论文信息 - Ore Polynomials in Sage

Ore Polynomials in Sage

We present a Sage implementation of Ore algebras. The main features for the most common instances include basic arithmetic and actions; GCRD and LCLM; D-finite closure properties; natural transformations between related algebras; guessing; desingularization; solvers for polynomials, rational functions and (generalized) power series. This paper is a tutorial on how to use the package.

[1] Martin Rubey,et al. Extended rate, more GFUN , 2007, J. Symb. Comput..

[2] Manuel Bronstein,et al. An Introduction to Pseudo-Linear Algebra , 1996, Theor. Comput. Sci..

[3] Frédéric Chyzak,et al. Fonctions holonomes en calcul formel , 1998 .

[4] Christian Mallinger,et al. Algorithmic Manipulations and Transformations of Univariate Holonomic Functions and Sequences , 2001 .

[5] Mark van Hoeij,et al. Integration of solutions of linear functional equations , 1999 .

[6] Christoph Koutschan,et al. Advanced applications of the holonomic systems approach , 2010, ACCA.

[7] Maximilian Jaroschek,et al. Improved polynomial remainder sequences for Ore polynomials , 2013, ACCA.

[8] Manuel Kauers,et al. The Holonomic Toolkit , 2013 .

[9] Manuel Kauers,et al. Desingularization explains order-degree curves for ore operators , 2013, ISSAC '13.

[10] O. Ore. Theory of Non-Commutative Polynomials , 1933 .

[11] Bruno Salvy,et al. GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable , 1994, TOMS.

[12] Bruno Salvy,et al. Non-Commutative Elimination in Ore Algebras Proves Multivariate Identities , 1998, J. Symb. Comput..