leftLcm

Usage

leftLcm(A, B)
leftLcm(p, q)

Parameter	Type	Description
A, B	${\mathbb{Q}}[n,E]$	Difference operators
p, q	${\mathbb{Q}}[n]$	Polynomials

Returns

leftLcm(A, B) returns $L$ such that $L = S A = T B$, and every other left multiple of $A$ and $B$ is a left multiple of $L$, while leftLcm(p, q) returns $\mbox{lcm}(p, q)$.

Example

An annihilator of $2^n + n!$ can be obtained by computing the least common left multiple of the annihilators $L_1 = E - 2$ and $L_2 = E - n - 1$ of $2^n$ and $n!$ respectively:

1 --> L1 := E-2;
2 --> L2 := E-n-1;
3 --> L := leftLcm(L1, L2);
4 --> tex(L);

$$E^{2}+{{-n^{2}-3\,n+2} \over {n-1}}\,E+{{2\,n^{2}+2\,n} \over {n-1}}$$

See Also

leftGcd, rightGcd, rightLcm