def __new__(cls, *args, **options):
args = [_sympify(arg) for arg in args]
argset = multiset(args) # dictionary
args_final = []
# xor is commutative and is false if count of x is even and x
# if count of x is odd. Here x can be True, False or any Symbols
for x, freq in argset.items():
if freq % 2 == 0:
argset[x] = false
else:
argset[x] = x
for _, z in argset.items():
args_final.append(z)
argset = set(args_final)
truecount = 0
for x in args:
if isinstance(x, Number) or x in [True, False]: # Includes 0, 1
argset.discard(x)
if x:
truecount += 1
if len(argset) < 1:
return true if truecount % 2 != 0 else false
if truecount % 2 != 0:
return Not(Xor(*argset))
_args = frozenset(argset)
obj = super(Xor, cls).__new__(cls, *_args, **options)
if isinstance(obj, Xor):
obj._argset = _args
return obj
def test_multiset_permutations():
ans = [
'abby', 'abyb', 'aybb', 'baby', 'bayb', 'bbay', 'bbya', 'byab', 'byba',
'yabb', 'ybab', 'ybba'
]
assert [''.join(i) for i in multiset_permutations('baby')] == ans
assert [''.join(i) for i in multiset_permutations(multiset('baby'))] == ans
assert list(multiset_permutations([0, 0, 0], 2)) == [[0, 0]]
assert list(multiset_permutations([0, 2, 1],
2)) == [[0, 1], [0, 2], [1, 0], [1, 2],
[2, 0], [2, 1]]
assert len(list(multiset_permutations('a', 0))) == 1
assert len(list(multiset_permutations('a', 3))) == 0
def test():
for i in range(1, 7):
print(i)
for p in multiset_permutations([0, 0, 1, 0, 1], i):
print(p)
assert capture(lambda: test()) == dedent('''\
1
[0]
[1]
2
[0, 0]
[0, 1]
[1, 0]
[1, 1]
3
[0, 0, 0]
[0, 0, 1]
[0, 1, 0]
[0, 1, 1]
[1, 0, 0]
[1, 0, 1]
[1, 1, 0]
4
[0, 0, 0, 1]
[0, 0, 1, 0]
[0, 0, 1, 1]
[0, 1, 0, 0]
[0, 1, 0, 1]
[0, 1, 1, 0]
[1, 0, 0, 0]
[1, 0, 0, 1]
[1, 0, 1, 0]
[1, 1, 0, 0]
5
[0, 0, 0, 1, 1]
[0, 0, 1, 0, 1]
[0, 0, 1, 1, 0]
[0, 1, 0, 0, 1]
[0, 1, 0, 1, 0]
[0, 1, 1, 0, 0]
[1, 0, 0, 0, 1]
[1, 0, 0, 1, 0]
[1, 0, 1, 0, 0]
[1, 1, 0, 0, 0]
6\n''')
def __new__(cls, *args, **options):
args = [_sympify(arg) for arg in args]
argset = multiset(args) # dictionary
args_final=[]
# xor is commutative and is false if count of x is even and x
# if count of x is odd. Here x can be True, False or any Symbols
for x, freq in argset.items():
if freq % 2 == 0:
argset[x] = false
else:
argset[x] = x
for _, z in argset.items():
args_final.append(z)
argset = set(args_final)
truecount = 0
for x in args:
if isinstance(x, Number) or x in [True, False]: # Includes 0, 1
argset.discard(x)
if x:
truecount += 1
if len(argset) < 1:
return true if truecount % 2 != 0 else false
if truecount % 2 != 0:
return Not(Xor(*argset))
_args = frozenset(argset)
obj = super(Xor, cls).__new__(cls, *_args, **options)
if isinstance(obj, Xor):
obj._argset = _args
return obj
def test_multiset_combinations():
