Abstract
We describe in this chapter solutions to several integration-related problems involving parameters. Those problems arise as subproblems in the integration algorithm: the limited integration problem, which arises from integrating polynomials in a primitive extension (Sect. 5.8) and the parametric logarithmic derivative problem, which arises from recognizing logarithmic derivatives (Sect. 5.12) and from bounding orders and degrees of solutions of the Risch differential equation (Sects. 6.2 and 6.3). The common thread between those problems is that they ask whether there exists constants for which a given parametric differential equation has a solution in a given differential field.
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© 1997 Springer-Verlag Berlin Heidelberg
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Bronstein, M. (1997). Parametric Problems. In: Symbolic Integration I. Algorithms and Computation in Mathematics, vol 1. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03386-9_7
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DOI: https://doi.org/10.1007/978-3-662-03386-9_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-03388-3
Online ISBN: 978-3-662-03386-9
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