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 algorithms from sections 3.1 and 4.


Absolute_Factorization.mw

	Maple worksheet to illustrate the algorithm.

Absolute_Factorization.pdf

	pdf version of the worksheet

Giles_Levy_implementation 
        
        folder containing maple worksheets for Giles Levy's code, needed for the OEIS worksheets. 

ProjHom
        
        folder containing maple worksheets for projective homomorphism, needed for the OEIS worksheets. 
        
OEIS A178808.mw

        Maple worksheet for example 5.3.2.

OEIS A178808.pdf
        
        pdf version of the worksheet

OEIS A268138.mw
        
        Maple worksheet for example 5.3.3.

OEIS A268138.pdf
      
        pdf version of the worksheet