実行例（３）
CGS-EQ の深作亮也先生（東京理科大）のサイト
http://www.rs.tus.ac.jp/fukasaku/software/CGSQE-20160509/benchmark/computation-time/
http://www.rs.tus.ac.jp/fukasaku/software/CGSQE-20160509/benchmark/input/04/log/
出典
http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.642.8545&rep=rep1&type=pdf Example 9
Maxima 5.39.0 http://maxima.sourceforge.net
using Lisp CMU Common Lisp 21b (21B Unicode)
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) (qvpeds ([ex,ex],[x,y,z],0,0,r11,0 ),
qe( bfpcad(ext( '( x^2+y^2*z+z^3=0 and 3*x^2+3*y^2+z^2-1=0 and x^2+z^2-y^3*(y-1)^3<0 ) ))) );
Evaluation took 34.9400 seconds (34.9500 elapsed) using 4777.359 MB.
(%o1) [[root(387420489*x^36+473513931*x^34+1615049199*x^32-5422961745*x^30
+2179233963*x^28-14860773459*x^26+43317737551*x^24
-45925857657*x^22+60356422059*x^20
-126478283472*x^18+164389796305*x^16
-121571730573*x^14+54842719755*x^12
-16059214980*x^10+3210573925*x^8-446456947*x^6
+43657673*x^4-1631864*x^2-40328,1)
< x
and x < root(387420489*x^36+473513931*x^34+1615049199*x^32
-5422961745*x^30+2179233963*x^28
-14860773459*x^26+43317737551*x^24
-45925857657*x^22+60356422059*x^20
-126478283472*x^18+164389796305*x^16
-121571730573*x^14+54842719755*x^12
-16059214980*x^10+3210573925*x^8
-446456947*x^6+43657673*x^4-1631864*x^2
-40328,2),true,true]]
(%i2) (qvpeds ([ex,ex],[x,y,z],1,0,r11,0 ),
qe( bfpcad(ext( '( x^2+y^2*z+z^3=0 and 3*x^2+3*y^2+z^2-1=0 and x^2+z^2-y^3*(y-1)^3<0 ) ))) );
[fpprec,fpprintprec,%ez,ratepsilon]: [16,30,1.0b-3,1.0b-16]
equal(z^3+y^2*z+x^2,0) and equal(z^2+3*y^2+3*x^2-1,0)
and z^2-y^6+3*y^5-3*y^4+y^3+x^2 < 0
["and",z^2-y^6+3*y^5-3*y^4+y^3+x^2 < 0,equal(z^2+3*y^2+3*x^2-1,0),
equal(z^3+y^2*z+x^2,0)]
[[z^2+3*y^2+3*x^2-1],[z^2-y^6+3*y^5-3*y^4+y^3+x^2],[z^3+y^2*z+x^2]]
[[3*y^2+3*x^2-1],[y^6-3*y^5+3*y^4-y^3-x^2],
[y^6-3*y^5+3*y^4-y^3+3*y^2+2*x^2-1],[4*y^6+27*x^4],
[12*y^6+48*x^2*y^4-16*y^4+63*x^4*y^2-42*x^2*y^2+7*y^2+27*x^6-26*x^4+9*x^2-1],
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13-3*x^2*y^12+114*y^12
+18*x^2*y^11-76*y^11-45*x^2*y^10+40*y^10+60*x^2*y^9-16*y^9-49*x^2*y^8
+5*y^8+30*x^2*y^7-y^7+3*x^4*y^6-15*x^2*y^6-9*x^4*y^5+4*x^2*y^5+9*x^4*y^4
-x^2*y^4-3*x^4*y^3+2*x^4*y^2-x^6-x^4]]
[[x,x^2-2,2*x^2-1,3*x^2-1,27*x^6-155*x^4+9*x^2-1,27*x^6-26*x^4+9*x^2-1,
54*x^6-297*x^4+18*x^2-2,108*x^6-837*x^4+36*x^2-4,
729*x^12+729*x^10+1215*x^8-6129*x^6+4185*x^4-504*x^2-8,
387420489*x^36+473513931*x^34+926301663*x^32-4590725139*x^30+3855398877*x^28
-5886383967*x^26+14051402938*x^24-13565732679*x^22
+9151246767*x^20-15472018962*x^18+21618673717*x^16
-15614937665*x^14+6066412333*x^12-1269760998*x^10
+127675066*x^8-3130295*x^6-196075*x^4-2296*x^2-8,
387420489*x^36+473513931*x^34+1615049199*x^32-5422961745*x^30
+2179233963*x^28-14860773459*x^26+43317737551*x^24
-45925857657*x^22+60356422059*x^20-126478283472*x^18
+164389796305*x^16-121571730573*x^14+54842719755*x^12
-16059214980*x^10+3210573925*x^8-446456947*x^6+43657673*x^4
-1631864*x^2-40328,
387420489*x^36+1162261467*x^34+4649045868*x^32-9125904852*x^30
