lolsympy.py

from sympy import *
import itertools


def do_replacement(expr):
    queue = [expr]
    permutations = []

    while len(queue) > 0:
        next_queue = []
        for item in queue:
            permutations.append(str(item))

            for replacement in replacements:
                replaced_item = item.replace(*replacement)

                if item == replaced_item:
                    continue
#                print item, replaced_item, replacement

                if str(replaced_item) not in permutations:
                    next_queue.append(replaced_item)
        queue = next_queue[:]
    for item in permutations:
        print item


sn, sm, rn, rm, e = symbols('sn sm rn rm e', commutative = False)
a = Wild('a', exclude=[1])
b = Wild('b', exclude=[1])

W = Function('W')
WT = Function('WT')
Q = Function('Q')
QT = Function('QT')
U = Function('U')
UT = Function('UT')



replacements = [(QT(a)*Q(a), 1),
                (Q(a)*QT(a), 1),
                (WT(a)*W(a), 1),
                (W(a)*WT(a), 1),
                (UT(a)*U(a), 1),
                (U(a)*UT(a), 1),
                (Q(a)*b, W(b)*a),
                (a*WT(b), b*QT(a)),
                (QT(a)*a, e),
                (a*Q(a),e),
                (WT(a)*a, e),
                (a*W(a), e),
                (U(a)*a, e),
                (a*UT(a), e),
                (UT(a)*a,e),
                (a*U(a),e),
                (Q(Q(a)*b),Q(a)*Q(b)),
                (W(W(a)*b),W(a)*W(b)),
                (Q(a)*WT(b), WT(b)*Q(a)),
                (W(a)*QT(b), QT(b)*W(a)),
                (WT(a)*QT(b), QT(b)*WT(a)),
                (Q(a)*W(b),W(b)*Q(a)),
                (W(a)*UT(b), UT(a)*QT(b)),
                (U(b)*WT(a), Q(b)*U(a)),
                (W(a)*U(b), UT(a)*WT(b)),
                (W(a)*U(b), Q(b)*UT(a)),
                (W(a)*U(b), U(b)*QT(a)),
                (UT(a)*WT(b), Q(b)*UT(a)),
                (UT(a)*WT(b), U(b)*QT(a)),
                (Q(b)*UT(a), U(b)*QT(a)),
                (UT(b)*WT(a), W(b)*U(a)),
                (UT(b)*WT(a), U(a)*QT(b)),
                (UT(b)*WT(a), Q(b)*UT(b)),
                (W(b)*U(a),U(a)*QT(b)),
                (W(b)*U(a), Q(b)*UT(b)),
                (U(a)*QT(b), Q(b)*UT(b)),
                (WT(a)*UT(b), U(a)*W(b)),
                (WT(a)*UT(b), QT(b)*U(a)),
                (WT(a)*UT(b), UT(b)*Q(a)),
                (U(a)*W(b), QT(b)*U(a)),
                (U(a)*W(b), UT(b)*Q(a)),
                (QT(b)*U(a), UT(b)*Q(a)),
                (U(b)*W(a), WT(b)*UT(a)),
                (U(b)*W(a), UT(a)*Q(b)),
                (U(b)*W(a), QT(b)*U(b)),
                (WT(b)*UT(a),UT(a)*Q(b)),
                (WT(b)*UT(a), QT(b)*U(b)),
                (UT(a)*Q(b), QT(b)*U(b)),
                (WT(a)*U(b), U(b)*Q(a)),
                (UT(b)*W(a), QT(a)*UT(b)),
                (U(a)*UT(b), Q(a)*QT(b)),
                (U(a)*U(b), Q(a)*WT(b)),
                (UT(a)*UT(b), W(a)*QT(b)),
                (UT(a)*U(b), W(a)*WT(b)),
                (rn*rn, 1),
                (rn*sn, 1),
                (rm*rm, 1),
                (rm*sm, 1) ]

expr = sn*W(rn)*WT(rm)*sm
do_replacement(expr)