Hello, I made a lot of research in that area of approximation of 1 real by a vector of reals. The thing is : There has been a lot of papers written on the generalisation of cont. frac. T - fractions , U -fractions, any_letter- fractions. one problem being that there are no natural way of doing that, well at least not any which is simple enough that will give the 'best possible ' approximation. Let's say you have the simplest case where there is more than 1 number to approximate by real numbers, take pi and e or exp(1), if we ask what is the best rational approximation to both of them at the same time , well there is no clear answer, One simple algorithm is this one : for example take 2 numbers a and b in pseudo - code : do { | a - b | } = c a <-- b b <-- c od So this will find X, Y, Z such that aX + bY + Z = 0 or said differently, you find 2 integers mutiplied by (in this example) by Pi and E so that the error is as small as possible If you do a couple of iterations then one can find : 9257454 * E - 5824723 * pi = 6865462 BUT this example is not very good , with LLL or PSLQ it is possible to find smaller integers that will give a better approximation and this is the whole point. There are many ways to do that, When you have a vector of reals then there are many- many possible ways. if you look at the Maple doc. on ?kronecker or ?numtheory[minkowski] the algorithms shown are interesting in a sense that it adresses the problem without necessarly finding the best answer. ... Best regards Simon plouffe