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pythonprecisionsympy
Bob Smith
Bob Smith

Reputation: 262

What is the Precision of SymPy's 'expand' Function?

I am trying to expand a function of the form (X + Y + Z) ^ N where N is sufficiently large so that the expanded product will contain terms with coefficients much greater than 2 ^ 64; for the sake of this discussion let's just say that N is greater than 200. This is an issue because I am hoping to do an analysis of the expanded form of this function, and this analysis requires exact precision for all of the terms and their coefficients.

To expand the function I am using the Python module SymPy, which has seemed very promising thus far and been able to expand functions where N is > 150 in a relatively short amount of time. My concern though is that after looking through some of the expanded functions, I am seeing coefficients with more trailing zeroes than I might expect. I know that I can run everything through mpmath for my analysis after the function has been expanded, but as of now, I am unsure as to whether or not some of the larger coefficients are even exactly correct in the first place.

Under the documentation for SymPy's expand function, there is no clarification of how precise the coefficients of the expansion are when working with very large numbers. I know for a fact that SymPy uses the mpmath module for some of its functions, so I know that it is capable of arbitrary precision, I just don't know if arbitrary precision explicitly applies to this case.

I know that I could also confirm if the expand function is arbitrarily precise or not by summing all of the coefficients of a given function and checking whether or not that sum is equal to N, but I'd rather not spend a few hours coding all the necessary pieces to make that assessment, only to find out that expand is imprecise.

If anyone has any suggestions for easier ways to confirm the precision of expand, then I would appreciate that if direct confirmation of its precision cannot be given.

Upvotes: 0

Views: 110

Answers (1)

smichr
smichr

Reputation: 19115

Although PR 18960 has not yet been merged, you can affirm there that the coefficients are correct:

>>> multinomial(15,16,14)
50151543548788717200
>>> ((x+y+z)**(15+16+14)).expand().coeff(x**15*y**16*z**14)
50151543548788717200
>>> _ > 2**64
True

Since Python supports unlimited integers and the coefficients are integers, I don't know any reason that they would not be accurate.

Upvotes: 1

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