Loading image file :/home/winfried/development/lisp/psl/linux/red/reduce.img 
REDUCE Development Version, 28-Jan-2003 ...

1: 
*** airy_ai already defined as operator 

*** airy_bi already defined as operator 

*** odesolve-specfn* already defined as operator 

*** odesolve-solns* already defined as operator 
The name of this new session is: "bu933-15-Sep-"

2: If this file is loaded just for printing then in addition do:

in drvlist$
depend {f,b},t,s,x$
lisp <<use_new_crackout:=t$
       fblist:='((f 1) (b 1))$
       put('f,'prifn,'myfpri)$ % if only one fermion else
                               % put('f,'prifn,nil);     
       put('b,'prifn,'myfpri)$ % if only one boson else  
                               % put('b,'prifn,nil);     
       N_:=1>>$

3: 
#######  This is the case N1f0b1t2s13w1.  #######

The equation:

    3
b =b *p1 + b *p2
 t          x

It's symmetry:

    14                              2                               4
b =b  *q38 + Db  *Db*q39 + Db  *Db*b *q16 + Db  *Db *q40 + Db  *Db*b *q14
 s             5x            4x               4x   x         3x

                                                2                6
 + Db  *Db*b *b*q15 + Db  *Db  *q41 + Db  *Db *b *q13 + Db  *Db*b *q9
     3x     x           3x   2x         3x   x            2x

                                 2                   3                 4
 + Db  *Db*b  *b*q12 + Db  *Db*b  *q11 + Db  *Db*b *b *q10 + Db  *Db *b *q7
     2x     2x           2x     x          2x     x            2x   x

                              8                                    3
 + Db  *Db *b *b*q8 + Db *Db*b *q1 + Db *Db*b  *b*q6 + Db *Db*b  *b *q5
     2x   x  x          x              x     3x          x     2x

                               2  2                 5
 + Db *Db*b  *b *q4 + Db *Db*b  *b *q2 + Db *Db*b *b *q3 + b  *b*q17
     x     2x  x        x     x            x     x          6x

        3                         5                             2          2
 + b  *b *q19 + b  *b *q18 + b  *b *q22 + b  *b  *q20 + b  *b *b *q21 + b   *q27
    5x           5x  x        4x           4x  2x        4x  x           3x

        7                2             2                 4          2  4
 + b  *b *q26 + b  *b  *b *q23 + b  *b  *b*q25 + b  *b *b *q24 + b   *b *q32
    3x           3x  2x           3x  x           3x  x           2x

      2                 9             3             2  3               6
 + b   *b *b*q31 + b  *b *q33 + b  *b  *q28 + b  *b  *b *q30 + b  *b *b *q29
    2x   x          2x           2x  x         2x  x            2x  x

     4  2         3  5         2  8           11
 + b  *b *q34 + b  *b *q35 + b  *b *q36 + b *b  *q37
    x            x            x            x

{q41,q40,q39,q16,q15,q14,q13,q12,q11,q10,q9,q8,q7,q6,q5,q4,q3,q2,q1}
{p2,p1}
Generating all terms of total degree 2
   Pairing now degree 1 terms from the system
          with degree 1 terms from the symmetry

df(b,t)=p2*b
            x

df(b,s)=0
Generating all terms of total degree 3
   Pairing now degree 1 terms from the system
          with degree 2 terms from the symmetry

df(b,t)=p2*b
            x

df(b,s)=Db  *Db*q39 + Db  *Db *q40 + Db  *Db  *q41 + b  *b*q17 + b  *b *q18
          5x            4x   x         3x   2x        6x          5x  x

                            2
         + b  *b  *q20 + b   *q27
            4x  2x        3x
   Pairing now degree 2 terms from the system
          with degree 1 terms from the symmetry

df(b,t)=0

df(b,s)=0
Generating all terms of total degree 4
   Pairing now degree 1 terms from the system
          with degree 3 terms from the symmetry

df(b,t)=p2*b
            x

df(b,s)=0
   Pairing now degree 2 terms from the system
          with degree 2 terms from the symmetry

df(b,t)=0

df(b,s)=Db  *Db*q39 + Db  *Db *q40 + Db  *Db  *q41 + b  *b*q17 + b  *b *q18
          5x            4x   x         3x   2x        6x          5x  x

