Recognize a power series in two variables as a rational function

asked 2022-03-15 03:16:44 +0100

HughThomas gravatar image


I can get Sage to calculate a power series in two variables to any desired precision. I expect that the power series is in fact the ratio of two low-degree polynomials. Is there a way to get Sage to guess what rational function it is? Thanks for your help!

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Welcome to Ask Sage! Thank you for your question.

slelievre gravatar imageslelievre ( 2022-03-15 11:22:29 +0100 )edit

You could look into the ore_algebra package:

slelievre gravatar imageslelievre ( 2022-03-15 11:23:37 +0100 )edit

This looks great! However, it seems like it only handles power series in a single variable, so I think it doesn't actually solve my problem.

Edited to add: once I set the two variables equal, so as to get a power series in one variable, I was able to recognize the power series by the traditional approach, i.e., looking the series of coefficients up in OEIS. (And then I was able to guess how to put the two variables back in.) So my specific problem is solved. Thanks for the help!

HughThomas gravatar imageHughThomas ( 2022-03-17 02:59:55 +0100 )edit

Any chance to provide a toy example here?

slelievre gravatar imageslelievre ( 2022-03-19 14:55:13 +0100 )edit