def allcombinations(A, B, ordered):
"""
Restructure A and B to have the same number of elements
ordered must be either 'commutative' or 'associative'
A and B can be rearranged so that the larger of the two lists is
reorganized into smaller sublists.
>>> from sympy.unify.core import allcombinations
>>> for x in allcombinations((1, 2, 3), (5, 6), 'associative'): print(x)
(((1,), (2, 3)), ((5,), (6,)))
(((1, 2), (3,)), ((5,), (6,)))
>>> for x in allcombinations((1, 2, 3), (5, 6), 'commutative'): print(x)
(((1,), (2, 3)), ((5,), (6,)))
(((1, 2), (3,)), ((5,), (6,)))
(((1,), (3, 2)), ((5,), (6,)))
(((1, 3), (2,)), ((5,), (6,)))
(((2,), (1, 3)), ((5,), (6,)))
(((2, 1), (3,)), ((5,), (6,)))
(((2,), (3, 1)), ((5,), (6,)))
(((2, 3), (1,)), ((5,), (6,)))
(((3,), (1, 2)), ((5,), (6,)))
(((3, 1), (2,)), ((5,), (6,)))
(((3,), (2, 1)), ((5,), (6,)))
(((3, 2), (1,)), ((5,), (6,)))
"""
sm, bg = (A, B) if len(A) < len(B) else (B, A)
for part in kbins(range(len(bg)), len(sm), None):
if bg == B:
yield list((a, ) for a in A), core_partition(B, part)
else:
yield core_partition(A, part), list((b, ) for b in B)
def allcombinations(A, B, ordered):
"""
Restructure A and B to have the same number of elements
ordered must be either 'commutative' or 'associative'
A and B can be rearranged so that the larger of the two lists is
reorganized into smaller sublists.
>>> from sympy.unify.core import allcombinations
>>> for x in allcombinations((1, 2, 3), (5, 6), 'associative'): print(x)
(((1,), (2, 3)), ((5,), (6,)))
(((1, 2), (3,)), ((5,), (6,)))
>>> for x in allcombinations((1, 2, 3), (5, 6), 'commutative'): print(x)
(((1,), (2, 3)), ((5,), (6,)))
(((1, 2), (3,)), ((5,), (6,)))
(((1,), (3, 2)), ((5,), (6,)))
(((1, 3), (2,)), ((5,), (6,)))
(((2,), (1, 3)), ((5,), (6,)))
(((2, 1), (3,)), ((5,), (6,)))
(((2,), (3, 1)), ((5,), (6,)))
(((2, 3), (1,)), ((5,), (6,)))
(((3,), (1, 2)), ((5,), (6,)))
(((3, 1), (2,)), ((5,), (6,)))
(((3,), (2, 1)), ((5,), (6,)))
(((3, 2), (1,)), ((5,), (6,)))
"""
sm, bg = (A, B) if len(A) < len(B) else (B, A)
for part in kbins(range(len(bg)), len(sm), None):
if bg == B:
yield list((a,) for a in A), core_partition(B, part)
else:
yield core_partition(A, part), list((b,) for b in B)
def unify_assoccomm(u, v, s, ordering=None):
u = walk(u, s)
v = walk(v, s)
res = unify(u, v, s)
if res is not False:
yield res
if isinstance(u, tuple) and isinstance(v, tuple):
uop, u = u[0], u[1:]
vop, v = v[0], v[1:]
s = unify(uop, vop, s)
if s is False:
raise StopIteration()
op = walk(uop, s)
sm, lg = (u, v) if len(u) <= len(v) else (v, u)
for part in kbins(range(len(lg)), len(sm), ordering):
lg2 = makeops(op, partition(lg, part))