                            2
         + b  *b  *q20 + b   *q27
            4x  2x        3x
   Pairing now degree 3 terms from the system
          with degree 1 terms from the symmetry

         3
df(b,t)=b *p1

df(b,s)=0
Generating all terms of total degree 5
   Pairing now degree 1 terms from the system
          with degree 4 terms from the symmetry

df(b,t)=p2*b
            x

                 2                                    2
df(b,s)=Db  *Db*b *q16 + Db  *Db*b *b*q15 + Db  *Db *b *q13 + Db  *Db*b  *b*q12
          4x               3x     x           3x   x            2x     2x

                     2
         + Db  *Db*b  *q11 + Db  *Db *b *b*q8 + Db *Db*b  *b*q6
             2x     x          2x   x  x          x     3x

                                   3               2                2
         + Db *Db*b  *b *q4 + b  *b *q19 + b  *b *b *q21 + b  *b  *b *q23
             x     2x  x       5x           4x  x           3x  2x

                 2            2                  3
         + b  *b  *b*q25 + b   *b *b*q31 + b  *b  *q28
            3x  x           2x   x          2x  x
   Pairing now degree 2 terms from the system
          with degree 3 terms from the symmetry

df(b,t)=0

df(b,s)=0
   Pairing now degree 3 terms from the system
          with degree 2 terms from the symmetry

         3
df(b,t)=b *p1

df(b,s)=Db  *Db*q39 + Db  *Db *q40 + Db  *Db  *q41 + b  *b*q17 + b  *b *q18
          5x            4x   x         3x   2x        6x          5x  x

                            2
         + b  *b  *q20 + b   *q27
            4x  2x        3x
Generating all terms of total degree 6
   Pairing now degree 1 terms from the system
          with degree 5 terms from the symmetry
*** Garbage collection starting 
*** GC 1 15-Sep-2003 14:28:40, 20 ms (0%), 1019207 occupied, 26980741 free

df(b,t)=p2*b
            x

df(b,s)=0
   Pairing now degree 2 terms from the system
          with degree 4 terms from the symmetry

df(b,t)=0

                 2                                    2
df(b,s)=Db  *Db*b *q16 + Db  *Db*b *b*q15 + Db  *Db *b *q13 + Db  *Db*b  *b*q12
          4x               3x     x           3x   x            2x     2x

                     2
         + Db  *Db*b  *q11 + Db  *Db *b *b*q8 + Db *Db*b  *b*q6
             2x     x          2x   x  x          x     3x

                                   3               2                2
         + Db *Db*b  *b *q4 + b  *b *q19 + b  *b *b *q21 + b  *b  *b *q23
             x     2x  x       5x           4x  x           3x  2x

                 2            2                  3
         + b  *b  *b*q25 + b   *b *b*q31 + b  *b  *q28
            3x  x           2x   x          2x  x
   Pairing now degree 3 terms from the system
          with degree 3 terms from the symmetry

         3
df(b,t)=b *p1

df(b,s)=0
Generating all terms of total degree 7
   Pairing now degree 1 terms from the system
          with degree 6 terms from the symmetry

df(b,t)=p2*b
            x

         2           2                                    2
df(b,s)=b *(Db  *Db*b *q14 + Db  *Db*b *b*q10 + Db  *Db *b *q7 + Db *Db*b  *b*q5
              3x               2x     x           2x   x           x     2x

                        2           3               2          2  2
             + Db *Db*b  *q2 + b  *b *q22 + b  *b *b *q24 + b   *b *q32
                 x     x        4x           3x  x           2x

                     2           4
             + b  *b  *b*q30 + b  *q34)
                2x  x           x
   Pairing now degree 2 terms from the system
          with degree 5 terms from the symmetry

df(b,t)=0

df(b,s)=0
   Pairing now degree 3 terms from the system
          with degree 4 terms from the symmetry

