Brief overview of my implementations for Maple's LREtools package.

Folders 2002, 2020, 2026 contain the implementations I added to LREtools in those years.

2026:
	Files ReduceOrder.mpl and AbsFactorization.mpl:

		These algorithms are described in the PhD thesis of Heba Bou KaedBey.

	Files IntegralBasis.mpl and NormalForm.mpl:

		These algorithms are described in the PhD thesis of Safiah Bawazeer.

	File SearchTable.mpl:

		The closest reference is: Solving Recurrence Relations using Local Invariants
		by Yongjae Cha, Mark van Hoeij, and Giles Levy, in ISSAC'2010.  However, the
		new implementation here is based on NormalForm instead of Local Invariants.

	File Homomorphism.mpl:

		See www.math.fsu.edu/~hoeij/papers/Hom for more details.

	File FiniteSingularities.mpl:

		Needed by the other files. It calls g_p.mpl (in folder 2002) to analyze singularities.

	File IsIrreducible.mpl:

		An addition to the factoring code.

	File SolveLRE.mpl

		Uses RightFactors (see folder 2020) and the above programs to solve linear homogeneous
		recurrence relations in closed form.

2020:

	Files: RightFactors.mpl and RFactors.mm

		Factoring recurrence operators, see "Factoring Linear Recurrence Operators"
		and "Hypergeometric Solutions of Linear Difference Systems" in section
		Difference Equations at https://www.math.fsu.edu/~hoeij/papers.html
		and the PhD thesis of Yi Zhou.

	File: GeneralizedExponents.mm

		Generalized exponents, needed for factoring.

	File: MinimalRecurrence.mm

		The degree-bounds computed with generalized exponents give a way to determine the
		recurrence of provably minimal order.

	File: RationalDense.mm

		To make RightFactors more efficient, I implemented an algorithm to solve linear
		equations over Q that is much faster than what Maple had before.

2002:

	See www.math.fsu.edu/~hoeij/papers/comments/mega1998.html

	This implementation for LREtools[hypergeomsols] is obsolete because my newer implementation RightFactors
	is faster. The only file from this folder that is still relevant is g_p.mpl  (it computes the "Finite
	Singularities", and this data is used in the 2026 code).



For my algorithms on other topics see www.math.fsu.edu/~hoeij/algorithms