Reduce_Order_Algorithm.txt:

	The main file.  It contains implementations for Theorem 5.1 and ReduceOrder.
	For ReduceOrder to work, one must also load "Conic.txt".


Reduce_Order_Algorithm.mw:

	Maple worksheet to demonstrate ReduceOrder. The computation needs to load the files
	  Reduce_Order_Algorithm.txt, Conic.txt, and Hom.txt
	Make sure to download these files and to edit the pathname in the worksheet so
	that Maple can find these files.

Reduce_Order_Algorithm.pdf:

	pdf version of the Maple file (only needed if you do not have Maple)


Hom.txt:

	Implementation by Yongjae Cha for "Hom" which computes the following:

	Given L1, L2 in D,  compute a basis of operators G in C(x)[tau]
	for which G(V(L1)) is contained in V(L2),  where V(L) = solution space of L.
	Here tau denotes the shift operator that sends f(x) to f(x+1).

	For more  (Yongjae's slides/abstract/implementation)  see:
	https://www.math.fsu.edu/~hoeij/papers/Hom/index.html
	
Conic.txt:

	Solve a quadratic equation of the form a*X^2 + b*y^2 + c*Z^2 = 0 where a,b,c
	are rational functions over Q.  For more see:
	https://www.math.fsu.edu/~hoeij/files/ConicProgram/


Absolute_Factorization.txt

	Contains the algorithm from sections 3.1 and 4.


Absolute_Factorization.mw

	Maple worksheet to illustrate the algorithm.

Absolute_Factorization.pdf

	pdf version of the worksheet