The applyopr command computes the result of applying an operator w of the Ore algebra A to a function f.

The default actions of the predefined operators can be overwritten.  For more information, see the action option in Ore_algebra[declaration_options] and the corresponding examples.

$\mathrm{with}\left(\mathrm{Ore\_algebra}\right)\:$

$A≔\mathrm{skew\_algebra}\left(\mathrm{diff}=\left[\mathrm{Dx}\,x\right]\,\mathrm{shift}=\left[\mathrm{Sn}\,n\right]\right)\:$

$f≔a\cos \left(x\right)+b\sin \left(x\right)\:$

$w≔{\mathrm{Dx}}^2+1\:$

$\mathrm{applyopr}\left(w\,f\,A\right)$

$0$

$\mathrm{applyopr}\left(w\,\exp \left(kx\right)\,A\right)$

$k^2{\ⅇ}^{kx}+{\ⅇ}^{kx}$