eigenring

Usage

eigenring L
eigenring A

Parameter	Type	Description
L	${\mathbb{Q}}[n,E]$	A difference operator
A	${\mathbb{Q}}(n)^{m,m}$	A matrix of fractions

Description

eigenring(L) returns a basis $R_1,\dots,R_m$ of the eigenring of L, i.e.the set of operators $R\in {\mathbb{Q}}(n)[E]$ of order strictly less than the order of L and such that $L R = S L$ for some operator S.
eigenring(A) returns an $m$ by $mt$ matrix $M = [B_1\vert\dots\vert B_t]$ such that $B_1,\dots,B_t$ for a basis of the eigenring of $Y(n+1) = A Y$, i.e. the set of matrices $B\in {\mathbb{Q}}(x)^{m,m}$ such that $A B = B(n+1) A$.

Example

We compute the eigenring of the difference equation

$$y(n+2) = 2n(n+1)y(n)$$ (2)

as follows:

1 --> L := E^2-2*n*(n+1);
2 --> e := eigenring(L);
3 --> tex(e);

$$\left[ 1 , {{1} \over {n}}\,E \right]$$

Usage within MAPLE

When using eigenring(A,D,x) from inside MAPLE, the matrix $[B_1\vert\dots\vert B_t]$ returned from SHASTA is transformed into the array of matrices $[B_1,\dots,B_t]$.