Let factorint() act as an iterator

[asmeurer]

factorint sometimes hangs forever, because the factors are very large. But it also finds small factors very quickly. If someone is only interested in checking factors for some property, and possibly exiting early if one is found, it would be useful to have factorint act as an iterator, which yields the factors as they are found. 

The same is true of factor(), if the algorithm works that way.

Original issue for #6919: http://code.google.com/p/sympy/issues/detail?id=3820
Original author: https://code.google.com/u/asmeurer@gmail.com/

[smichr]

(And don't forget to use isprime, and the equivalent for polys, if you just want to know if there is no factor.)

Original comment: http://code.google.com/p/sympy/issues/detail?id=3820#c1
Original author: https://code.google.com/u/117933771799683895267/

[asmeurer]

Actually, there currently is no equivalent. Poly.is_irreducible just calls factor.

Original comment: http://code.google.com/p/sympy/issues/detail?id=3820#c2
Original author: https://code.google.com/u/asmeurer@gmail.com/

[vivonk]

I checked out it's Pollard rho algorithm for finding factors. I think to put this feature with factorint() but how this should be because I am bit confused by your issue @asmeurer . Is it like checking a number as a factor (which already exists, so this may be not). Or just gives a condition and we have to give the solution as bool or as a number, is it?

[asmeurer]

@vivonk I recommend reading up on how iterators work in Python.

[lilithxxx]

I would like to take up this issue.Please guide me in solving this as I am new to open source contributions

[coffe2code]

I would like to take this up if the issue is still open.

[variable-jain]

I would like to work on this issue. If I am not understanding the issue incorrectly @asmeurer , the request is for factorint() to act as a factor generator to output factors on the go. Please guide me in solving this issue.

[smichr]

Right now, factorint returns a dictionary. A new keyword allowing for an iterator result could be added but the original behavior should be retained when the iterator flag is False (which, IMO, would be the default).

[sylee957]

I'm unmarking the Easy to Fix label because the expected change doesn't look trivial.

[asmeurer]

We would need to make the internals operate as generators. I would suggest making factorint(iterator=True) iterate {prime: multiplicity} dictionaries. The non-iterator version, which should remain the default, would manually exhaust the iterator and merge the dictionaries.

[oscarbenjamin]

I would suggest making factorint(iterator=True) iterate {prime: multiplicity} dictionaries.

I haven't looked into the internals but do you mean that it would literally return dicts with a single key? Why would that be better than a tuple (prime, multiplicity)?

[asmeurer]

My thinking is that it would be easy to merge those into a single dictionary and also to use the same code to manipulate them as the full case. Although tuples would work as well.