ans = [
"iii",
"iim",
"iip",
"iis",
"imp",
"ims",
"ipp",
"ips",
"iss",
"mpp",
"mps",
"mss",
"pps",
"pss",
"sss",
]
assert ["".join(i) for i in list(multiset_combinations("mississippi", 3))] == ans
M = multiset("mississippi")
assert ["".join(i) for i in list(multiset_combinations(M, 3))] == ans
assert ["".join(i) for i in multiset_combinations(M, 30)] == []
assert list(multiset_combinations([[1], [2, 3]], 2)) == [[[1], [2, 3]]]
assert len(list(multiset_combinations("a", 3))) == 0
assert len(list(multiset_combinations("a", 0))) == 1
assert list(multiset_combinations("abc", 1)) == [["a"], ["b"], ["c"]]
def test_multiset_permutations():
ans = ["abby", "abyb", "aybb", "baby", "bayb", "bbay", "bbya", "byab", "byba", "yabb", "ybab", "ybba"]
assert ["".join(i) for i in multiset_permutations("baby")] == ans
assert ["".join(i) for i in multiset_permutations(multiset("baby"))] == ans
assert list(multiset_permutations([0, 0, 0], 2)) == [[0, 0]]
assert list(multiset_permutations([0, 2, 1], 2)) == [[0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 1]]
assert len(list(multiset_permutations("a", 0))) == 1
assert len(list(multiset_permutations("a", 3))) == 0
def test():
for i in range(1, 7):
print(i)
for p in multiset_permutations([0, 0, 1, 0, 1], i):
print(p)
assert capture(lambda: test()) == dedent(
"""\
1
[0]
[1]
2
[0, 0]
[0, 1]
[1, 0]
[1, 1]
3
[0, 0, 0]
[0, 0, 1]
[0, 1, 0]
[0, 1, 1]
[1, 0, 0]
[1, 0, 1]
[1, 1, 0]
4
[0, 0, 0, 1]
[0, 0, 1, 0]
[0, 0, 1, 1]
[0, 1, 0, 0]
[0, 1, 0, 1]
[0, 1, 1, 0]
[1, 0, 0, 0]
[1, 0, 0, 1]
[1, 0, 1, 0]
[1, 1, 0, 0]
5
[0, 0, 0, 1, 1]
[0, 0, 1, 0, 1]
[0, 0, 1, 1, 0]
[0, 1, 0, 0, 1]
[0, 1, 0, 1, 0]
[0, 1, 1, 0, 0]
[1, 0, 0, 0, 1]
[1, 0, 0, 1, 0]
[1, 0, 1, 0, 0]
[1, 1, 0, 0, 0]
6\n"""
)
def test_multiset_permutations():
ans = ['abby', 'abyb', 'aybb', 'baby', 'bayb', 'bbay', 'bbya', 'byab',
'byba', 'yabb', 'ybab', 'ybba']
assert [''.join(i) for i in multiset_permutations('baby')] == ans
assert [''.join(i) for i in multiset_permutations(multiset('baby'))] == ans
assert list(multiset_permutations([0, 0, 0], 2)) == [[0, 0]]
assert list(multiset_permutations([0, 2, 1], 2)) == [
[0, 1], [0, 2], [1, 0], [1, 2], [2, 0], [2, 1]]
assert len(list(multiset_permutations('a', 0))) == 1
assert len(list(multiset_permutations('a', 3))) == 0
def test():
for i in range(1, 7):
print i
for p in multiset_permutations([0, 0, 1, 0, 1], i):
print p
assert capture(lambda: test()) == dedent('''\
1
[0]
[1]
2
[0, 0]
[0, 1]
[1, 0]
[1, 1]
3
[0, 0, 0]
[0, 0, 1]
[0, 1, 0]
[0, 1, 1]
[1, 0, 0]
[1, 0, 1]
[1, 1, 0]
4
[0, 0, 0, 1]
[0, 0, 1, 0]
[0, 0, 1, 1]
[0, 1, 0, 0]
[0, 1, 0, 1]
[0, 1, 1, 0]
[1, 0, 0, 0]
[1, 0, 0, 1]
[1, 0, 1, 0]
[1, 1, 0, 0]
5
[0, 0, 0, 1, 1]
[0, 0, 1, 0, 1]
[0, 0, 1, 1, 0]
