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| from sympy.combinatorics.fp_groups import FpGroup | |
| from sympy.combinatorics.free_groups import free_group | |
| from sympy.testing.pytest import raises | |
| def test_rewriting(): | |
| F, a, b = free_group("a, b") | |
| G = FpGroup(F, [a*b*a**-1*b**-1]) | |
| a, b = G.generators | |
| R = G._rewriting_system | |
| assert R.is_confluent | |
| assert G.reduce(b**-1*a) == a*b**-1 | |
| assert G.reduce(b**3*a**4*b**-2*a) == a**5*b | |
| assert G.equals(b**2*a**-1*b, b**4*a**-1*b**-1) | |
| assert R.reduce_using_automaton(b*a*a**2*b**-1) == a**3 | |
| assert R.reduce_using_automaton(b**3*a**4*b**-2*a) == a**5*b | |
| assert R.reduce_using_automaton(b**-1*a) == a*b**-1 | |
| G = FpGroup(F, [a**3, b**3, (a*b)**2]) | |
| R = G._rewriting_system | |
| R.make_confluent() | |
| # R._is_confluent should be set to True after | |
| # a successful run of make_confluent | |
| assert R.is_confluent | |
| # but also the system should actually be confluent | |
| assert R._check_confluence() | |
| assert G.reduce(b*a**-1*b**-1*a**3*b**4*a**-1*b**-15) == a**-1*b**-1 | |
| # check for automaton reduction | |
| assert R.reduce_using_automaton(b*a**-1*b**-1*a**3*b**4*a**-1*b**-15) == a**-1*b**-1 | |
| G = FpGroup(F, [a**2, b**3, (a*b)**4]) | |
| R = G._rewriting_system | |
| assert G.reduce(a**2*b**-2*a**2*b) == b**-1 | |
| assert R.reduce_using_automaton(a**2*b**-2*a**2*b) == b**-1 | |
| assert G.reduce(a**3*b**-2*a**2*b) == a**-1*b**-1 | |
| assert R.reduce_using_automaton(a**3*b**-2*a**2*b) == a**-1*b**-1 | |
| # Check after adding a rule | |
| R.add_rule(a**2, b) | |
| assert R.reduce_using_automaton(a**2*b**-2*a**2*b) == b**-1 | |
| assert R.reduce_using_automaton(a**4*b**-2*a**2*b**3) == b | |
| R.set_max(15) | |
| raises(RuntimeError, lambda: R.add_rule(a**-3, b)) | |
| R.set_max(20) | |
| R.add_rule(a**-3, b) | |
| assert R.add_rule(a, a) == set() | |