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I was working on finding a reasonable expression for a Pade approximation to sin(x). The HP Prime has pade(f(x),x,n,p) which outputs a rational function approximation to f(x) of order less than or equal to n+1 with numerator of degree <p.

It works OK, for example pade(sin(x),x,5,4) returns (-7*x^3+60*x)/(3*x^2+60) as expected.

But for some values of the parameters n, p, the Prime gives a warning before returning the answer. For example pade(sin(x),x,5,3) shows Solution may be wrong since a and b are not prime together.

Does anyone know what is happening? What are a and b?


It means that the extended euclidean algorithm used to solve for Pade approximation returns 2 polynomials that are not prime together, therefore the approxmant will probably loose one or more order.
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