         3
df(b,t)=b *p1

                 2                                    2
df(b,s)=Db  *Db*b *q16 + Db  *Db*b *b*q15 + Db  *Db *b *q13 + Db  *Db*b  *b*q12
          4x               3x     x           3x   x            2x     2x

                     2
         + Db  *Db*b  *q11 + Db  *Db *b *b*q8 + Db *Db*b  *b*q6
             2x     x          2x   x  x          x     3x

                                   3               2                2
         + Db *Db*b  *b *q4 + b  *b *q19 + b  *b *b *q21 + b  *b  *b *q23
             x     2x  x       5x           4x  x           3x  2x

                 2            2                  3
         + b  *b  *b*q25 + b   *b *b*q31 + b  *b  *q28
            3x  x           2x   x          2x  x
Generating all terms of total degree 8
   Pairing now degree 1 terms from the system
          with degree 7 terms from the symmetry

df(b,t)=p2*b
            x

df(b,s)=0
   Pairing now degree 2 terms from the system
          with degree 6 terms from the symmetry

df(b,t)=0

         2           2                                    2
df(b,s)=b *(Db  *Db*b *q14 + Db  *Db*b *b*q10 + Db  *Db *b *q7 + Db *Db*b  *b*q5
              3x               2x     x           2x   x           x     2x

                        2           3               2          2  2
             + Db *Db*b  *q2 + b  *b *q22 + b  *b *b *q24 + b   *b *q32
                 x     x        4x           3x  x           2x

                     2           4
             + b  *b  *b*q30 + b  *q34)
                2x  x           x
   Pairing now degree 3 terms from the system
          with degree 5 terms from the symmetry

         3
df(b,t)=b *p1

df(b,s)=0
Generating all terms of total degree 9
   Pairing now degree 1 terms from the system
          with degree 8 terms from the symmetry

df(b,t)=p2*b
            x

         5                                     2                        3
df(b,s)=b *(Db  *Db*b*q9 + Db *Db*b *q3 + b  *b *q26 + b  *b *b*q29 + b  *q35)
              2x             x     x       3x           2x  x          x
   Pairing now degree 2 terms from the system
          with degree 7 terms from the symmetry

df(b,t)=0

df(b,s)=0
*** Garbage collection starting 
*** GC 2 15-Sep-2003 14:28:47, 30 ms (0%), 1023721 occupied, 26976227 free
   Pairing now degree 3 terms from the system
          with degree 6 terms from the symmetry

         3
df(b,t)=b *p1

         2           2                                    2
df(b,s)=b *(Db  *Db*b *q14 + Db  *Db*b *b*q10 + Db  *Db *b *q7 + Db *Db*b  *b*q5
              3x               2x     x           2x   x           x     2x

                        2           3               2          2  2
             + Db *Db*b  *q2 + b  *b *q22 + b  *b *b *q24 + b   *b *q32
                 x     x        4x           3x  x           2x

                     2           4
             + b  *b  *b*q30 + b  *q34)
                2x  x           x
Generating all terms of total degree 10
   Pairing now degree 1 terms from the system
          with degree 9 terms from the symmetry

df(b,t)=p2*b
            x

df(b,s)=0
   Pairing now degree 2 terms from the system
          with degree 8 terms from the symmetry

df(b,t)=0

         5                                     2                        3
df(b,s)=b *(Db  *Db*b*q9 + Db *Db*b *q3 + b  *b *q26 + b  *b *b*q29 + b  *q35)
              2x             x     x       3x           2x  x          x
   Pairing now degree 3 terms from the system
          with degree 7 terms from the symmetry

         3
df(b,t)=b *p1

df(b,s)=0
Generating all terms of total degree 11
   Pairing now degree 1 terms from the system
          with degree 10 terms from the symmetry

df(b,t)=p2*b
            x

         8                            2
df(b,s)=b *(Db *Db*q1 + b  *b*q33 + b  *q36)
              x          2x          x
   Pairing now degree 2 terms from the system
          with degree 9 terms from the symmetry

df(b,t)=0

df(b,s)=0
   Pairing now degree 3 terms from the system
          with degree 8 terms from the symmetry

