leftLcm

Usage

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

Parameter	Type	Description
A, B	$\mathbbm{Q}[x,\frac d{dx}]$	Differential operators
p, q	$\mathbbm{Q}[x]$	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 $\log(x) + \log(x+1)$ can be obtained by computing the least common left multiple of the annihilators $L_1 = x d/dx + 1$ and $L_2 = (x + 1) d^2/dx^2 + d/dx$ of $\log(x)$ and $\log(x+1)$ respectively:

1 --> L1 := x*D^2 + D;
2 --> L2 := (x+1)*D^2 + D;
3 --> L := leftLcm(L1, L2);
4 --> tex(L);

$$D^{3}+{{4\,x+2} \over {x^{2}+x}}\,D^{2}+{{2} \over {x^{2}+x}}\,D$$

See Also

leftGcd, rightGcd, rightLcm