The following call declares an Ore algebra built on a differential operator Dx and on a shift operator Sn. It also prepares the use of a function $\mathrm{\eta}\left(n\right)$ in the coefficients of the polynomials.
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$\mathrm{with}\left(\mathrm{Ore\_algebra}\right)\:$

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$A\u2254\mathrm{skew\_algebra}\left(\mathrm{diff}\=\left[\mathrm{Dx}\,x\right]\,\mathrm{shift}\=\left[\mathrm{Sn}\,n\right]\,\mathrm{func}\=\mathrm{\η}\right)$

${A}{\u2254}{\mathrm{Ore\_algebra}}$
 (1) 
This is the name of a table. Products in the algebra are performed using skew_product.
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$\mathrm{skew\_product}\left(\mathrm{Dx}\,x\,A\right)\,\mathrm{skew\_product}\left(\mathrm{Sn}\,n\,A\right)$

${\mathrm{Dx}}{}{x}{+}{1}{,}\left({n}{+}{1}\right){}{\mathrm{Sn}}$
 (2) 
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$\mathrm{skew\_product}\left(\mathrm{Dx}\mathrm{Sn}\,xn\,A\right)$

$\left({x}{}{n}{+}{x}\right){}{\mathrm{Dx}}{}{\mathrm{Sn}}{+}\left({n}{+}{1}\right){}{\mathrm{Sn}}$
 (3) 
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$\mathrm{skew\_product}\left(\mathrm{Dx}\,\frac{1}{x}\,A\right)$

$\frac{{\mathrm{Dx}}}{{x}}{}\frac{{1}}{{{x}}^{{2}}}$
 (4) 
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$\mathrm{skew\_product}\left(\mathrm{Sn}\,\mathrm{\η}\left(n\right)\,A\right)$

${\mathrm{\eta}}{}\left({n}{+}{1}\right){}{\mathrm{Sn}}$
 (5) 
The following declaration, however, is forbidden.
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$\mathrm{skew\_algebra}\left(\mathrm{diff}\=\left[\mathrm{Dx}\,x\right]\,\mathrm{shift}\=\left[\mathrm{Sx}\,x\right]\right)$
