exteriorPower

Usage

exteriorPower(L, m)

Parameter	Type	Description
L	${\mathbb{Q}}[n,E]$	A difference operator
m	${\mathbb{Z}}$	A positive integer

Returns

Returns a difference operator ${L}^{\wedge_{n}}$ of minimal order whose kernel is generated by the Casoratians of $n$ elements of a basis of $\mbox{Ker}(L)$.

Example

The second exterior power of

$$L = E^4-E-n$$

can be computed as follows:

1 --> L :=  E^4-E-n;
2 --> Le2 := exteriorPower(L,2);
3 --> tex(Le2);

$$E^{6}+\left(n+2\right)\,E^{4}-E^{3}-\left(n^{2}+5\,n+6\right)\, E^{2}-n^{3}-3\,n^{2}-2\,n$$

To prove that $L$ is irreducible, it is sufficient to check that neither $L$, its adjoint or its second exterior power has a hypergeometric solution over ${\mathbb{Q}}$, and that the eigenring of $L$ is trivial:

4 --> tex(hyper(L));

$$[~]$$

5 --> tex(hyper(adjoint(L)));

$$[~]$$

6 --> tex(hyper(Le2));

$$[~]$$

7 --> tex(eigenring(L));

$$[ 1 ]$$