         3
df(b,t)=b *p1

         5                                     2                        3
df(b,s)=b *(Db  *Db*b*q9 + Db *Db*b *q3 + b  *b *q26 + b  *b *b*q29 + b  *q35)
              2x             x     x       3x           2x  x          x
Generating all terms of total degree 12
   Pairing now degree 1 terms from the system
          with degree 11 terms from the symmetry

df(b,t)=p2*b
            x

df(b,s)=0
   Pairing now degree 2 terms from the system
          with degree 10 terms from the symmetry

df(b,t)=0

         8                            2
df(b,s)=b *(Db *Db*q1 + b  *b*q33 + b  *q36)
              x          2x          x
   Pairing now degree 3 terms from the system
          with degree 9 terms from the symmetry

         3
df(b,t)=b *p1

df(b,s)=0
Generating all terms of total degree 13
   Pairing now degree 1 terms from the system
          with degree 12 terms from the symmetry

df(b,t)=p2*b
            x

         11
df(b,s)=b  *q37*b
                 x
   Pairing now degree 2 terms from the system
          with degree 11 terms from the symmetry

df(b,t)=0

df(b,s)=0
*** Garbage collection starting 
*** GC 3 15-Sep-2003 14:28:51, 20 ms (0%), 1024047 occupied, 26975901 free
   Pairing now degree 3 terms from the system
          with degree 10 terms from the symmetry

         3
df(b,t)=b *p1

         8                            2
df(b,s)=b *(Db *Db*q1 + b  *b*q33 + b  *q36)
              x          2x          x
Generating all terms of total degree 14
   Pairing now degree 1 terms from the system
          with degree 13 terms from the symmetry

df(b,t)=p2*b
            x

df(b,s)=0
   Pairing now degree 2 terms from the system
          with degree 12 terms from the symmetry

df(b,t)=0

         11
df(b,s)=b  *q37*b
                 x
   Pairing now degree 3 terms from the system
          with degree 11 terms from the symmetry

         3
df(b,t)=b *p1

df(b,s)=0
Generating all terms of total degree 15
   Pairing now degree 1 terms from the system
          with degree 14 terms from the symmetry

df(b,t)=p2*b
            x

         14
df(b,s)=b  *q38
   Pairing now degree 2 terms from the system
          with degree 13 terms from the symmetry

df(b,t)=0

df(b,s)=0
   Pairing now degree 3 terms from the system
          with degree 12 terms from the symmetry

         3
df(b,t)=b *p1

         11
df(b,s)=b  *q37*b
                 x
Generating all terms of total degree 16
   Pairing now degree 2 terms from the system
          with degree 14 terms from the symmetry

df(b,t)=0

         14
df(b,s)=b  *q38
   Pairing now degree 3 terms from the system
          with degree 13 terms from the symmetry

         3
df(b,t)=b *p1

df(b,s)=0
Generating all terms of total degree 17
   Pairing now degree 3 terms from the system
          with degree 14 terms from the symmetry

         3
df(b,t)=b *p1

         14
df(b,s)=b  *q38
Now crack is called.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is CRACK - a solver for overdetermined partial differential equations
Enter `h' for help.

The list of inequalities got extended by: 
An expression with 19 terms

The list of inequalities got extended by: 

g0024*p2 + g0025*p1

*** Garbage collection starting 
*** GC 4 15-Sep-2003 14:28:56, 20 ms (0%), 1026318 occupied, 26973630 free

old input: l
Select a method by its number that is to be executed repeatedly:
old input: 2

To repeat this method as often as possible, enter `;' 
To repeat this method as often as possible, 
but at most a number of n times, enter n :
old input: ;


Step 1:

separation w.r.t. x
linear independent expressions : 
 10
b  *Db*Db
         x


 11
b  *b
     2x


 10   2
b  *b
     x


Separation of e_5 yields (e_19 e_18 e_17)



