Representation as sums of squares built-in function

edit

@slelievre, thank you! I have confused my self a lot and I was actually looking for a built in function that outputs r_k(n) which is the number of ways of writing a given number n as a sum of k-squares. For instance r_4(1) = 8. There is SquaresR[] built-in function in Mathematica but I can't interface to it within Sage. Is there such a built-in function in Sage?

I don't believe we have that. For some values of k this would be easy but for others I think it's an open problem (haven't looked at this for a bit).

I see. Thanks.

@Holden If you have Mathematica and Sage on the same computer, you should be able to use Mathematica from within Sage.

@Holden: maybe open a separate question "Number of representations of an integer as a sum of k squares"

@Holden: see also Waring's problem.

@slelievre, thank you so much. I installed mathematica 10.3(latest issue) and was not able to call mathematica even if I followed all the instructions on how to use mathematica within sage. From what I read around the web, I have to downgrade to version 8 to be able to interface to mathematica from within Sage. Is that true or am I missing something with integrating version 10.3?

According to Sage trac ticket #16703, the interface to Mathematica 10 was fixed.

(Though see http://trac.sagemath.org/ticket/18888.)

@slelievre, cool. Thanks.