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### 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 of L, i.e.the set of operators of order strictly less than the order of L and such that for some operator S.
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

 (3)

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);


Next: element Up: Supported functions Previous: diff   Contents   Index
Manuel Bronstein 2002-09-04