# TODO: we use logpy code within python within logpy
# There must be a more elegant way
for res in conde((eq_assoccomm, a, b) for a, b in zip(sm, lg2))(s):
yield res
def test2():
for orderedval in [None, 0, 1, 10, 11]:
print('ordered =', orderedval)
for p in kbins(list(range(3)), 2, ordered=orderedval):
print(' ', p)
def test1():
for orderedval in [None, 0, 1, 10, 11]:
print('ordered =', orderedval)
for p in kbins([0, 0, 1], 2, ordered=orderedval):
print(' ', p)
def test_kbins():
assert len(list(kbins('1123', 2, ordered=1))) == 24
assert len(list(kbins('1123', 2, ordered=11))) == 36
assert len(list(kbins('1123', 2, ordered=10))) == 10
assert len(list(kbins('1123', 2, ordered=0))) == 5
assert len(list(kbins('1123', 2, ordered=None))) == 3
def test1():
for orderedval in [None, 0, 1, 10, 11]:
print('ordered =', orderedval)
for p in kbins([0, 0, 1], 2, ordered=orderedval):
print(' ', p)
assert capture(lambda: test1()) == dedent('''\
ordered = None
[[0], [0, 1]]
[[0, 0], [1]]
ordered = 0
[[0, 0], [1]]
[[0, 1], [0]]
ordered = 1
[[0], [0, 1]]
[[0], [1, 0]]
[[1], [0, 0]]
ordered = 10
[[0, 0], [1]]
[[1], [0, 0]]
[[0, 1], [0]]
[[0], [0, 1]]
ordered = 11
[[0], [0, 1]]
[[0, 0], [1]]
[[0], [1, 0]]
[[0, 1], [0]]
[[1], [0, 0]]
[[1, 0], [0]]\n''')
def test2():
for orderedval in [None, 0, 1, 10, 11]:
print('ordered =', orderedval)
for p in kbins(list(range(3)), 2, ordered=orderedval):
print(' ', p)
assert capture(lambda: test2()) == dedent('''\
ordered = None
[[0], [1, 2]]
[[0, 1], [2]]
ordered = 0
[[0, 1], [2]]
[[0, 2], [1]]
[[0], [1, 2]]
ordered = 1
[[0], [1, 2]]
[[0], [2, 1]]
[[1], [0, 2]]
[[1], [2, 0]]
[[2], [0, 1]]
[[2], [1, 0]]
ordered = 10
[[0, 1], [2]]
[[2], [0, 1]]
[[0, 2], [1]]
[[1], [0, 2]]
[[0], [1, 2]]
[[1, 2], [0]]
ordered = 11
[[0], [1, 2]]
[[0, 1], [2]]
[[0], [2, 1]]
[[0, 2], [1]]
[[1], [0, 2]]
[[1, 0], [2]]
[[1], [2, 0]]
[[1, 2], [0]]
[[2], [0, 1]]
[[2, 0], [1]]
[[2], [1, 0]]
[[2, 1], [0]]\n''')
def test():
for ordered in [None, 0, 1, 10, 11]:
print 'ordered =', ordered
for p in kbins(range(3), 2, ordered=ordered):
print ' ', p
def test_kbins():
assert len(list(kbins('1123', 2, ordered=01))) == 24
assert len(list(kbins('1123', 2, ordered=11))) == 36
assert len(list(kbins('1123', 2, ordered=10))) == 10
assert len(list(kbins('1123', 2, ordered=0))) == 5
assert len(list(kbins('1123', 2, ordered=None))) == 3
def test():
for ordered in [None, 0, 1, 10, 11]:
print 'ordered =', ordered
for p in kbins([0, 0, 1], 2, ordered=ordered):
print ' ', p
assert capture(lambda : test()) == dedent('''\
ordered = None
[[0], [0, 1]]
[[0, 0], [1]]
ordered = 0
[[0, 0], [1]]
[[0, 1], [0]]
ordered = 1
[[0], [0, 1]]
[[0], [1, 0]]
[[1], [0, 0]]
ordered = 10
[[0, 0], [1]]
[[1], [0, 0]]
[[0, 1], [0]]
[[0], [0, 1]]
ordered = 11
[[0], [0, 1]]
[[0, 0], [1]]
