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Ore_algebra

 applyopr
 apply an operator to a function

 Calling Sequence applyopr(w, f, A)

Parameters

 w - operator of the Ore algebra A f - expression denoting a mathematical function A - Ore algebra table

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Ore_algebra}\right):$
 > $A≔\mathrm{skew_algebra}\left(\mathrm{diff}=\left[\mathrm{Dx},x\right],\mathrm{shift}=\left[\mathrm{Sn},n\right]\right):$
 > $f≔a\mathrm{cos}\left(x\right)+b\mathrm{sin}\left(x\right):$
 > $w≔{\mathrm{Dx}}^{2}+1:$
 > $\mathrm{applyopr}\left(w,f,A\right)$
 ${0}$ (1)
 > $\mathrm{applyopr}\left(w,\mathrm{exp}\left(kx\right),A\right)$
 ${{k}}^{{2}}{}{{ⅇ}}^{{k}{}{x}}{+}{{ⅇ}}^{{k}{}{x}}$ (2)