EXAMPLE (5)
===========
The maple calculations below are used in the proof
of Ramanujan's identity for p(5n+4).

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> read "FUNCS.txt":
> x:=expand( (J0-q+q^2*J2)^3 );
       3       2         2  2            2         3            4   2    3
x := J0  - 3 J0  q - 3 J0  q  J2 + 3 J0 q  + 6 J0 q  J2 + 3 J0 q  J2  - q

          4         5   2    6   3
     - 3 q  J2 - 3 q  J2  - q  J2


> dissectq(x,q,5);
  3      5   2           2    5   3                      2                  3
J0  - 3 q  J2  + q (-3 J0  + q  J2 ) + 3 J0 (J0 J2 + 1) q  - (6 J0 J2 + 1) q

                         4
     + 3 J2 (J0 J2 + 1) q

> zeta:=RootOf(1+z+z^2+z^3+z^4=0):
> simplify(zeta^5);
                                       1

> v:=q->J0 - q - q^2/J0:
> y:=mul(v(zeta^j*q),j=1..4);
     /              2  2\ /               4  2\ /               6  2\
     |            %1  q | |       2     %1  q | |       3     %1  q |
y := |J0 - %1 q - ------| |J0 - %1  q - ------| |J0 - %1  q - ------|
     \              J0  / \               J0  / \               J0  /

    /               8  2\
    |       4     %1  q |
    |J0 - %1  q - ------|
    \               J0  /

                        2     3     4
%1 := RootOf(1 + _Z + _Z  + _Z  + _Z )

> expand(y):
> simplify(%);
   8       7      3   5      2   6      4   4      5   3      6   2    7
(J0  + q J0  + 3 q  J0  + 2 q  J0  + 5 q  J0  - 3 q  J0  + 2 q  J0  - q  J0

        8    /   4
     + q )  /  J0
           /

> a:=expand(%);
                                                      5      6    7     8
           4       3         3      2   2      4   3 q    2 q    q     q
    a := J0  + q J0  + 3 J0 q  + 2 q  J0  + 5 q  - ---- + ---- - --- + ---
                                                    J0      2      3     4
                                                          J0     J0    J0

> dissectq(a,q,5);
       5      5        5      5     2       5    5     3      5    5
    -J0  + 3 q    q (J0  + 2 q )   q  (-2 J0  + q )   q  (3 J0  + q )      4
  - ----------- + -------------- - ---------------- + --------------- + 5 q
        J0               2                 3                  4
                       J0                J0                 J0

> 

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