Residue Reduced Form of a Rational Function as an Iterated Laurent Series

  • Xin Guo Ce
  • Zhou Yue
Keywords: diagonal, residue, algebraic, D-finite


Lipshitz showed that the diagonal of a D-finite power series is still D-finite, but his proof seems hard to implement. This paper may be regarded as the first step towards an efficient algorithm realizing Lipshitz's theory. We show that the idea of a reduced form may be a big saving for computing the D-finite functional equation. For the residue in one variable of a rational function, we develop an algorithm for computing its minimal algebraic functional equation.
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