[0, 1, 0, 0, 1]
[0, 1, 0, 1, 0]
[0, 1, 1, 0, 0]
[1, 0, 0, 0, 1]
[1, 0, 0, 1, 0]
[1, 0, 1, 0, 0]
[1, 1, 0, 0, 0]
6\n''')
def test_multiset_combinations():
ans = ["iii", "iim", "iip", "iis", "imp", "ims", "ipp", "ips", "iss", "mpp", "mps", "mss", "pps", "pss", "sss"]
assert ["".join(i) for i in list(multiset_combinations("mississippi", 3))] == ans
M = multiset("mississippi")
assert ["".join(i) for i in list(multiset_combinations(M, 3))] == ans
assert ["".join(i) for i in multiset_combinations(M, 30)] == []
assert list(multiset_combinations([[1], [2, 3]], 2)) == [[[1], [2, 3]]]
assert len(list(multiset_combinations("a", 3))) == 0
assert len(list(multiset_combinations("a", 0))) == 1
assert list(multiset_combinations("abc", 1)) == [["a"], ["b"], ["c"]]
def test_multiset_combinations():
ans = ['iii', 'iim', 'iip', 'iis', 'imp', 'ims', 'ipp', 'ips',
'iss', 'mpp', 'mps', 'mss', 'pps', 'pss', 'sss']
assert [''.join(i) for i in
list(multiset_combinations('mississippi', 3))] == ans
M = multiset('mississippi')
assert [''.join(i) for i in
list(multiset_combinations(M, 3))] == ans
assert [''.join(i) for i in list(multiset_combinations(M, 30))] == []
assert list(multiset_combinations([[1], [2, 3]], 2)) == [[[1], [2, 3]]]
assert len(list(multiset_combinations('a', 3))) == 0
assert list(multiset_combinations('abc', 1)) == [['a'], ['b'], ['c']]
def test_nD_derangements():
from sympy.utilities.iterables import (partitions, multiset,
multiset_derangements,
multiset_permutations)
from sympy.functions.combinatorial.numbers import nD
got = []
for i in partitions(8, k=4):
s = []
it = 0
for k, v in i.items():
for i in range(v):
s.extend([it] * k)
it += 1
ms = multiset(s)
c1 = sum(1 for i in multiset_permutations(s)
if all(i != j for i, j in zip(i, s)))
assert c1 == nD(ms) == nD(ms, 0) == nD(ms, 1)
v = [tuple(i) for i in multiset_derangements(s)]
c2 = len(v)
assert c2 == len(set(v))
assert c1 == c2
got.append(c1)
assert got == [
1, 4, 6, 12, 24, 24, 61, 126, 315, 780, 297, 772, 2033, 5430, 14833
]
assert nD('1112233456', brute=True) == nD('1112233456') == 16356
assert nD('') == nD([]) == nD({}) == 0
assert nD({1: 0}) == 0
raises(ValueError, lambda: nD({1: -1}))
assert nD('112') == 0
assert nD(i='112') == 0
assert [nD(n=i) for i in range(6)] == [0, 0, 1, 2, 9, 44]
assert nD((i for i in range(4))) == nD('0123') == 9
assert nD(m=(i for i in range(4))) == 3
assert nD(m={0: 1, 1: 1, 2: 1, 3: 1}) == 3
assert nD(m=[0, 1, 2, 3]) == 3
raises(TypeError, lambda: nD(m=0))
raises(TypeError, lambda: nD(-1))
assert nD({-1: 1, -2: 1}) == 1
assert nD(m={0: 3}) == 0
raises(ValueError, lambda: nD(i='123', n=3))
raises(ValueError, lambda: nD(i='123', m=(1, 2)))
raises(ValueError, lambda: nD(n=0, m=(1, 2)))
raises(ValueError, lambda: nD({1: -1}))
