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Is there a routine to find a integer base?

Hi, Sage fans. Probably a simple Sage routine does the job, but I tried hard to find it but yet without successÂ…

My problem. Consider two rows (in QQ):



How to find (x,y) such that [(xaa[i]+ybb[i]) for i in xrange(7)] yields the row [3, -3, -3, 3, -4, 7, -3] with the smallest set integers?

For the above example (x,y)=(3,3) does the job, but is there a general routine to find the optimal (x,y)?

Many thanks in advance for your suggestions! Roland