system

Usage

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

Parameter	Type	Description
$a_{ij}$	${\mathbb{Q}}(x)$	The entries of a square matrix
L	${\mathbb{Q}}[n,E]$	A difference operator

Returns

system( $a_{11},\dots,a_{nn}$) returns the system $Y(n+1) = A Y(n)$, 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

$$\left(\begin{array}{c} y_1(n+1) \\ y_2(n+1) \end{array}\righ... ...ht) \left(\begin{array}{c} y_1(n) \\ y_2(n) \end{array}\right)$$

has the following rational kernel:

1 --> A := system((2*n^2+4*n)/(n^2+n),(-n^2-3*n-2)/(n^2+n),1,0);
2 --> K := kernel(A);
3 --> tex(K);

$$\pmatrix{ {{1} \over {2}}\,n^{2}+{{1} \over {2}}\,n & -{{1} ... ...over {2}}\,n & -{{1} \over {2}}\,n^{2}+{{3} \over {2}}\,n\cr }$$