Abstract
We describe an algorithm that computes polynomials whose roots are the coefficients of any specific order of the Laurent series of a rational function. The algorithm uses only rational operations in the coefficient field of the function. This allows us to compute with the principal parts of the Laurent series, in particular with the residues of the function, without factoring or splitting its denominator. As applications, we get a generalisation of the residue formulas used in symbolic integration algorithms ton th-order formulas. We also get an algorithm that computes explicitly the principal parts at all the poles simultaneously, while computing in the field generated by the coefficients of the series instead of the one generated by the poles of the function. This yields an improved version of the necessary conditions for the various cases of Kovacic's algorithm, that expresses those conditions in the smallest possible extension field.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Applicable Algebra in Engineering, Communication and Computing
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