Step 2:

separation w.r.t. x
linear independent expressions : 
 8
b *Db*Db
        2x


 7
b *b *Db*Db
    x      x


 9
b *b
    3x


 8
b *b *b
    x  2x


 7   3
b *b
    x


Separation of e_7 yields (e_24 e_22 e_23 e_21 e_20)



Step 3:

separation w.r.t. x
linear independent expressions : 
 6
b *Db*Db
        3x


 5
b *b *Db*Db
    x      2x


 6
b *Db *Db
     x   2x


 5
b *b  *Db*Db
    2x      x


 4   2
b *b  *Db*Db
    x       x


 7
b *b
    4x


 6
b *b *b
    x  3x


 6    2
b *b
    2x


 5   2
b *b  *b
    x   2x


 4   4
b *b
    x


Separation of e_9 yields (e_34 e_32 e_29 e_28 e_27 e_33 e_31 e_25 e_26 e_30)



Step 4:

separation w.r.t. x
linear independent expressions : 
 2
b *Db*Db
        5x


b*b *Db*Db
   x      4x


 2
b *Db *Db
     x   4x


b*b  *Db*Db
   2x      3x


  2
b  *Db*Db
 x       3x


 2
b *Db  *Db
     2x   3x


b*b *Db *Db
   x   x   3x


b*b  *Db*Db
   3x      2x


b *b  *Db*Db
 x  2x      2x


b*b  *Db *Db
   2x   x   2x


  2
b  *Db *Db
 x    x   2x


b*b  *Db*Db
   4x      x


b *b  *Db*Db
 x  3x      x


   2
b   *Db*Db
 2x       x


 3
b *b
    6x


 2
b *b *b
    x  5x


 2
b *b  *b
    2x  4x


    2
b*b  *b
   x   4x


 2    2
b *b
    3x


b*b *b  *b
   x  2x  3x


  3
b  *b
 x   3x


     3
b*b
   2x


  2    2
b  *b
 x   2x


Separation of e_13 yields (e_52 e_50 e_48 e_43 e_51 e_49 e_47 e_46 e_45 e_44 
e_42 e_41 e_39 e_37 e_36 e_35 e_40 e_38)



Step 5:

separation w.r.t. x
linear independent expressions : 
 4
b *Db*Db
        4x


 3
b *b *Db*Db
    x      3x


 4
b *Db *Db
     x   3x


 3
b *b  *Db*Db
    2x      2x


 2   2
b *b  *Db*Db
    x       2x


 3
b *b *Db *Db
    x   x   2x


 3
b *b  *Db*Db
    3x      x


 2
b *b *b  *Db*Db
    x  2x      x


    3
b*b  *Db*Db
   x       x


 5
b *b
    5x


 4
b *b *b
    x  4x


 4
b *b  *b
    2x  3x


 3   2
b *b  *b
    x   3x


 3       2
b *b *b
    x  2x


 2   3
b *b  *b
    x   2x


    5
b*b
   x

*** Garbage collection starting 
*** GC 5 15-Sep-2003 14:29:01, 20 ms (0%), 1034836 occupied, 26965112 free

Separation of e_11 yields (e_68 e_66 e_59 e_65 e_63 e_58 e_57 e_53 e_67 e_62 
e_56 e_55 e_64 e_60 e_54 e_61)



Step 6:

old input: cp

Please type in a list of the numbers 1 .. 60, like 1,2,5,4,..,15; which
will be the new priority list of procedures done by CRACK.
Numbers stand for the following actions:

