def test_multinomial_coefficients():
assert multinomial_coefficients(1, 1) == {(1,): 1}
assert multinomial_coefficients(1, 2) == {(2,): 1}
assert multinomial_coefficients(1, 3) == {(3,): 1}
assert multinomial_coefficients(2, 0) == {(0, 0): 1}
assert multinomial_coefficients(2, 1) == {(0, 1): 1, (1, 0): 1}
assert multinomial_coefficients(2, 2) == {(2, 0): 1, (0, 2): 1, (1, 1): 2}
assert multinomial_coefficients(2, 3) == {(3, 0): 1, (1, 2): 3, (0, 3): 1,
(2, 1): 3}
assert multinomial_coefficients(3, 1) == {(1, 0, 0): 1, (0, 1, 0): 1,
(0, 0, 1): 1}
assert multinomial_coefficients(3, 2) == {(0, 1, 1): 2, (0, 0, 2): 1,
(1, 1, 0): 2, (0, 2, 0): 1, (1, 0, 1): 2, (2, 0, 0): 1}
mc = multinomial_coefficients(3, 3)
assert mc == {(2, 1, 0): 3, (0, 3, 0): 1,
(1, 0, 2): 3, (0, 2, 1): 3, (0, 1, 2): 3, (3, 0, 0): 1,
(2, 0, 1): 3, (1, 2, 0): 3, (1, 1, 1): 6, (0, 0, 3): 1}
assert dict(multinomial_coefficients_iterator(2, 0)) == {(0, 0): 1}
assert dict(
multinomial_coefficients_iterator(2, 1)) == {(0, 1): 1, (1, 0): 1}
assert dict(multinomial_coefficients_iterator(2, 2)) == \
{(2, 0): 1, (0, 2): 1, (1, 1): 2}
assert dict(multinomial_coefficients_iterator(3, 3)) == mc
it = multinomial_coefficients_iterator(7, 2)
assert [next(it) for i in range(4)] == \
[((2, 0, 0, 0, 0, 0, 0), 1), ((1, 1, 0, 0, 0, 0, 0), 2),
((0, 2, 0, 0, 0, 0, 0), 1), ((1, 0, 1, 0, 0, 0, 0), 2)]
def test_multinomial_coefficients():
assert multinomial_coefficients(1, 1) == {(1,): 1}
assert multinomial_coefficients(1, 2) == {(2,): 1}
assert multinomial_coefficients(1, 3) == {(3,): 1}
assert multinomial_coefficients(2, 0) == {(0, 0): 1}
assert multinomial_coefficients(2, 1) == {(0, 1): 1, (1, 0): 1}
assert multinomial_coefficients(2, 2) == {(2, 0): 1, (0, 2): 1, (1, 1): 2}
assert multinomial_coefficients(2, 3) == {(3, 0): 1, (1, 2): 3, (0, 3): 1,
(2, 1): 3}
assert multinomial_coefficients(3, 1) == {(1, 0, 0): 1, (0, 1, 0): 1,
(0, 0, 1): 1}
assert multinomial_coefficients(3, 2) == {(0, 1, 1): 2, (0, 0, 2): 1,
(1, 1, 0): 2, (0, 2, 0): 1, (1, 0, 1): 2, (2, 0, 0): 1}
mc = multinomial_coefficients(3, 3)
assert mc == {(2, 1, 0): 3, (0, 3, 0): 1,
(1, 0, 2): 3, (0, 2, 1): 3, (0, 1, 2): 3, (3, 0, 0): 1,
(2, 0, 1): 3, (1, 2, 0): 3, (1, 1, 1): 6, (0, 0, 3): 1}
assert dict(multinomial_coefficients_iterator(2, 0)) == {(0, 0): 1}
assert dict(
multinomial_coefficients_iterator(2, 1)) == {(0, 1): 1, (1, 0): 1}
assert dict(multinomial_coefficients_iterator(2, 2)) == \
{(2, 0): 1, (0, 2): 1, (1, 1): 2}
assert dict(multinomial_coefficients_iterator(3, 3)) == mc
it = multinomial_coefficients_iterator(7, 2)
assert [next(it) for i in range(4)] == \
[((2, 0, 0, 0, 0, 0, 0), 1), ((1, 1, 0, 0, 0, 0, 0), 2),
((0, 2, 0, 0, 0, 0, 0), 1), ((1, 0, 1, 0, 0, 0, 0), 2)]
def test_multinomial_coefficients():
assert multinomial_coefficients(1, 1) == {(1,): 1}
assert multinomial_coefficients(1, 2) == {(2,): 1}
assert multinomial_coefficients(1, 3) == {(3,): 1}
