eigenring

**Usage**

eigenring L

eigenring A

Parameter |
Type |
Description |
---|---|---|

L |
A differential operator | |

A |
A matrix of fractions |

**Description**

eigenring(L) returns a basis of the eigenring ofL,i.e.the set of operators of order strictly less than the order ofLand such that for some operatorS.

eigenring(A) returns an by matrix such that for a basis of the eigenring of ,i.e.the set of matrices such that .

**Example**

We compute the eigenring of the differential system

as follows:

1 --> A := system(x^3,(x^5+x^2-3+x^4)/x^2,(-3+x^4+3*x)/x^2, -x^3,-(x^5-3+x^4)/x^2,-(-x^2-3+x^4+3*x)/x^2, x^3,(x^5-3+x^4)/x^2,(-3+x^4+3*x)/x^2); 2 --> e := eigenring(A); 3 --> tex(e);

This means that a basis of the eigenring of (3) is

**Usage within MAPLE **

- When using eigenring(A,D,x) from inside MAPLE, the matrix
returned from BERNINA is transformed into the array of matrices
.
So the above example in MAPLE would be:
> A := matrix(3, 3, [x^3,(x^5+x^2-3+x^4)/x^2,(-3+x^4+3*x)/x^2, -x^3,-(x^5-3+x^4)/x^2,-(-x^2-3+x^4+3*x)/x^2, x^3,(x^5-3+x^4)/x^2,(-3+x^4+3*x)/x^2]); > eigenring(A, D, x);