Updates:
        Summary: Product() is seriously broken
        Cc: [email protected]
        Labels: -Priority-Medium Priority-High

Comment #1 on issue 2639 by asmeurer: Product() is seriously broken
http://code.google.com/p/sympy/issues/detail?id=2639

Actually, Product is seriously broken.

- It should be unevaluated by default (as I said above).

- Product(f(n), n, 1, k) syntax is allowed, and, furthermore, it does something different than Product(f(n), (n, 1, k))! (the former returns an unevaluated product and the latter raises NotImplementedError)

- Product() tries to evaluate, but using a different algorithm than product()!

- Product(f(n), (n, 1, k)) prints as Product(f(n), n, 1, k)

This class (except for the algorithms) probably needs to be completely rewritten, so that it's more like Sum(), or Integral (the latter I know for a fact is well used and has a good design). There was also some talk at some point of unifying some of the common logic behind the three.

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