[[0], [1, 0]]
[[0, 1], [0]]
[[1], [0, 0]]
[[1, 0], [0]]\n''')
def test():
for ordered in [None, 0, 1, 10, 11]:
print 'ordered =', ordered
for p in kbins(range(3), 2, ordered=ordered):
print ' ', p
assert capture(lambda : test()) == dedent('''\
ordered = None
[[0], [1, 2]]
[[0, 1], [2]]
ordered = 0
[[0, 1], [2]]
[[0, 2], [1]]
[[0], [1, 2]]
ordered = 1
[[0], [1, 2]]
[[0], [2, 1]]
[[1], [0, 2]]
[[1], [2, 0]]
[[2], [0, 1]]
[[2], [1, 0]]
ordered = 10
[[0, 1], [2]]
[[2], [0, 1]]
[[0, 2], [1]]
[[1], [0, 2]]
[[0], [1, 2]]
[[1, 2], [0]]
ordered = 11
[[0], [1, 2]]
[[0, 1], [2]]
[[0], [2, 1]]
[[0, 2], [1]]
[[1], [0, 2]]
[[1, 0], [2]]
[[1], [2, 0]]
[[1, 2], [0]]
[[2], [0, 1]]
[[2, 0], [1]]
[[2], [1, 0]]
[[2, 1], [0]]\n''')
def test():
for ordered in [None, 0, 1, 10, 11]:
print('ordered =', ordered)
for p in kbins(list(range(3)), 2, ordered=ordered):
print(' ', p)
def test():
for ordered in [None, 0, 1, 10, 11]:
print('ordered =', ordered)
for p in kbins([0, 0, 1], 2, ordered=ordered):
print(' ', p)
def test():
for ordered in [None, 0, 1, 10, 11]:
print("ordered =", ordered)
for p in kbins([0, 0, 1], 2, ordered=ordered):
print(" ", p)
def test_kbins():
assert len(list(kbins("1123", 2, ordered=1))) == 24
assert len(list(kbins("1123", 2, ordered=11))) == 36
assert len(list(kbins("1123", 2, ordered=10))) == 10
assert len(list(kbins("1123", 2, ordered=0))) == 5
assert len(list(kbins("1123", 2, ordered=None))) == 3
def test():
for ordered in [None, 0, 1, 10, 11]:
print("ordered =", ordered)
for p in kbins([0, 0, 1], 2, ordered=ordered):
print(" ", p)
assert capture(lambda: test()) == dedent(
"""\
ordered = None
[[0], [0, 1]]
[[0, 0], [1]]
ordered = 0
[[0, 0], [1]]
[[0, 1], [0]]
ordered = 1
[[0], [0, 1]]
[[0], [1, 0]]
[[1], [0, 0]]
ordered = 10
[[0, 0], [1]]
[[1], [0, 0]]
[[0, 1], [0]]
[[0], [0, 1]]
ordered = 11
[[0], [0, 1]]
[[0, 0], [1]]
[[0], [1, 0]]
[[0, 1], [0]]
[[1], [0, 0]]
[[1, 0], [0]]\n"""
)
def test():
for ordered in [None, 0, 1, 10, 11]:
print("ordered =", ordered)
for p in kbins(list(range(3)), 2, ordered=ordered):
print(" ", p)
assert capture(lambda: test()) == dedent(
"""\
ordered = None
[[0], [1, 2]]
[[0, 1], [2]]
ordered = 0
[[0, 1], [2]]
[[0, 2], [1]]
[[0], [1, 2]]
ordered = 1
[[0], [1, 2]]
[[0], [2, 1]]
[[1], [0, 2]]
[[1], [2, 0]]
[[2], [0, 1]]
[[2], [1, 0]]
ordered = 10
[[0, 1], [2]]
[[2], [0, 1]]
[[0, 2], [1]]
[[1], [0, 2]]
[[0], [1, 2]]
[[1, 2], [0]]
ordered = 11
[[0], [1, 2]]
[[0, 1], [2]]
[[0], [2, 1]]
[[0, 2], [1]]
[[1], [0, 2]]
[[1, 0], [2]]
[[1], [2, 0]]
[[1, 2], [0]]
[[2], [0, 1]]
[[2, 0], [1]]
[[2], [1, 0]]
[[2, 1], [0]]\n"""
)
def test():
for ordered in [None, 0, 1, 10, 11]:
print 'ordered =', ordered
for p in kbins(range(3), 2, ordered=ordered):
print ' ', p