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### decompose

Usage

decompose L

Parameter Type Description
L A difference 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 difference equation

 (1)

as follows:
1 --> L := E^3+(n+2)*E^2+(3*n^2+9*n+6)*E-3*n^3-9*n^2-6*n;
2 --> v := decompose(L);
3 --> tex(v);


This means that the operator of (1) is a least common left multiple of where ranges over the roots of .

Usage within MAPLE

When using decompose from inside MAPLE, the result returned from SHASTA 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 difference operators, in which case L is a least common left multiple of .
(iii)
An object of the form LeftLcm where is a difference 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 := E^3+(n+2)*E^2+(3*n^2+9*n+6)*E-3*n^3-9*n^2-6*n;
> decompose(L, E, n);