|\^/|     Maple V Release 5.1 (WMI MVR5.1 Campus Wide License)
._|\|   |/|_. Copyright (c) 1981-1998 by Waterloo Maple Inc. All rights
 \  MAPLE  /  reserved. Maple and Maple V are registered trademarks of
 <____ ____>  Waterloo Maple Inc.
      |       Type ? for help.
#Theorem38iv.final
#
#   This file completes the demonstration of Theorem 3.9 (iv)
# We first take the Gr\"obner basis computed by Singular, and then 
# we eliminate the variables c,d,e,f, simply by dropping the equations
# containing them.  We next successively eliminate the variable b, leaving a
# single degree 8 equation in a and the parameters s and t.   This is
# factored into quadratics, each of which is solved.
#
#
> with(Groebner):
> 
> G:=[]:for i from 1 to 65 do G:=[G[],0]: od:
> 
> read("Theorem39iveqs"):
> 
> nops(G);
                                       65

> 
> H:=[]:
> 
> for i from 1 to nops(G) do 
> if (indets(op(i,G)) minus {a,b,s,t} )={} then H:=[H[],op(i,G)]: fi: od:
bytes used=1000048, alloc=786288, time=0.45
> 
> nops(H);
                                       8

> 
> HH:=gbasis(H,wdeg([1,1],[a,b])):
bytes used=2000552, alloc=1179432, time=0.96
bytes used=3001456, alloc=1441528, time=1.29
> HH:=gbasis(HH,wdeg([1,4],[a,b])):
bytes used=4002100, alloc=1572576, time=1.63
bytes used=5002864, alloc=1572576, time=1.94
> HH:=gbasis(HH,wdeg([1,6],[a,b])):
bytes used=6003364, alloc=1703624, time=2.26
bytes used=7020072, alloc=1703624, time=2.60
bytes used=8032884, alloc=1900196, time=2.85
bytes used=9038876, alloc=1900196, time=3.14
bytes used=10050228, alloc=1900196, time=3.38
> HH:=gbasis(HH,wdeg([2,13],[a,b])):
bytes used=11054704, alloc=1900196, time=3.68
bytes used=12060792, alloc=1900196, time=3.95
bytes used=13064184, alloc=1900196, time=4.25
bytes used=14065988, alloc=1900196, time=4.50
> HH:=gbasis(HH,wdeg([2,14],[a,b])):
bytes used=15103200, alloc=1900196, time=4.80
bytes used=16104392, alloc=1900196, time=5.07
bytes used=17108528, alloc=1900196, time=5.36
bytes used=18131028, alloc=1965720, time=5.61
> HH:=gbasis(HH,wdeg([3,22],[a,b])):
bytes used=19131536, alloc=1965720, time=5.91
bytes used=20147160, alloc=1965720, time=6.25
bytes used=21157756, alloc=1965720, time=6.54
bytes used=22163572, alloc=1965720, time=6.77
bytes used=23165108, alloc=1965720, time=7.03
bytes used=24181380, alloc=1965720, time=7.27
> 
> for i from 1 to nops(HH) do indets(HH[i]); od;
                                  {a, b, t, s}

                                   {a, t, s}

> 
> elim:=HH[2]:
> 
> FAC:=factor(elim):
bytes used=25188088, alloc=1965720, time=7.59
> lprint(FAC);
(6*s*t-12*t*a+36*a^2-30*s*a+5*s^2)*(s*t-2*t*a+3*a^2-2*s*a)*(5*t^2-30*t*a+36*a^2
+14*s*t-30*s*a+5*s^2)*(5*t^2-30*t*a+36*a^2+6*s*t-12*s*a)
> solve(op(1,FAC)=0,a);
                          2              2 1/2
1/6 t + 5/12 s + 1/12 (4 t  - 4 s t + 5 s )   ,

                              2              2 1/2
    1/6 t + 5/12 s - 1/12 (4 t  - 4 s t + 5 s )

> solve(op(2,FAC)=0,a);
                       2          2 1/2                        2          2 1/2
 1/3 t + 1/3 s + 1/3 (t  - s t + s )   , 1/3 t + 1/3 s - 1/3 (t  - s t + s )

> solve(op(3,FAC)=0,a);
bytes used=26188632, alloc=1965720, time=8.02
                           2              2 1/2
5/12 s + 5/12 t + 1/12 (5 s  - 6 s t + 5 t )   ,

                               2              2 1/2
    5/12 s + 5/12 t - 1/12 (5 s  - 6 s t + 5 t )

> solve(op(4,FAC)=0,a);
                          2              2 1/2
5/12 t + 1/6 s + 1/12 (5 t  - 4 s t + 4 s )   ,

                              2              2 1/2
    5/12 t + 1/6 s - 1/12 (5 t  - 4 s t + 4 s )

> 
> quit;\
bytes used=26307676, alloc=1965720, time=8.07