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, ol/\md, ol/\yn, md/\yn,
a/\b, a/\c, a/\d, b/\c, b/\d, c/\d, 
n1/\a, a/\n5, n2/\b, b/\n6, n3/\c, c/\n7, n4/\d, d/\n8,
n1/\n2, n1/\n3, n1/\n4, n1/\n5, n1/\n6, n1/\n7, n1/\n8,
n2/\n3, n2/\n4, n2/\n5, n2/\n6, n2/\n7, n2/\n8,
n3/\n4, n3/\n5, n3/\n6, n3/\n7, n3/\n8,
n4/\n5, n4/\n6, n4/\n7, n4/\n8,
n5/\n6, n5/\n7, n5/\n8, n6/\n7, n6/\n8, n7/\n8,
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, 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, b/\ko,
c/\we/\ko, c/\j , c/\md ,
subseteq(d/\yn,x5), d/\ol,
n1/\ma, n3/\ma, n5/\ma, x6+x6*n6, x6+x6*ma, x7+x7*n6, x7+x7*ma, x6*x7, x8+x8*n8, 
x8+x8*ma, x9+x9*n8, x9+x9*ma, x8*x9, 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 order type.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Here we have to input a list of order type.
Following is the benchmarks of our calculations for 9 different term orders.
We give only the computation time and the last outputs concerning the number
of produced S-polynomials etc.
All the computations are done by a  DOS/V machine(Pentium II 450MH, FreeBSD 2.2.8).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

---------------------------input-------------------------------------------
[[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]
].

11235 s-polynomials created.
4400 s-polynomials removed.
0 cs-polynomials created.
2785 vs-polynomials created.

0:14(0 minites and 14 seconds)
---------------------------input-------------------------------------------
[[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]
].

12243 s-polynomials created.
5163 s-polynomials removed.
0 cs-polynomials created.
3101 vs-polynomials created.

0:13
---------------------------input-------------------------------------------
[[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]
].

12226 s-polynomials created.
5162 s-polynomials removed.
0 cs-polynomials created.
3087 vs-polynomials created.

0:14
---------------------------input-------------------------------------------
[[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]].

12415 s-polynomials created.
5011 s-polynomials removed.
0 cs-polynomials created.
3093 vs-polynomials created.

0:14
---------------------------input-------------------------------------------
[[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]
].

14416 s-polynomials created.
6929 s-polynomials removed.
0 cs-polynomials created.
3361 vs-polynomials created.

0:20
---------------------------input-------------------------------------------
[[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]
].

14408 s-polynomials created.
6929 s-polynomials removed.
0 cs-polynomials created.
3357 vs-polynomials created.

0:20


%%%%% All the above calculations were done by s_setsolver. %%%%%

---------------------------input-------------------------------------------
[[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]
].

14513 s-polynomials created.
6952 s-polynomials removed.
0 cs-polynomials created.
3447 vs-polynomials created.

0:21 (by s_setsolver)

36290 s-polynomials created.
103024 s-polynomials removed.
1441 cs-polynomials created.
4190 vs-polynomials created.

7:59 (by setsolver)

---------------------------input-------------------------------------------
[[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]
].

14513 s-polynomials created.
6952 s-polynomials removed.
0 cs-polynomials created.
3483 vs-polynomials created.

0:21 (by s_setsolver)

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

8:02 (by setsolver)
---------------------------input-------------------------------------------
[[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]].

180613 s-polynomials created.
423219 s-polynomials removed.
0 cs-polynomials created.
20799 vs-polynomials created.

13:48 (by s_setsolver)

21404 s-polynomials created.
43698 s-polynomials removed.
914 cs-polynomials created.
2620 vs-polynomials created.

2:12 setsolver (by setsolver)

In this example, setsolver looks much faster than s_setsolver.
However, parallel computation gives us a faster calculation.

By using a parallel virsion p_setsolver
(by p_setsolver -p 11 in the following example), we get the following.

23916  p1  S+     1:50.45 /home/ysato/itaku98/p_setsolver -=parent_tid=262146 --
23917  p1  S+     1:25.72 /home/ysato/itaku98/p_setsolver -=parent_tid=262146 --
23918  p1  S+     1:25.11 /home/ysato/itaku98/p_setsolver -=parent_tid=262146 --
23919  p1  S+     1:26.16 /home/ysato/itaku98/p_setsolver -=parent_tid=262146 --
23920  p1  S+     1:25.98 /home/ysato/itaku98/p_setsolver -=parent_tid=262146 --
23921  p1  S+     1:25.63 /home/ysato/itaku98/p_setsolver -=parent_tid=262146 --
23922  p1  S+     1:25.68 /home/ysato/itaku98/p_setsolver -=parent_tid=262146 --
23923  p1  S+     1:25.28 /home/ysato/itaku98/p_setsolver -=parent_tid=262146 --
23924  p1  S+     1:23.60 /home/ysato/itaku98/p_setsolver -=parent_tid=262146 --
23925  p1  S+     1:24.57 /home/ysato/itaku98/p_setsolver -=parent_tid=262146 --
23926  p1  S+     0:07.35 /home/ysato/itaku98/p_setsolver -=parent_tid=262146 --
23927  p1  S+     0:05.92 /home/ysato/itaku98/p_setsolver -=parent_tid=262146 --

23833  p1  I+     0:35.66 /home/ysato/pvm3/lib/FREEBSD/pvmd3

(The above is given by using a unix command "ps -axu|grep p_setsolver".)
The most longest process(the first line) takes about 1 munite and 50 seconds.
Which means computaion time is 1 munite and 50 seconds by a parallel computation,
although the computation is done by a computer with a single processor.