 1 : Hot list of urgent steps
 2 : Direct separation
 3 : Substitution of <=2 terms, only fcts. of less vars., no cases
 4 : Substitution of <=2 terms, alg. expressions, no cases
 5 : Substitution of <=1000 terms, alg. expressions, no cases
 6 : Substitution, minimal growth, with max 100 add. terms, no cases
 7 : Integration of a first order de with at most two terms.
 8 : Factorization to subcases leading to substitutions
 9 : Substitution of derivatives by new functions
10 : Indirect separation of <6 or >300 terms
11 : Algebraic length reduction of equations
12 : Find and drop linear dependent general equations
13 : Find a linear dependent equation with only 1 term
14 : Triangularize a linear algebraic system
15 : Substitution of <=8 terms in <=1000 terms, fcts. of less vars.
16 : Substitution of <=20 terms in <=1000 terms
17 : Substitution of <=1000 terms, minimal growth
18 : Substitution of <=1000 terms, fcts. of less vars., no cases
19 : Substitution of <=1000 terms only linear expressions, f-indep. coeff.
20 : Substitution of <=1000 terms, no cases
21 : Substitution of <=1000 terms
22 : The parametric solution of underdetermined ODE
23 : The parametric solution of underdetermined PDE
24 : Integration of a pde such that a function can be subst.
25 : Any integration
26 : Indirect separation of equations of any size
27 : Length reducing decoupling steps
28 : Delete redundant equations
29 : Integrate an identity
30 : Do one decoupling step
31 : Differentiate pdes with nonlinear leading derivs
32 : Differentiate indirectly separable equations
33 : Find an integrating factor for a set of pde's
34 : Solving an algebraic equation.
35 : Solving equations for fnct.s or deriv.s algebraically
36 : Undo Substitutions of derivatives by new functions
37 : Changing the list of priorities
38 : Stop batch mode
39 : Find a transformation to integrate a 1st order PDE
40 : Drop redundant functions and constants
41 : Solve a subset of equations first
42 : Find and drop linear dependent bi-linear equations
43 : Find factorizable bi-linear equations
44 : Consider a given expression to be zero and non-zero
45 : Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases
46 : Find symmetries and then first integrals for an ODE
47 : Any factorization
48 : Alternative indirect separation of non-lin equations
49 : Find sub-systems with 2 non-flin_ functions
50 : Find sub-systems with 3 non-flin_ functions
51 : Find sub-systems with 4 non-flin_ functions
52 : Find sub-systems with 5 non-flin_ functions
53 : Find sub-systems with 2 flin_ functions
54 : Find sub-systems with 3 flin_ functions
55 : Find sub-systems with 4 flin_ functions
56 : Find sub-systems with 5 flin_ functions
57 : Do one high priority decoupling step
58 : user_defined
59 : Computation of the algebraic Groebner basis
60 : Check whether a given solution is contained

The list so far was: 1,2,3,4,7,8,47,9,15,16,18,19,20,21,24,26,27,30,25,22,32,
34,36;
old input: (*comma* 1 3 45 11 27 8 20 30 47 21 38)

old input: s

number of equations : 54
total no of terms   : 124
total no of factors :  178
54 equations in 0 variables: 
e_61(7#),e_30(5#),e_64(5#),e_60(5#),e_54(5#),e_26(4#),e_38(4#),e_56(4#),
e_55(4#),e_20(3#),e_33(3#),e_31(3#),e_25(3#),e_40(3#),e_67(3#),e_62(3#),
e_17(2#),e_23(2#),e_21(2#),e_28(2#),e_27(2#),e_51(2#),e_49(2#),e_47(2#),
e_46(2#),e_45(2#),e_44(2#),e_42(2#),e_41(2#),e_39(2#),e_37(2#),e_36(2#),
e_35(2#),e_65(2#),e_63(2#),e_58(2#),e_57(2#),e_53(2#),e_1(1#),e_3(1#),
e_19(1#),e_18(1#),e_24(1#),e_22(1#),e_34(1#),e_32(1#),e_29(1#),e_52(1#),
e_50(1#),e_48(1#),e_43(1#),e_68(1#),e_66(1#),e_59(1#)
43 constants : p1,p2,q1,q2,q3,q4,q5,q6,q7,q8,
q9,q10,q11,q12,q13,q14,q15,q16,q17,q18,q19,
q20,q21,q22,q23,q24,q25,q26,q27,q28,q29,q30,
q31,q32,q33,q34,q35,q36,q37,q38,q39,q40,q41

