本文整理汇总了Python中sympy.polys.polyutils.basic_from_dict函数的典型用法代码示例。如果您正苦于以下问题：Python basic_from_dict函数的具体用法？Python basic_from_dict怎么用？Python basic_from_dict使用的例子？那么恭喜您, 这里精选的函数代码示例或许可以为您提供帮助。
在下文中一共展示了basic_from_dict函数的3个代码示例，这些例子默认根据受欢迎程度排序。您可以为喜欢或者感觉有用的代码点赞，您的评价将有助于系统推荐出更棒的Python代码示例。
示例1: _eval_expand_multinomial
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
#.........这里部分代码省略.........
示例2: to_sympy
def to_sympy(self, a):
"""Convert `a` to a SymPy object. """
return basic_from_dict(a.to_sympy_dict(), *self.gens)示例3: _eval_expand_multinomial
#.........这里部分代码省略.........
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