-4864279473*x^28-75245668308*x^26+228853906389*x^24
-233182493334*x^22+526458209184*x^20-1632367306233*x^18
+2577322981359*x^16-2213846330418*x^14+1103473933785*x^12
-328088633355*x^10+61540990272*x^8-7555532337*x^6
+598204197*x^4-19509336*x^2-512072],
[3*y^2+3*x^2-1,y^6-3*y^5+3*y^4-y^3-x^2,y^6-3*y^5+3*y^4-y^3+3*y^2+2*x^2-1,
4*y^6+27*x^4,
12*y^6+(48*x^2-16)*y^4+(63*x^4-42*x^2+7)*y^2+27*x^6-26*x^4+9*x^2-1,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4],
[z^2+3*y^2+3*x^2-1,z^2-y^6+3*y^5-3*y^4+y^3+x^2,z^3+y^2*z+x^2]]
1 multi-roots: 0.0b0 0.0b0 [3*y^2+3*x^2-1,3*y^2]
dist: 0.0b0
1 multi-roots: 0.0b0 0.0b0
[12*y^6+(48*x^2-16)*y^4+(63*x^4-42*x^2+7)*y^2+27*x^6-26*x^4+9*x^2-1,
12*y^6-5.72536737891363b0*y^4+8.963235209558525b-1*y^2]
dist: 0.0b0
common-roots: -3.990820394214746b-1 -3.990820394214746b-1
dist: 6.938893903907228b-18
common-roots: -3.990820394214746b-1 -3.990820394214746b-1
dist: 6.938893903907228b-18
common-roots: -3.731302026563126b-1 -3.731302026563127b-1
dist: 4.163336342344337b-17
common-roots: -4.492182869390443b-1 -4.492182869390443b-1
dist: 6.938893903907228b-17
common-roots: -4.293461173741275b-1 -4.293461173741276b-1
dist: 4.163336342344337b-17
common-roots: -4.293461173741276b-1 -4.293461173741276b-1
dist: 2.081668171172169b-17
common-roots: 1.242338414099984b0 1.241578377687144b0
dist: 7.600364128400594b-4
1 multi-roots: 0.0b0 0.0b0 [y^6-3*y^5+3*y^4-y^3-x^2,y^6-3*y^5+3*y^4-y^3]
dist: 0.0b0
2 multi-roots: 0.0b0 0.0b0 [y^6-3*y^5+3*y^4-y^3-x^2,y^6-3*y^5+3*y^4-y^3]
dist: 0.0b0
3 multi-roots: 9.999999999999998b-1-1.908195823574488b-16*%i
1.006139616066548b-16*%i+1.0b0 [y^6-3*y^5+3*y^4-y^3-x^2,y^6-3*y^5+3*y^4-y^3]
dist: 4.425687238657765b-16
4 multi-roots: 1.006139616066548b-16*%i+1.0b0 9.020562075079397b-17*%i+1.0b0
[y^6-3*y^5+3*y^4-y^3-x^2,y^6-3*y^5+3*y^4-y^3]
dist: 1.040834085586084b-17
1 multi-roots: 0.0b0 0.0b0 [4*y^6+27*x^4,4*y^6]
dist: 0.0b0
2 multi-roots: 0.0b0 0.0b0 [4*y^6+27*x^4,4*y^6]
dist: 0.0b0
3 multi-roots: 0.0b0 0.0b0 [4*y^6+27*x^4,4*y^6]
dist: 0.0b0
4 multi-roots: 0.0b0 0.0b0 [4*y^6+27*x^4,4*y^6]
dist: 0.0b0
5 multi-roots: 0.0b0 0.0b0 [4*y^6+27*x^4,4*y^6]
dist: 0.0b0
1 multi-roots: (-3.118675378203367b-11*%i)-7.071067811740978b-1
3.11867695771263b-11*%i-7.071067811989973b-1
[12*y^6+(48*x^2-16)*y^4+(63*x^4-42*x^2+7)*y^2+27*x^6-26*x^4+9*x^2-1,
12*y^6-16*y^4+7*y^2-1]
dist: 6.715982037737266b-11
2 multi-roots: 7.071067811770959b-1-1.273326148703733b-11*%i
1.273326308308289b-11*%i+7.071067811959992b-1
[12*y^6+(48*x^2-16)*y^4+(63*x^4-42*x^2+7)*y^2+27*x^6-26*x^4+9*x^2-1,
12*y^6-16*y^4+7*y^2-1]
dist: 3.171562834653794b-11
1 multi-roots: (-6.025654200204613b-1*%i)-1.891279438990948b-2
(-6.025654199767368b-1*%i)-1.891279438040217b-2
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+114*y^12-76*y^11+40*y^10
-16*y^9+5*y^8-y^7]
dist: 4.474615144603693b-11
2 multi-roots: 6.025654209207471b-1*%i-1.891280116685924b-2
6.025654190764511b-1*%i-1.89127876034522b-2
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+114*y^12-76*y^11+40*y^10