old input: w

Enter a list of equations, like e2,e5,e35; from: 
e_59,e_66,e_68,e_43,e_48,e_50,e_52,e_29,e_32,e_34,e_22,e_24,e_18,e_19,e_3,e_1,
e_53,e_57,e_58,e_63,e_65,e_35,e_36,e_37,e_39,e_41,e_42,e_44,e_45,e_46,e_47,e_49,
e_51,e_27,e_28,e_21,e_23,e_17,e_62,e_67,e_40,e_25,e_31,e_33,e_20,e_55,e_56,e_38,
e_26,e_54,e_60,e_64,e_30,e_61
To write all equations just enter ; 
old input: nil
Shall the name of the equation be written? (y/n) old input: n
Please give the name of the file in double quotes
without `;' : old input: w

old input: cr
These are all the user defined rules: 

{}
You can either
- give the number of a rule above to be dropped, or 
- give the name of a rule list activated before 
  the call of CRACK which should be disabled: old input: ssrules
Rule list ssrules has been disabled.

old input: dp

old input: sb

Please give the name of the file in double quotes
without `;' : old input: 0

next: next: 
Step 7: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations : 
*** Garbage collection starting 
*** GC 6 15-Sep-2003 14:29:07, 20 ms (0%), 1040199 occupied, 26959749 free
 --- 
Length reducing decoupling steps : Eliminate 
q19

from e_59 and e_57. e_57: 

0=(12*q19 + q23)*p1

is replaced by e_15: 

0=p1*q23


Step 8: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q19

from e_59 and e_58. e_58: 

0=(6*q19 + q21)*p1

is replaced by e_5: 

0=p1*q21


Step 9: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q13

from e_66 and e_63. e_63: 

0=(18*q13 + 7*q8)*p1

is replaced by e_9: 

0=p1*q8


Step 10: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q16

from e_68 and e_65. e_65: 

0=(7*q12 + 36*q16)*p1

is replaced by e_11: 

0=p1*q12


Step 11: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q17

from e_43 and e_36. e_36: 

0=(5*q17 + q20)*p1

is replaced by e_70: 

0=p1*q20


Step 12: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q20

from e_70 and e_35. e_35: 

0=(5*q18 + 2*q20)*p1

is replaced by e_72: 

0=p1*q18


Step 13: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_72 and e_37. e_37: 

0=(5*q18 + q27)*p1

is replaced by e_74: 

0=p1*q27


Step 14: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q27

from e_74 and e_39. e_39: 

0=(20*q17 + q27)*p1

is replaced by e_76: 

0=p1*q17


e_76 is a consequence of e_43.
Step 15: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_72 and e_42. e_42: 

0=(12*q17 + q18)*p1

is replaced by e_77: 

0=p1*q17


e_77 is a consequence of e_43.
Step 16: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q20

from e_70 and e_41. e_41: 

0=(30*q17 + q20)*p1

is replaced by e_78: 

0=p1*q17


e_78 is a consequence of e_43.
Step 17: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q41

from e_48 and e_45. e_45: 

0=(2*q40 - q41)*p1

is replaced by e_79: 

0=p1*q40


e_79 is a consequence of e_50.
Step 18: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q41

from e_48 and e_46. e_46: 

0=(10*q39 - q41)*p1

is replaced by e_80: 

0=p1*q39


e_80 is a consequence of e_52.
Step 19: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : A length reducing simplification (27
) was prevented
to avoid a cycle.
A length reducing simplification (27) was prevented
to avoid a cycle.
Eliminate 
q40

from e_50 and e_44. e_44: 

0=(5*q39 - q40)*p1

is replaced by e_81: 

0=p1*q39


e_81 is a consequence of e_52.
Step 20: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q40

from e_50 and e_47. e_47: 

0=(2*q40 + q41)*p1

is replaced by e_82: 

0=p1*q41


e_82 is a consequence of e_48.
Step 21: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : A length reducing simplification (27
) was prevented
to avoid a cycle.
Eliminate 
q39

from e_52 and e_49. e_49: 

