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Given a linear differential system with singularities (poles) d/dx F = A(x) F, miniISOLDE provides funcationalities for constructing locally a fundamental matrix of formal solutions and studying the properties of the system. In what follows, we give examples on three of these functionalities.
miniISOLDE is a growing package and it contains some but not all functionalitities of ISOLDE written in MAPLE by M.A.Barkatou and E. Pfluegel (1995-2012): http://isolde.sourceforge.net/ miniISOLDE is the analogous package to the package Lindalg which is written in the open source software MATHEMAGIX:
www.mathemagix.org
For description and proper citations of the algorithms implemented herein, please refer to the accompanying tutorial, the manual of Lindalg package, or the following papers and references therein:
- Barkatou, Moulay A. "An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system." Applicable Algebra in Engineering, Communication and Computing 8.1 (1997): 1-23.
- Barkatou, A. "A rational version of Moser's algorithm." Proceedings of the 1995 international symposium on Symbolic and algebraic computation. ACM, 1995.
Splitting Lemma
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Moser-Barkatou Rank Reduction
Exponential Part
More Functionalities...