rightGcd

Usage

rightGcd(A, B)
rightGcd(p, q)

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

Returns

rightGcd(A, B) returns $G$ such that $A = S G$, $B = T G$, and every other exact right divisor of $A$ and $B$ is a right divisor of $G$, while rightGcd(p, q) returns $\gcd(p, q)$.

Example

To look for closed-form common solutions of the difference equations

$$y(n+3)-\left(n+4\right)\,y(n+2)+2\,y(n+1)+(n^{2}+n) y(n) = 0$$ (5)

and

$$y(n+2)-\left(n+4\right)\,y(n+1)+(2\,n+2)y(n) = 0$$ (6)

we look for solutions of their greatest right common divisor as follows:

1 --> L1 := E^3-(n+4)*E^2+2*E+n^2+n;
2 --> L2 := E^2-(n+4)*E+2*n+2;
3 --> L := rightGcd(L1, L2);
4 --> tex(L);

$$E-n-1;$$

This means that the solutions of the system (5)-(6) are of the form $y = c n!$ for any constant $c$.

See Also

leftGcd, leftLcm, rightLcm