assert multinomial_coefficients(2, 1) == {(0, 1): 1, (1, 0): 1}
assert multinomial_coefficients(2, 2) == {(2, 0): 1, (0, 2): 1, (1, 1): 2}
assert multinomial_coefficients(2, 3) == {(3, 0): 1, (1, 2): 3, (0, 3): 1, (2, 1): 3}
assert multinomial_coefficients(3, 1) == {(1, 0, 0): 1, (0, 1, 0): 1, (0, 0, 1): 1}
assert multinomial_coefficients(3, 2) == {
(0, 1, 1): 2,
(0, 0, 2): 1,
(1, 1, 0): 2,
(0, 2, 0): 1,
(1, 0, 1): 2,
(2, 0, 0): 1,
}
assert multinomial_coefficients(3, 3) == {
(2, 1, 0): 3,
(0, 3, 0): 1,
(1, 0, 2): 3,
(0, 2, 1): 3,
(0, 1, 2): 3,
(3, 0, 0): 1,
(2, 0, 1): 3,
(1, 2, 0): 3,
(1, 1, 1): 6,
(0, 0, 3): 1,
}
def test_multinomial_coefficients():
assert multinomial_coefficients(1, 1) == {(1,): 1}
assert multinomial_coefficients(1, 2) == {(2,): 1}
assert multinomial_coefficients(1, 3) == {(3,): 1}
assert multinomial_coefficients(2, 1) == {(0, 1): 1, (1, 0): 1}
assert multinomial_coefficients(2, 2) == {(2, 0): 1, (0, 2): 1, (1, 1): 2}
assert multinomial_coefficients(2, 3) == {(3, 0): 1, (1, 2): 3, (0, 3): 1,
(2, 1): 3}
assert multinomial_coefficients(3, 1) == {(1, 0, 0): 1, (0, 1, 0): 1,
(0, 0, 1): 1}
assert multinomial_coefficients(3, 2) == {(0, 1, 1): 2, (0, 0, 2): 1,
(1, 1, 0): 2, (0, 2, 0): 1, (1, 0, 1): 2, (2, 0, 0): 1}
assert multinomial_coefficients(3, 3) == {(2, 1, 0): 3, (0, 3, 0): 1,
(1, 0, 2): 3, (0, 2, 1): 3, (0, 1, 2): 3, (3, 0, 0): 1,
(2, 0, 1): 3, (1, 2, 0): 3, (1, 1, 1): 6, (0, 0, 3): 1}
def match_matrices_gen(tRNAs, aaRSs, cache):
keyss = key_tuples()
if cache:
getmm = get_match_matrix_cache
else:
getmm = get_match_matrix
for key_tuple in keyss:
#pdb.set_trace()
m = getmm(tRNAs, aaRSs, key_tuple)
d = get_degeneracy(key_tuple)
if mask:
o = get_offmask(key_tuple)
ei = get_eips(key_tuple)
else:
o = 0
ei = 0
c = Counter(key_tuple)
nu = len(c)
k = tuple(c.values())
mc = multinomial_coefficients(nu, width)
d *= mc[k]
yield m, d, o, ei
def _eval_expand_multinomial(self, **hints):
"""(a+b+..) ** n -> a**n + n*a**(n-1)*b + .., n is nonzero integer"""
base, exp = self.args
result = self
if exp.is_Rational and exp.p > 0 and base.is_Add:
if not exp.is_Integer:
n = Integer(exp.p // exp.q)
if not n:
return result
else:
radical, result = self.func(base, exp - n), []
expanded_base_n = self.func(base, n)
if expanded_base_n.is_Pow:
expanded_base_n = \
expanded_base_n._eval_expand_multinomial()
for term in Add.make_args(expanded_base_n):
result.append(term*radical)
return Add(*result)
n = int(exp)
if base.is_commutative:
order_terms, other_terms = [], []
for b in base.args:
if b.is_Order:
order_terms.append(b)
else:
other_terms.append(b)
if order_terms:
# (f(x) + O(x^n))^m -> f(x)^m + m*f(x)^{m-1} *O(x^n)
f = Add(*other_terms)
o = Add(*order_terms)
if n == 2:
return expand_multinomial(f**n, deep=False) + n*f*o
else:
g = expand_multinomial(f**(n - 1), deep=False)
return expand_mul(f*g, deep=False) + n*g*o
if base.is_number:
# Efficiently expand expressions of the form (a + b*I)**n
# where 'a' and 'b' are real numbers and 'n' is integer.
a, b = base.as_real_imag()
if a.is_Rational and b.is_Rational:
if not a.is_Integer:
if not b.is_Integer:
k = self.func(a.q * b.q, n)
a, b = a.p*b.q, a.q*b.p
else:
k = self.func(a.q, n)
a, b = a.p, a.q*b
elif not b.is_Integer:
k = self.func(b.q, n)
a, b = a*b.q, b.p
else:
k = 1
a, b, c, d = int(a), int(b), 1, 0
while n:
if n & 1:
c, d = a*c - b*d, b*c + a*d
n -= 1
a, b = a*a - b*b, 2*a*b
n //= 2
I = S.ImaginaryUnit
if k == 1:
return c + I*d
else:
return Integer(c)/k + I*d/k
p = other_terms
# (x+y)**3 -> x**3 + 3*x**2*y + 3*x*y**2 + y**3
# in this particular example:
# p = [x,y]; n = 3
# so now it's easy to get the correct result -- we get the
# coefficients first:
from sympy import multinomial_coefficients
from sympy.polys.polyutils import basic_from_dict
expansion_dict = multinomial_coefficients(len(p), n)
# in our example: {(3, 0): 1, (1, 2): 3, (0, 3): 1, (2, 1): 3}
# and now construct the expression.
return basic_from_dict(expansion_dict, *p)
else:
if n == 2:
return Add(*[f*g for f in base.args for g in base.args])
else:
multi = (base**(n - 1))._eval_expand_multinomial()
if multi.is_Add:
return Add(*[f*g for f in base.args
for g in multi.args])
else:
# XXX can this ever happen if base was an Add?
return Add(*[f*multi for f in base.args])
elif (exp.is_Rational and exp.p < 0 and base.is_Add and
abs(exp.p) > exp.q):
return 1 / self.func(base, -exp)._eval_expand_multinomial()
elif exp.is_Add and base.is_Number:
# a + b a b
# n --> n n , where n, a, b are Numbers
coeff, tail = S.One, S.Zero
for term in exp.args:
if term.is_Number:
coeff *= self.func(base, term)
else:
tail += term
return coeff * self.func(base, tail)
else:
return result
def _eval_expand_multinomial(self, deep=True, **hints):
"""(a+b+..) ** n -> a**n + n*a**(n-1)*b + .., n is nonzero integer"""
if deep:
b = self.base.expand(deep=deep, **hints)
e = self.exp.expand(deep=deep, **hints)
else:
b = self.base
e = self.exp
if b is None:
base = self.base
else:
base = b
if e is None:
exp = self.exp
else:
exp = e
if e is not None or b is not None:
result = Pow(base, exp)
if result.is_Pow:
base, exp = result.base, result.exp
else:
return result
else:
result = None
if exp.is_Rational and exp.p > 0 and base.is_Add:
if not exp.is_Integer:
n = Integer(exp.p // exp.q)
if not n:
return Pow(base, exp)
else:
radical, result = Pow(base, exp - n), []
for term in Add.make_args(
Pow(base, n)._eval_expand_multinomial(deep=False)):
result.append(term * radical)
return Add(*result)
n = int(exp)
if base.is_commutative:
order_terms, other_terms = [], []
for order in base.args:
if order.is_Order:
order_terms.append(order)
else:
other_terms.append(order)
if order_terms:
# (f(x) + O(x^n))^m -> f(x)^m + m*f(x)^{m-1} *O(x^n)
f = Add(*other_terms)
g = (f**(n - 1)).expand()
return (f * g).expand() + n * g * Add(*order_terms)
if base.is_number:
# Efficiently expand expressions of the form (a + b*I)**n
# where 'a' and 'b' are real numbers and 'n' is integer.
a, b = base.as_real_imag()
if a.is_Rational and b.is_Rational:
if not a.is_Integer:
if not b.is_Integer:
k = Pow(a.q * b.q, n)
a, b = a.p * b.q, a.q * b.p
else:
k = Pow(a.q, n)
a, b = a.p, a.q * b
elif not b.is_Integer:
k = Pow(b.q, n)
a, b = a * b.q, b.p
else:
k = 1
a, b, c, d = int(a), int(b), 1, 0
while n:
if n & 1:
c, d = a * c - b * d, b * c + a * d
n -= 1
a, b = a * a - b * b, 2 * a * b
n //= 2
I = S.ImaginaryUnit
if k == 1:
return c + I * d
else:
return Integer(c) / k + I * d / k
p = other_terms
# (x+y)**3 -> x**3 + 3*x**2*y + 3*x*y**2 + y**3
# in this particular example:
# p = [x,y]; n = 3
# so now it's easy to get the correct result -- we get the
# coefficients first:
from sympy import multinomial_coefficients
expansion_dict = multinomial_coefficients(len(p), n)
# in our example: {(3, 0): 1, (1, 2): 3, (0, 3): 1, (2, 1): 3}
# and now construct the expression.
# An elegant way would be to use Poly, but unfortunately it is
# slower than the direct method below, so it is commented out:
#b = {}
#for k in expansion_dict:
# b[k] = Integer(expansion_dict[k])
#return Poly(b, *p).as_expr()
from sympy.polys.polyutils import basic_from_dict
result = basic_from_dict(expansion_dict, *p)
return result
else:
if n == 2:
return Add(*[f * g for f in base.args for g in base.args])
else:
multi = (base**(n -
1))._eval_expand_multinomial(deep=False)
if multi.is_Add:
return Add(
*[f * g for f in base.args for g in multi.args])
else:
return Add(*[f * multi for f in base.args])
elif exp.is_Rational and exp.p < 0 and base.is_Add and abs(
exp.p) > exp.q:
return 1 / Pow(base, -exp)._eval_expand_multinomial(deep=False)
elif exp.is_Add and base.is_Number:
# a + b a b
# n --> n n , where n, a, b are Numbers
coeff, tail = S.One, S.Zero
for term in exp.args:
if term.is_Number:
coeff *= Pow(base, term)
else:
tail += term
return coeff * Pow(base, tail)
else:
return result
def _eval_expand_multinomial(self, **hints):
"""(a+b+..) ** n -> a**n + n*a**(n-1)*b + .., n is nonzero integer"""
base, exp = self.args
result = self
if exp.is_Rational and exp.p > 0 and base.is_Add:
if not exp.is_Integer:
n = Integer(exp.p // exp.q)
if not n:
return result
else:
radical, result = Pow(base, exp - n), []
expanded_base_n = Pow(base, n)
if expanded_base_n.is_Pow:
expanded_base_n = \
expanded_base_n._eval_expand_multinomial()
for term in Add.make_args(expanded_base_n):
result.append(term*radical)
return Add(*result)
n = int(exp)
if base.is_commutative:
order_terms, other_terms = [], []
for b in base.args:
if b.is_Order:
order_terms.append(b)
else:
other_terms.append(b)
if order_terms:
# (f(x) + O(x^n))^m -> f(x)^m + m*f(x)^{m-1} *O(x^n)
f = Add(*other_terms)
o = Add(*order_terms)
if n == 2:
return expand_multinomial(f**n, deep=False) + n*f*o
else:
g = expand_multinomial(f**(n - 1), deep=False)
return expand_mul(f*g, deep=False) + n*g*o
if base.is_number:
# Efficiently expand expressions of the form (a + b*I)**n
# where 'a' and 'b' are real numbers and 'n' is integer.
a, b = base.as_real_imag()
if a.is_Rational and b.is_Rational:
if not a.is_Integer:
if not b.is_Integer:
k = Pow(a.q * b.q, n)
a, b = a.p*b.q, a.q*b.p
else:
k = Pow(a.q, n)
a, b = a.p, a.q*b
elif not b.is_Integer:
k = Pow(b.q, n)
a, b = a*b.q, b.p
else:
k = 1
a, b, c, d = int(a), int(b), 1, 0
while n:
if n & 1:
c, d = a*c - b*d, b*c + a*d
n -= 1
a, b = a*a - b*b, 2*a*b
n //= 2
I = S.ImaginaryUnit
if k == 1:
return c + I*d
else:
return Integer(c)/k + I*d/k
p = other_terms
# (x+y)**3 -> x**3 + 3*x**2*y + 3*x*y**2 + y**3
# in this particular example:
# p = [x,y]; n = 3
# so now it's easy to get the correct result -- we get the
# coefficients first:
from sympy import multinomial_coefficients
from sympy.polys.polyutils import basic_from_dict
expansion_dict = multinomial_coefficients(len(p), n)
