rightGcd

Usage

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

Parameter	Type	Description
A, B	$\mathbbm{Q}[x,\frac d{dx}]$	Differential operator
p, q	$\mathbbm{Q}[x]$	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 differential equations

$$\frac{d^3 y}{dx^3} - \frac{d^2 y}{dx^2} - x \frac{dy}{dx} + x y = 0$$ (8)

and

$$\frac{d^2 y}{dx^2} + (x - 1) \frac{dy}{dx} - x y = 0$$ (9)

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

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

$$D-1$$

This means that the solutions of the system (8)-(9) are of the form $y = c e^x$ for any constant $c$.

See Also

leftGcd, leftLcm, rightLcm