system

Usage

system( $a_{11},a_{12},\dots,a_{nn}$)
system(L)

Parameter	Type	Description
$a_{ij}$	$\mathbbm{Q}(x)$	The entries of a square matrix
L	$\mathbbm{Q}[x,\frac d{dx}]$	A differential operator

parametricKRetvalsystem( $a_{11},\dots,a_{nn}$) returns the system $Y' = A Y$, where $A$ is the square matrix given by the $a_{ij}$'s, while system(L) returns the companion system associated with the operator L.

Remarks

The entries of the matrix must be listed by rows.

Example

The system

$$\left(\begin{array}{c} y_1' \\ y_2' \end{array}\right) = \le... ...} \right) \left(\begin{array}{c} y_1 \\ y_2 \end{array}\right)$$

has the following rational kernel:

1 --> A := system(x, -1/x^2, x^2-x^4, x);
2 --> K := kernel(A);
3 --> tex(K);

$$\pmatrix{ {{1} \over {x}} \cr x^{2}+1\cr }$$