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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)*E3*n^39*n^26*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)*E3*n^39*n^26*n;
> decompose(L, E, n);
See Also
factor,Loewy
Next: degree
Up: Supported functions
Previous: coefficient
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Manuel Bronstein
20020904