# in our example: {(3, 0): 1, (1, 2): 3, (0, 3): 1, (2, 1): 3}
# and now construct the expression.
return basic_from_dict(expansion_dict, *p)
else:
if n == 2:
return Add(*[f*g for f in base.args for g in base.args])
else:
multi = (base**(n - 1))._eval_expand_multinomial()
if multi.is_Add:
return Add(*[f*g for f in base.args
for g in multi.args])
else:
# XXX can this ever happen if base was an Add?
return Add(*[f*multi for f in base.args])
elif (exp.is_Rational and exp.p < 0 and base.is_Add and
abs(exp.p) > exp.q):
return 1 / Pow(base, -exp)._eval_expand_multinomial()
elif exp.is_Add and base.is_Number:
# a + b a b
# n --> n n , where n, a, b are Numbers
coeff, tail = S.One, S.Zero
for term in exp.args:
if term.is_Number:
coeff *= Pow(base, term)
else:
tail += term
return coeff * Pow(base, tail)
else:
return result
def _eval_expand_basic(self):
"""
(a*b)**n -> a**n * b**n
(a+b+..) ** n -> a**n + n*a**(n-1)*b + .., n is positive integer
"""
b = self.base._eval_expand_basic()
e = self.exp._eval_expand_basic()
if b is None:
base = self.base
else:
base = b
if e is None:
exp = self.exp
else:
exp = e
if e is not None or b is not None:
result = base ** exp
if result.is_Pow:
base, exp = result.base, result.exp
else:
return result
else:
result = None
if exp.is_Integer and exp.p > 0 and base.is_Add:
n = int(exp)
if base.is_commutative:
order_terms, other_terms = [], []
for order in base.args:
if order.is_Order:
order_terms.append(order)
else:
other_terms.append(order)
if order_terms:
# (f(x) + O(x^n))^m -> f(x)^m + m*f(x)^{m-1} *O(x^n)
f = Add(*other_terms)
g = (f ** (n - 1)).expand()
return (f * g).expand() + n * g * Add(*order_terms)
if base.is_number:
# Efficiently expand expressions of the form (a + b*I)**n
# where 'a' and 'b' are real numbers and 'n' is integer.
a, b = base.as_real_imag()
if a.is_Rational and b.is_Rational:
if not a.is_Integer:
if not b.is_Integer:
k = (a.q * b.q) ** n
a, b = a.p * b.q, a.q * b.p
else:
k = a.q ** n
a, b = a.p, a.q * b
elif not b.is_Integer:
k = b.q ** n
a, b = a * b.q, b.p
else:
k = 1
a, b, c, d = int(a), int(b), 1, 0
while n:
if n & 1:
c, d = a * c - b * d, b * c + a * d
n -= 1
a, b = a * a - b * b, 2 * a * b
n //= 2
I = S.ImaginaryUnit
if k == 1:
return c + I * d
else:
return Integer(c) / k + I * d / k
p = other_terms
# (x+y)**3 -> x**3 + 3*x**2*y + 3*x*y**2 + y**3
# in this particular example:
# p = [x,y]; n = 3
# so now it's easy to get the correct result -- we get the
# coefficients first:
from sympy import multinomial_coefficients
expansion_dict = multinomial_coefficients(len(p), n)