0=(10*q39 + q41)*p1

is replaced by e_83: 

0=p1*q41


e_83 is a consequence of e_48.
Step 22: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q39

from e_52 and e_51. e_51: 

0=(5*q39 + q40)*p1

is replaced by e_84: 

0=p1*q40


e_84 is a consequence of e_50.
Step 23: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q22

from e_29 and e_27. e_27: 

0=(18*q22 + 7*q32)*p1

is replaced by e_85: 

0=p1*q32


Step 24: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q22

from e_29 and e_28. e_28: 

0=(24*q22 + 7*q24)*p1

is replaced by e_87: 

0=p1*q24


Step 25: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_22 and e_21. e_21: 

0=(2*q26 + q29)*p1

is replaced by e_89: 

0=p1*q29


Step 26: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q9

from e_24 and e_23. e_23: 

0=(11*q3 + 12*q9)*p1

is replaced by e_91: 

0=p1*q3


Step 27: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q33

from e_18 and e_17. e_17: 

0=(6*q33 + 11*q36)*p1

is replaced by e_93: 

0=p1*q36


Step 28: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q29

from e_89 and e_20. e_20: 
(#) 3 terms, 4 factors, with derivatives of functions of all variables: 

 (q35,q29,q26,p1)

is replaced by e_95: 

0=(6*q26 + 11*q35)*p1


Step 29: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q26

from e_22 and e_95. e_95: 

0=(6*q26 + 11*q35)*p1

is replaced by e_98: 

0=p1*q35


Step 30: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q24

from e_87 and e_25. e_25: 
(#) 3 terms, 4 factors, with derivatives of functions of all variables: 

 (q34,q30,q24,p1)

is replaced by e_100: 

0=(6*q30 + 11*q34)*p1


Step 31: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q18

from e_72 and e_40. e_40: 

0=(15*q17 + 5*q18 + q20)*p1

is replaced by e_103: 

0=(15*q17 + q20)*p1


Step 32: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q20

from e_70 and e_103. e_103: 

0=(15*q17 + q20)*p1

is replaced by e_106: 

0=p1*q17


e_106 is a consequence of e_43.
Step 33: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q13

from e_66 and e_62. e_62: 
(#) 3 terms, 4 factors, with derivatives of functions of all variables: 

 (q16,q13,q6,p1)

is replaced by e_107: 

0=(24*q16 + 7*q6)*p1


Step 34: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q16

from e_68 and e_107. e_107: 

0=(24*q16 + 7*q6)*p1

is replaced by e_110: 

0=p1*q6


Step 35: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q13

from e_66 and e_67. e_67: 
(#) 3 terms, 4 factors, with derivatives of functions of all variables: 

 (q16,q15,q13,p1)

is replaced by e_112: 

0=(7*q15 + 24*q16)*p1


Step 36: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q16

from e_68 and e_112. e_112: 

0=(7*q15 + 24*q16)*p1

is replaced by e_115: 

0=p1*q15


Step 37: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q7

from e_32 and e_31. e_31: 
(#) 3 terms, 4 factors, with derivatives of functions of all variables: 

 (q14,q7,q5,p1)

is replaced by e_117: 

0=(2*q14 + q5)*p1


Step 38: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q14

from e_34 and e_117. e_117: 

0=(2*q14 + q5)*p1

is replaced by e_120: 

0=p1*q5


Step 39: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
Algebraic length reduction of equations :  --- 
Length reducing decoupling steps : Eliminate 
q7

from e_32 and e_33. e_33: 
(#) 3 terms, 4 factors, with derivatives of functions of all variables: 

 (q14,q10,q7,p1)

is replaced by e_122: 

0=(q10 + 2*q14)*p1


Step 40: 
Hot list of urgent steps :  --- 
Substitution of <=2 terms, only fcts. of less vars., no cases :  --- 
Substitution of <=8 terms in <=1000 terms, alg. expressions, no cases :  --- 
