polynomialSolution

Usage

polynomialSolution(L, g)

Parameter	Type	Description
L	${\mathbb{Q}}[n,E]$	A difference operator
g	${\mathbb{Q}}[n]$	A polynomial

Description

polynomialSolution($L,g$) returns either $[p]$ where $p \in {\mathbb{Q}}[n]$ satisfies $L p = g$, or $[]$ if $L y = g$ has no solution in ${\mathbb{Q}}[n]$.

Remarks

polynomialSolution($L,0$) returns $[0]$ only when $L y = 0$ has no nonzero polynomial solution.

Example

A particular polynomial solution of

$$y(n+1) - y(n) = 5 n^4$$

can be computed in the following way:

1 --> p := polynomialSolution(E-1,5*n^4);
2 --> tex(p);

$$[ n^{5}-{{5} \over {2}}\,n^{4}+{{5} \over {3}}\,n^{3}-{{1} \over {6}}\,n ]$$

Usage within MAPLE

When using polynomialSolution from inside MAPLE, the output is modified and either a polynomial solution in $p \in {\mathbb{Q}}[n]$ or $[]$ is returned. So the above example in MAPLE would be:

> polynomialSolution(E-1,5*n^4,E,n);

$$n^{5}-{{5} \over {2}}\,n^{4}+{{5} \over {3}}\,n^{3}-{{1} \over {6}}\,n$$

See Also

kernel, rationalSolution