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SymPy cannot cheat product

I am using SymPy 1.0 and Python 2.7. I want to calculate the sum of the first 100 integers:

This code is working successfully

import sympy as sy
from sympy.tensor import IndexedBase, Idx
import numpy as np

x = sy.IndexedBase('x')
i = sy.symbols('i', cls=Idx)
s = sy.Sum(x[i], (i, 0, 100))
s_lambda = sy.lambdify(sy.DeferredVector('x'), s, 'numpy')
s_lambda(np.arange(101))

And gives 5050, as expected. But when I try to do the same with Productinstead Sum:

import sympy as sy
from sympy.tensor import IndexedBase, Idx
import numpy as np

x = sy.IndexedBase('x')
i = sy.symbols('i', cls=Idx)
s = sy.Product(x[i], (i, 0, 100))
s_lambda = sy.lambdify(sy.DeferredVector('x'), s, 'numpy')
s_lambda(np.arange(101))

I got NameError: global name 'Product' is not defined What am I doing wrong? Is there a workaround to get what I want?

Edit 1: What if I don't know the limit in advance Product. Let me say something like

import sympy as sy
from sympy.tensor import IndexedBase, Idx
import numpy as np

x = sy.IndexedBase('x')
i = sy.symbols('i', cls=Idx)
n = sy.symbols('n', integer=True, positive=True)
s = sy.Product(x[i], (i, 0, n))
s_lambda = sy.lambdify((sy.DeferredVector('x'), n) s.doit(), 'numpy')
s_lambda(np.arange(101), 5)

Edit 2: I am trying to find a workaround. Because of this, an error occurs NameError: global name 'Product' is not defined:

lambdastr((sy.DeferredVector('x'), n), p)

This gives:

lambda x,n: (Product(x[i], (i, 0, n)))

While for Sumwe got a working lambda function:

lambda x,n: ((builtins.sum(x[i] for i in range(0, n+1))))

At this point, the problem revolves around the definition of a function Product. According to the manual, I can enter through dictmy function definition

def my_prod(a, b):
    # my implementation
    pass

my_fun = {"Product" : my_prod}
f = sy.lambdify((sy.DeferredVector('x'), n), p, modules=['numpy', my_fun])
f([1,2,3,4,5], 2)

, list indices must be integers, not Symbol , lambdified f. , i, , . , integer, my_prod, Sum.

+4
1

Product

, .doit(), Product :

In [104]: s = sy.Product(x[i], (i, 1, 10)); s
Out[104]: Product(x[i], (i, 1, 10))

In [105]: s.doit()
Out[105]: x[1]*x[2]*x[3]*x[4]*x[5]*x[6]*x[7]*x[8]*x[9]*x[10]

,

import sympy as sy
from sympy.tensor import IndexedBase, Idx
import numpy as np

x = sy.IndexedBase('x')
i = sy.symbols('i', cls=Idx)
s = sy.Product(x[i], (i, 1, 10))
s_lambda = sy.lambdify(sy.DeferredVector('x'), s.doit(), 'numpy')
print(s_lambda(np.arange(11)))


3628800

, .doit() sy.Product(x[i], (i, 1, 100)), , np.arange(101) dtype int32 int64 ( ) 100!

In [109]: math.factorial(100)
Out[109]: 93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

, int32 int64.

In [118]: np.iinfo('int64').max
Out[118]: 9223372036854775807

In [119]: np.iinfo('int64').max < math.factorial(100)
Out[119]: True

,

s = sy.Product(x[i], (i, 1, 100))
s_lambda = sy.lambdify(sy.DeferredVector('x'), s.doit(), 'numpy')
print(s_lambda(np.arange(101)))


RuntimeWarning: overflow encountered in long_scalars

0.

dtype int64 Python int, :

import sympy as sy
from sympy.tensor import IndexedBase, Idx
import numpy as np

x = sy.IndexedBase('x')
i = sy.symbols('i', cls=Idx)
s = sy.Product(x[i], (i, 1, 100))
s_lambda = sy.lambdify(sy.DeferredVector('x'), s.doit(), 'numpy')
print(s_lambda(np.arange(101).tolist()))


93326215443944152681699238856266700490715968264381621468592963895217599993229915608941463976156518286253697920827223758251185210916864000000000000000000000000

Product

(AFAICS) . Sum , LambdaPrinter._print_Sum Sum(x[i], (i, 0, n)) builtins.sum(x[i] for i in range(0, n+1)).

_print_Product NumPyPrinter ( LambdaPrinter), lambdify, Product , NumPy :

import sympy as sy
from sympy.tensor import IndexedBase, Idx
import numpy as np
import sympy.printing.lambdarepr as SPL

def _print_Product(self, expr):
    loops = (
        'for {i} in range({a}, {b}+1)'.format(
            i=self._print(i),
            a=self._print(a),
            b=self._print(b))
        for i, a, b in expr.limits)
    return '(prod([{function} {loops}]))'.format(
        function=self._print(expr.function),
        loops=' '.join(loops))
SPL.NumPyPrinter._print_Product = _print_Product

x = sy.IndexedBase('x')
i = sy.symbols('i', cls=Idx)
n = sy.symbols('n', integer=True, positive=True)
s = sy.Product(x[i], (i, 1, n))
s_lambda = sy.lambdify((sy.DeferredVector('x'), n), s, 'numpy')
print(s_lambda(np.arange(101), 5))


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