Choose one or hit any other key to close the solver : 1.

Two types of canonical forms are available.

a. reduced groebner basis.
b. optimal groebner basis.

Which one do you like : b.

Session 1. started.

Input a list of polynomials.[
j=ja\/jo, k=kl\/kh\/ko, we/\ma=0, ol/\md=0, ol/\yn=0, md/\yn=0,
a/\b=0, a/\c=0, a/\d=0, b/\c=0, b/\d=0, c/\d=0, 
n1/\a=0, a/\n5=0, n2/\b=0, b/\n6=0, n3/\c=0, c/\n7=0, n4/\d=0, d/\n8=0,
n1/\n2=0, n1/\n3=0, n1/\n4=0, n1/\n5=0, n1/\n6=0, n1/\n7=0, n1/\n8=0,
n2/\n3=0, n2/\n4=0, n2/\n5=0, n2/\n6=0, n2/\n7=0, n2/\n8=0,
n3/\n4=0, n3/\n5=0, n3/\n6=0, n3/\n7=0, n3/\n8=0,
n4/\n5=0, n4/\n6=0, n4/\n7=0, n4/\n8=0,
n5/\n6=0, n5/\n7=0, n5/\n8=0, n6/\n7=0, n6/\n8=0, n7/\n8=0,
subseteq([s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],a\/b\/c\/d),
subseteq([s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],n1\/n2\/n3\/n4\/n5\/n6\/n7\/n8),
subseteq([s1,s2,s3,s4,s5,s6],ma), subseteq([s7,s8,s9,s10],we),
subseteq([s4,s5,s6,s9,s10],ol), subseteq([s3,s8],md), subseteq([s1,s2,s7],yn),
in(s1,kl), in(s1,kh), in(s1,jo), notin(s1,ko), notin(s1,ja),
in(s2,ja), notin(s2,jo), notin(s2,k), in(s3,ko), in(s3,kh), in(s3,jo), 
notin(s3,kl), notin(s3,ja), in(s4,kl), in(s4,jo), notin(s4,kh), notin(s4,ko),
notin(s4,ja), in(s5,kl), notin(s5,j), notin(s5,kh), notin(s5,ko), in(s6,jo),
notin(s6,k), notin(s6,ja), in(s7,kh), notin(s7,kl), notin(s7,ko), notin(s7,j),
in(s8,ko), notin(s8,kl), notin(s8,kh), notin(s8,j), in(s9,kl), notin(s9,kh),
notin(s9,ko), notin(s9,j), in(s10,kh), notin(s10,kl), notin(s10,ko), notin(s10,j),
a/\ja=0, x1=x1*a, x1=x1*we, x2=x2*a, x2=x2*we, x1*x2,
x3=x3*b, x3=x3*ol, x3=x3*k, x4=x4*b, x4=x4*ol, x4=x4*k, x3*x4, b/\yn=0, b/\ko=0,
c/\we/\ko=0, c/\j =0, c/\md =0,
subseteq(d/\yn,x5), d/\ol=0,
n1/\ma, n3/\ma, n5/\ma, x6=x6*n6, x6=x6*ma, x7=x7*n6, x7=x7*ma, x6*x7=0, x8=x8*n8, 
x8=x8*ma, x9=x9*n8, x9=x9*ma, x8*x9=0, subseteq(n7/\ma,x10),
x1=x1*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
x2=x2*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
x3=x3*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
x4=x4*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
x5=x5*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
x6=x6*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
x7=x7*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
x8=x8*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
x9=x9*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
x10=x10*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
y1=y1*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
y2=y2*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
y3=y3*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
y4=y4*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
y5=y5*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
y6=y6*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
y7=y7*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
y8=y8*[s1,s2,s3,s4,s5,s6,s7,s8,s9,s10],
y1=y1*n1, y2=y2*n2, y3=y3*n3, y4=y4*n4,
y5=y5*n5, y6=y6*n6, y7=y7*n7, y8=y8*n8
].

