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()
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 == False
R.make_confluent()
assert R.is_confluent == True
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)
G = FpGroup(F, [a**3, b**3, (a*b)**2])
R = G._rewriting_system
R.make_confluent()
assert R.is_confluent
assert G.reduce(b*a**-1*b**-1*a**3*b**4*a**-1*b**-15) == a**-1*b**-1
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 == False
R.make_confluent()
assert R.is_confluent == True
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)
G = FpGroup(F, [a**3, b**3, (a * b)**2])
R = G._rewriting_system
R.make_confluent()
assert R.is_confluent
assert G.reduce(b * a**-1 * b**-1 * a**3 * b**4 * a**-1 *
b**-15) == a**-1 * b**-1
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)
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
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)
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
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
