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products.py
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products.py
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from sympy.core import Basic, S, C, Add, Mul, Symbol, sympify
from sympy.polys import quo, roots
from sympy.simplify import powsimp
class Product(Basic):
"""Represents unevaluated product.
"""
def __new__(cls, term, *symbols, **assumptions):
term = sympify(term)
if term.is_Number:
if term is S.NaN:
return S.NaN
elif term is S.Infinity:
return S.NaN
elif term is S.NegativeInfinity:
return S.NaN
elif term is S.Zero:
return S.Zero
elif term is S.One:
return S.One
if len(symbols) == 1:
symbol = symbols[0]
if isinstance(symbol, C.Equality):
k = symbol.lhs
a = symbol.rhs.start
n = symbol.rhs.end
elif isinstance(symbol, (tuple, list)):
k, a, n = symbol
else:
raise ValueError("Invalid arguments")
k, a, n = map(sympify, (k, a, n))
if isinstance(a, C.Number) and isinstance(n, C.Number):
return Mul(*[term.subs(k, i) for i in xrange(int(a), int(n)+1)])
else:
raise NotImplementedError
obj = Basic.__new__(cls, **assumptions)
obj._args = (term, k, a, n)
return obj
@property
def term(self):
return self._args[0]
@property
def index(self):
return self._args[1]
@property
def lower(self):
return self._args[2]
@property
def upper(self):
return self._args[3]
def doit(self):
prod = self._eval_product()
if prod is not None:
return powsimp(prod)
else:
return self
def _eval_product(self, term=None):
k = self.index
a = self.lower
n = self.upper
if term is None:
term = self.term
if not term.has(k):
return term**(n-a+1)
elif term.is_polynomial(k):
poly = term.as_poly(k)
A = B = Q = S.One
C_= poly.LC
all_roots = roots(poly, multiple=True)
for r in all_roots:
A *= C.RisingFactorial(a-r, n-a+1)
Q *= n - r
if len(all_roots) < poly.degree:
B = Product(quo(poly, Q.as_poly(k)), (k, a, n))
return poly.LC**(n-a+1) * A * B
elif term.is_Add:
p, q = term.as_numer_denom()
p = self._eval_product(p)
q = self._eval_product(q)
return p / q
elif term.is_Mul:
exclude, include = [], []
for t in term.args:
p = self._eval_product(t)
if p is not None:
exclude.append(p)
else:
include.append(p)
if not exclude:
return None
else:
A, B = Mul(*exclude), Mul(*include)
return A * Product(B, (k, a, n))
elif term.is_Pow:
if not term.base.has(k):
s = sum(term.exp, (k, a, n))
if not isinstance(s, Sum):
return term.base**s
elif not term.exp.has(k):
p = self._eval_product(term.base)
if p is not None:
return p**term.exp
def product(*args, **kwargs):
prod = Product(*args, **kwargs)
if isinstance(prod, Product):
return prod.doit()
else:
return prod