raises(ValueError, lambda: nD(m={-1: 1, 2: 1}))
raises(ValueError, lambda: nD(m={1: -1, 2: 1}))
raises(ValueError, lambda: nD(m=[-1, 2]))
raises(TypeError, lambda: nD({1: x}))
raises(TypeError, lambda: nD(m={1: x}))
raises(TypeError, lambda: nD(m={x: 1}))
def test_multiset_combinations():
ans = ['iii', 'iim', 'iip', 'iis', 'imp', 'ims', 'ipp', 'ips',
'iss', 'mpp', 'mps', 'mss', 'pps', 'pss', 'sss']
assert [''.join(i) for i in
list(multiset_combinations('mississippi', 3))] == ans
M = multiset('mississippi')
assert [''.join(i) for i in
list(multiset_combinations(M, 3))] == ans
assert [''.join(i) for i in multiset_combinations(M, 30)] == []
assert list(multiset_combinations([[1], [2, 3]], 2)) == [[[1], [2, 3]]]
assert len(list(multiset_combinations('a', 3))) == 0
assert len(list(multiset_combinations('a', 0))) == 1
assert list(multiset_combinations('abc', 1)) == [['a'], ['b'], ['c']]
def check(*args):
# not using _value_check since there is a
# suggestion for the user
if len(set(args)) != len(args):
weights = multiset(args)
n = Integer(len(args))
for k in weights:
weights[k] /= n
raise ValueError(filldedent("""
Repeated args detected but set expected. For a
distribution having different weights for each
item use the following:""") + (
'\nS("FiniteRV(%s, %s)")' % ("'X'", weights)))
def count_digits(n, base=10):
"""
Returs an ordered dict. frequency counter for the digits of a decimal
integer ``n`` representing an integer in a base ``base``, where the
base digits are mapped to the positive decimal integers, e.g. the
base ``11`` integer ``10321``, with digits ``10``, ``3``, ``2``, ``1``
(from most significant to least), is equal to the decimal integer
``13696``, as ``10 * 11**3 + 3 * 11**2 + 2 * 11**1 + 1 * 11**0 = 13696``.
For binary, octal or hexadecimal bases the integer ``n``
can also be specified as a numeric literal in those bases, e.g. ``0xF321``.
Examples
========
>>> from sympy.ntheory import count_digits
>>> count_digits(1903413094, 10)
{0: 2, 1: 2, 3: 2, 4: 2, 9: 2}
>>> count_digits(122333, 10)
{1: 1, 2: 2, 3: 3}
>>> count_digits(0b1001001, 2)
{0: 4, 1: 3}
>>> count_digits(0xF321, 16)
{1: 1, 2: 1, 3: 1, 15: 1}
The base 11 number 10321, with digits 10, 3, 2, 1 (from most significant digit)
>>> count_digits(13696, 11)
{1: 1, 2: 1, 3: 1, 10: 1}
The base 100 number 990512, with digits 99, 0, 51, 2 (from most significant digit)
>>> count_digits(99005102, 100)
{0: 1, 2: 1, 51: 1, 99: 1}
"""
return defaultdict(int, multiset(_digits(n, base)[1:]).items())
def count_digits(n, b=10):
"""
Return a dictionary whose keys are the digits of ``n`` in the
given base, ``b``, with keys indicating the digits appearing in the
number and values indicating how many times that digit appeared.