-16*y^9+5*y^8-y^7]
dist: 1.368822261249517b-8
3 multi-roots: 0.0b0 0.0b0
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+114*y^12-76*y^11+40*y^10
-16*y^9+5*y^8-y^7]
dist: 0.0b0
4 multi-roots: 0.0b0 0.0b0
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+114*y^12-76*y^11+40*y^10
-16*y^9+5*y^8-y^7]
dist: 0.0b0
5 multi-roots: 0.0b0 0.0b0
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+114*y^12-76*y^11+40*y^10
-16*y^9+5*y^8-y^7]
dist: 0.0b0
6 multi-roots: 0.0b0 0.0b0
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+114*y^12-76*y^11+40*y^10
-16*y^9+5*y^8-y^7]
dist: 0.0b0
7 multi-roots: 0.0b0 0.0b0
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+114*y^12-76*y^11+40*y^10
-16*y^9+5*y^8-y^7]
dist: 0.0b0
8 multi-roots: 0.0b0 0.0b0
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+114*y^12-76*y^11+40*y^10
-16*y^9+5*y^8-y^7]
dist: 0.0b0
9 multi-roots: 2.717041990286581b-6*%i+9.99993414966278b-1
1.00000093787557b0-7.060909170695758b-6*%i
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+114*y^12-76*y^11+40*y^10
-16*y^9+5*y^8-y^7]
dist: 1.233703745313714b-5
10 multi-roots: 1.00000093787557b0-7.060909170695758b-6*%i
4.343867253830464b-6*%i+1.000005647158198b0
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+114*y^12-76*y^11+40*y^10
-16*y^9+5*y^8-y^7]
dist: 1.233881145655348b-5
11 multi-roots: 1.518912661150419b0-6.666097968941921b-1*%i
1.518912927619844b0-6.666098929698847b-1*%i
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+114*y^12-76*y^11+40*y^10
-16*y^9+5*y^8-y^7]
dist: 2.832604685158154b-7
12 multi-roots: 6.666098479459857b-1*%i+1.51891279382378b0
6.666098419180176b-1*%i+1.518912794946535b0
[y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+((-3*x^2)+114)*y^12
+(18*x^2-76)*y^11+((-45*x^2)+40)*y^10+(60*x^2-16)*y^9+((-49*x^2)+5)*y^8
+(30*x^2-1)*y^7+(3*x^4-15*x^2)*y^6+((-9*x^4)+4*x^2)*y^5+(9*x^4-x^2)*y^4
-3*x^4*y^3+2*x^4*y^2-x^6-x^4,
y^18-9*y^17+36*y^16-84*y^15+128*y^14-138*y^13+114*y^12-76*y^11+40*y^10
-16*y^9+5*y^8-y^7]
dist: 6.131637614094183b-9
common-roots: 1.000000000000015b0 1.0b0
dist: 1.515454428613339b-14
common-roots: 5.773502691896258b-1 5.773502691896257b-1
dist: 5.551115123125783b-17
common-roots: 0.0b0 0.0b0
dist: 0.0b0
common-roots: -5.773502691896258b-1 -5.773502691896258b-1
dist: 5.551115123125783b-17
common-roots: 1.242338414100015b0 1.241578377687144b0
dist: 7.600364128707848b-4
common-roots: -4.293461173741275b-1 -4.293461173741275b-1
dist: 1.387778780781446b-17
common-roots: -4.293461173741275b-1 -4.293461173741276b-1
dist: 3.469446951953614b-17
common-roots: -4.492182869390442b-1 -4.492182869390443b-1
dist: 9.020562075079397b-17
common-roots: -3.731302026563125b-1 -3.731302026563127b-1
dist: 2.012279232133096b-16
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[T,F]: [3,1064]
Evaluation took 32.3300 seconds (32.4100 elapsed) using 4531.459 MB.
(%o2) [[root(387420489*x^36+473513931*x^34+1615049199*x^32-5422961745*x^30
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