1898*x^2-1608*x-405)*y^2
+((-2*x^6)-92*x^5-284*x^4+148*x^3+852*x^2+684*x+162)*y+5*x^6+36*x^5
+48*x^4-46*x^3-144*x^2-108*x-27],
[(y-1)*z^4+x*z^3+((-x*y)+x)*z^2+(y-x-1)*z+y]]]
