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### factor

Usage

factor 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 is irreducible in .
(ii)
where and , in which case each is irreducible in , and L can be expressed in terms of the 's depending on as in the following table:
 m L 0 LeftLcm() 1 2 LeftLcm() 3 LeftLcm() 4 LeftLcm()
(iii)
, where , is irreducible and , , , in which case each is irreducible in , and L can be expressed depending on as in the following table:
 m L -1 LeftLcm( ) -4 LeftLcm( ) -5 LeftLcm( )
(iii)
, where , is irreducible and , , , in which case each is irreducible in , and L can be expressed depending on as in the following table:
 m L -1 LeftLcm( ) -4 LeftLcm( ) -5 LeftLcm( )
where ranges over all the roots of .

Example

We factor the difference equation

 (3)

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


This means that the operator of (3) can be written in the form

Usage within MAPLE

In order not to conflict with the factor function in MAPLE, factor is available under MAPLE under the name efactor. In addition, when using efactor from inside MAPLE, the result returned from SHASTA is further transformed as in the case of the decompose function. So the above example in MAPLE would be:
> L := E^3+(-n-2)*E^2+(3*n^2+3*n)*E-3*n^3-3*n^2;
> efactor(L, E, n);