Examples
========
>>> from sympy.ntheory import count_digits, digits
>>> count_digits(1111339)
{1: 4, 3: 2, 9: 1}
The digits returned are always represented in base-10
but the number itself can be entered in any format that is
understood by Python; the base of the number can also be
given if it is different than 10:
>>> n = 0xFA; n
250
>>> count_digits(_)
{0: 1, 2: 1, 5: 1}
>>> count_digits(n, 16)
{10: 1, 15: 1}
The default dictionary will return a 0 for any digit that did
not appear in the number. For example, which digits appear 7
times in ``77!``:
>>> from sympy import factorial
>>> c77 = count_digits(factorial(77))
>>> [i for i in range(10) if c77[i] == 7]
[1, 3, 7, 9]
"""
rv = defaultdict(int, multiset(digits(n, b)).items())
rv.pop(b) if b in rv else rv.pop(-b) # b or -b is there
return rv
def test_multiset_permutations():
ans = [
'abby', 'abyb', 'aybb', 'baby', 'bayb', 'bbay', 'bbya', 'byab', 'byba',
'yabb', 'ybab', 'ybba'
]
assert [''.join(i) for i in multiset_permutations('baby')] == ans
assert [''.join(i) for i in multiset_permutations(multiset('baby'))] == ans
assert list(multiset_permutations([0, 0, 0], 2)) == [[0, 0]]
assert list(multiset_permutations([0, 2, 1],
2)) == [[0, 1], [0, 2], [1, 0], [1, 2],
[2, 0], [2, 1]]
assert len(list(multiset_permutations('a', 0))) == 1
assert len(list(multiset_permutations('a', 3))) == 0
for nul in ([], {}, ''):
assert list(multiset_permutations(nul)) == [[]]
assert list(multiset_permutations(nul, 0)) == [[]]
# impossible requests give no result
assert list(multiset_permutations(nul, 1)) == []
assert list(multiset_permutations(nul, -1)) == []
def test():
for i in range(1, 7):
print(i)
for p in multiset_permutations([0, 0, 1, 0, 1], i):
print(p)
assert capture(lambda: test()) == dedent('''\
1
[0]
[1]
2
[0, 0]
[0, 1]
[1, 0]
[1, 1]
3
[0, 0, 0]
[0, 0, 1]
[0, 1, 0]
[0, 1, 1]
[1, 0, 0]
[1, 0, 1]
[1, 1, 0]
4
[0, 0, 0, 1]
[0, 0, 1, 0]
[0, 0, 1, 1]
[0, 1, 0, 0]
[0, 1, 0, 1]
[0, 1, 1, 0]
[1, 0, 0, 0]
[1, 0, 0, 1]
[1, 0, 1, 0]
[1, 1, 0, 0]
5
[0, 0, 0, 1, 1]
[0, 0, 1, 0, 1]
[0, 0, 1, 1, 0]
[0, 1, 0, 0, 1]
[0, 1, 0, 1, 0]
[0, 1, 1, 0, 0]
[1, 0, 0, 0, 1]
[1, 0, 0, 1, 0]
[1, 0, 1, 0, 0]
[1, 1, 0, 0, 0]
6\n''')
raises(ValueError, lambda: list(multiset_permutations({0: 3, 1: -1})))
def test_multiset_permutations():
ans = [
"abby",
"abyb",
"aybb",
"baby",
"bayb",
"bbay",
"bbya",
"byab",
"byba",
"yabb",
"ybab",
"ybba",
]
assert ["".join(i) for i in multiset_permutations("baby")] == ans
assert ["".join(i) for i in multiset_permutations(multiset("baby"))] == ans
assert list(multiset_permutations([0, 0, 0], 2)) == [[0, 0]]
assert list(multiset_permutations([0, 2, 1], 2)) == [
[0, 1],
[0, 2],
[1, 0],
[1, 2],
[2, 0],
[2, 1],
]
assert len(list(multiset_permutations("a", 0))) == 1
assert len(list(multiset_permutations("a", 3))) == 0
def test():
for i in range(1, 7):
print(i)
for p in multiset_permutations([0, 0, 1, 0, 1], i):
print(p)
assert capture(lambda: test()) == dedent(
"""\
1
[0]
[1]
2
[0, 0]
[0, 1]
[1, 0]
[1, 1]
3
[0, 0, 0]
[0, 0, 1]
[0, 1, 0]
[0, 1, 1]
[1, 0, 0]
[1, 0, 1]
[1, 1, 0]
4
[0, 0, 0, 1]
[0, 0, 1, 0]
[0, 0, 1, 1]
[0, 1, 0, 0]
[0, 1, 0, 1]
[0, 1, 1, 0]
[1, 0, 0, 0]
[1, 0, 0, 1]
[1, 0, 1, 0]
[1, 1, 0, 0]
5
[0, 0, 0, 1, 1]
[0, 0, 1, 0, 1]
[0, 0, 1, 1, 0]
[0, 1, 0, 0, 1]
[0, 1, 0, 1, 0]
[0, 1, 1, 0, 0]
[1, 0, 0, 0, 1]
[1, 0, 0, 1, 0]
[1, 0, 1, 0, 0]
[1, 1, 0, 0, 0]
6\n"""
)
