Next: degree Up: Supported functions Previous: Darboux   Contents   Index

### decompose

Usage

decompose L

Parameter Type Description
L A differential operator of order at most 3

Description

Returns one of the following possible results:
(i)
L, in which case L cannot be written as a least common left multiple of lower order operators (L can still be either reducible or irreducible in that case).
(ii)
where , in which case L is a least common left multiple of .
(iii)
, where is irreducible and ,
, , in which case L is a least common left multiple of and of where ranges over all the roots of .

Example

We decompose the differential equation

 (2)

as follows:
1 --> L := D^3-(x^2+3)/x*D^2-(2*x^4-x^2-3)/x^2*D + 2*x^3;
2 --> v := decompose(L);
3 --> tex(v);


This means that the operator of (2) is a least common left multiple of , and where and are the two roots of . Since and , our operator is a least common left multiple of , and .

Usage within MAPLE

• When using decompose from inside MAPLE, the result returned from BERNINA is further transformed into one of the following:
(i)
L, in which case L cannot be written as a least common left multiple of lower order operators.
(ii)
An object of the form LeftLcm where the 's are differential operators, in which case L is a least common left multiple of .
(iii)
An object of the form LeftLcm where is a differential operator containing an algebraic number , in which case L is a least common left multiple of all the conjugates of .
So the above example in MAPLE would be:
> L := D^3-(x^2+3)/x*D^2-(2*x^4-x^2-3)/x^2*D + 2*x^3;
> decompose(L, D, x);