# in our example: {(3, 0): 1, (1, 2): 3, (0, 3): 1, (2, 1): 3}
# and now construct the expression.
# An elegant way would be to use Poly, but unfortunately it is
# slower than the direct method below, so it is commented out:
# b = {}
# for k in expansion_dict:
# b[k] = Integer(expansion_dict[k])
# return Poly(b, *p).as_basic()
from sympy.polys.polynomial import multinomial_as_basic
result = multinomial_as_basic(expansion_dict, *p)
return result
else:
if n == 2:
return Add(*[f * g for f in base.args for g in base.args])
else:
return Mul(base, Pow(base, n - 1).expand()).expand()
elif exp.is_Add and base.is_Number:
# a + b a b
# n --> n n , where n, a, b are Numbers
coeff, tail = S.One, S.Zero
for term in exp.args:
if term.is_Number:
coeff *= base ** term
else:
tail += term
return coeff * base ** tail
else:
return result
def _eval_expand_multinomial(self, **hints):
"""(a+b+..) ** n -> a**n + n*a**(n-1)*b + .., n is nonzero integer"""
b = self.base
e = self.exp
if b is None:
base = self.base
else:
base = b
if e is None:
exp = self.exp
else:
exp = e
if e is not None or b is not None:
result = Pow(base, exp)
if result.is_Pow:
base, exp = result.base, result.exp
else:
return result
else:
result = None
if exp.is_Rational and exp.p > 0 and base.is_Add:
if not exp.is_Integer:
n = Integer(exp.p // exp.q)
if not n:
return Pow(base, exp)
else:
radical, result = Pow(base, exp - n), []
expanded_base_n = Pow(base, n)
if expanded_base_n.is_Pow:
expanded_base_n = expanded_base_n._eval_expand_multinomial()
for term in Add.make_args(expanded_base_n):
result.append(term*radical)
return Add(*result)
n = int(exp)
if base.is_commutative:
order_terms, other_terms = [], []
for order in base.args:
if order.is_Order:
order_terms.append(order)
else:
other_terms.append(order)
if order_terms:
# (f(x) + O(x^n))^m -> f(x)^m + m*f(x)^{m-1} *O(x^n)
f = Add(*other_terms)
if n == 2:
return expand_multinomial(f**n, deep=False) + n*f*Add(*order_terms)
else:
g = expand_multinomial(f**(n - 1), deep=False)
return expand_mul(f*g, deep=False) + n*g*Add(*order_terms)
if base.is_number:
# Efficiently expand expressions of the form (a + b*I)**n
# where 'a' and 'b' are real numbers and 'n' is integer.
a, b = base.as_real_imag()
if a.is_Rational and b.is_Rational:
if not a.is_Integer:
if not b.is_Integer:
k = Pow(a.q * b.q, n)
a, b = a.p*b.q, a.q*b.p
else:
k = Pow(a.q, n)
a, b = a.p, a.q*b
elif not b.is_Integer:
k = Pow(b.q, n)
a, b = a*b.q, b.p
else:
k = 1
a, b, c, d = int(a), int(b), 1, 0
while n:
if n & 1:
c, d = a*c-b*d, b*c+a*d
n -= 1
a, b = a*a-b*b, 2*a*b
n //= 2
I = S.ImaginaryUnit
if k == 1:
return c + I*d
else:
return Integer(c)/k + I*d/k
p = other_terms
# (x+y)**3 -> x**3 + 3*x**2*y + 3*x*y**2 + y**3
# in this particular example:
# p = [x,y]; n = 3
# so now it's easy to get the correct result -- we get the
# coefficients first:
from sympy import multinomial_coefficients
expansion_dict = multinomial_coefficients(len(p), n)
# in our example: {(3, 0): 1, (1, 2): 3, (0, 3): 1, (2, 1): 3}
# and now construct the expression.
# An elegant way would be to use Poly, but unfortunately it is
# slower than the direct method below, so it is commented out:
#b = {}
#for k in expansion_dict:
# b[k] = Integer(expansion_dict[k])
#return Poly(b, *p).as_expr()
from sympy.polys.polyutils import basic_from_dict
result = basic_from_dict(expansion_dict, *p)
return result
else:
if n == 2:
return Add(*[f*g for f in base.args for g in base.args])
else:
multi = (base**(n-1))._eval_expand_multinomial()
if multi.is_Add:
return Add(*[f*g for f in base.args for g in multi.args])
else:
return Add(*[f*multi for f in base.args])
elif exp.is_Rational and exp.p < 0 and base.is_Add and abs(exp.p) > exp.q:
return 1 / Pow(base, -exp)._eval_expand_multinomial()
elif exp.is_Add and base.is_Number:
# a + b a b
# n --> n n , where n, a, b are Numbers
coeff, tail = S.One, S.Zero
for term in exp.args:
if term.is_Number:
coeff *= Pow(base, term)
else:
tail += term
return coeff * Pow(base, tail)
else:
return result
def doit1(e):
f = e*(e+1)
f = f.expand()
return f
e = (x+y+z+1)**N
t_tot = clock()
a2 = doit1(e)
t_tot = clock()-t_tot
print "done"
t_mul = clock()
a= multinomial_coefficients(4, N)
b= multinomial_coefficients(4, 2*N)
a.items()
b.items()
t_mul = clock() - t_mul
print e
print "# of terms:", len(a2.args)
print "time doing multinomial_coefficients:", t_mul
print "total time2:", t_tot
#from sympy import ADD, MUL, POW, INTEGER, SYMBOL
#
#def csympy2sympy(a):
# import sympy
# if a.type == ADD:
# return sympy.Add(*[csympy2sympy(x) for x in a.args])
