The poly_algebra command defines an algebra of commutative polynomials and returns a table that can be used by other functions of the Ore_algebra package.

The name x_i may not be assigned.

The poly_algebra command allows the declaration of a commutative algebra as a particular case of Ore algebras.

Options are available to control the ground ring of the algebra.  See Ore_algebra[declaration_options].

All options described in the previous reference are available, except for the option polynom=s, which is the default.  This option is replaced with the option rational=s used to declare an indeterminate which may appear rationally.

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

$A≔\mathrm{poly\_algebra}\left(a\,b\,x\,y\right)$

$A≔\mathrm{Ore\_algebra}$

$\mathrm{skew\_product}\left(\left(a+1\right)x\,by\,A\right)$

$abxy+bxy$

$A≔\mathrm{poly\_algebra}\left(i\,x\,y\,\mathrm{alg\_relations}=\left\{i^2+1\right\}\right)\:$

$\mathrm{skew\_product}\left(x+i\,y-i\,A\right)$

$-ix+iy+yx+1$