Some remarks on Fitzpatrick and Flynn’s Gröbner basis technique for Padé approximation

In Fitzpatrick and Flynn (J. Symbolic Comput. 13 (1992) 133), a Gröbner basis technique for multivariable Padéapproximation problems was developed under a rather restrictive hypothesis on the shape of the numerator and denominator in relation to the approximation conditions desired. In this article, we show that their hypotheses can be replaced by other less stringent conditions, and we show how to compute some standard forms of multivariable approximants through several examples.