Input a list of polynomials.

Following is the benchmarks of our calculations of the above input polynomials 
by 8 different term orders, using a DOS/V machine(Pentium Pro 200MH, FreeBSD).

---------------------------------------------------------------------------
[[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,y1,y2,y3,y4,y5,y6,y7,y8
,j,ja,jo,k,kl,kh,ko,we,ma,ol,md,yn,a,b,c,d,n1,n2,n3,n4,n5,n6,n7,n8]
].

3331 s-polynomials created.
1111 s-polynomials removed.
426 cs-polynomials created.
750 vs-polynomials created.

0:24
---------------------------------------------------------------------------
[[x1],[x2],[x3],[x4],[x5],[x6],[x7],[x8],[x9],[x10],[y1],[y2],[y3],[y4],[y5],[y6],[y7],[y8],[j],[ja],[jo],[k],[kl],[kh],[ko],[we],[ma],[ol],[md],[yn],[a],[b],[c],[d],[n1],[n2],[n3],[n4],[n5],[n6],[n7],[n8]
].

4036 s-polynomials created.
1625 s-polynomials removed.
477 cs-polynomials created.
894 vs-polynomials created.

0:25
---------------------------------------------------------------------------
[[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,y1,y2,y3,y4,y5,y6,y7,y8]
,[j,ja,jo,k,kl,kh,ko,we,ma,ol,md,yn],[a],[b],[c],[d],[n1],[n2],[n3],[n4],[n5],[n6],[n7],[n8]
].

4035 s-polynomials created.
1630 s-polynomials removed.
477 cs-polynomials created.
894 vs-polynomials created.

0:26
---------------------------------------------------------------------------
[[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,y1,y2,y3,y4,y5,y6,y7,y8]
,[j,ja,jo,k,kl,kh,ko,we,ma,ol,md,yn],[n8],[n7],[n6],[n5],[n4],[n3],[n2],[n1],[d],[c],[b],[a]].

3255 s-polynomials created.
1197 s-polynomials removed.
408 cs-polynomials created.
734 vs-polynomials created.

0:26
---------------------------------------------------------------------------
[[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,y1,y2,y3,y4,y5,y6,y7,y8]
,[j,ja,jo,k,kh,kl,ko,ma,md,ol,we,yn,a,b,c,d,n1,n2,n3,n4,n5,n6,n7,n8]
].

5493 s-polynomials created.
2854 s-polynomials removed.
529 cs-polynomials created.
1060 vs-polynomials created.

0:49
---------------------------------------------------------------------------
[[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,y1,y2,y3,y4,y5,y6,y7,y8]
,[j,ja,jo,k,kh,kl,ko,ma,md,ol,we,yn],[a,b,c,d,n1,n2,n3,n4,n5,n6,n7,n8]
].

5450 s-polynomials created.
2854 s-polynomials removed.
525 cs-polynomials created.
1055 vs-polynomials created.

0:47
---------------------------------------------------------------------------
[[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,y1,y2,y3,y4,y5,y6,y7,y8]
,[a,b,c,d,j,ja,jo,k,kh,kl,ko,ma,md,n1,n2,n3,n4,n5,n6,n7,n8,ol,we,yn]
].

36266 s-polynomials created.
103014 s-polynomials removed.
1439 cs-polynomials created.
4186 vs-polynomials created.

18:29
---------------------------------------------------------------------------
[[x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,y1,y2,y3,y4,y5,y6,y7,y8]
,[a,b,c,d,n1,n2,n3,n4,n5,n6,n7,n8,j,ja,jo,k,kh,kl,ko,ma,md,ol,we,yn]
].

36227 s-polynomials created.
102214 s-polynomials removed.
1322 cs-polynomials created.
3972 vs-polynomials created.

16:45
---------------------------------------------------------------------------







