Ore_algebra
poly_algebra
create an algebra of commutative polynomials
Calling Sequence
Parameters
Description
Examples
poly_algebra(x_1,..., x_n)
x_i

indeterminates (variable names)
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.
$\mathrm{with}\left(\mathrm{Ore\_algebra}\right)\:$
$A\u2254\mathrm{poly\_algebra}\left(a\,b\,x\,y\right)$
${A}{\u2254}{\mathrm{Ore\_algebra}}$
$\mathrm{skew\_product}\left(\left(a+1\right)x\,by\,A\right)$
${a}{}{b}{}{x}{}{y}{+}{b}{}{x}{}{y}$
$A\u2254\mathrm{poly\_algebra}\left(i\,x\,y\,\mathrm{alg\_relations}=\left\{{i}^{2}+1\right\}\right)\:$
$\mathrm{skew\_product}\left(x+i\,yi\,A\right)$
${}{i}{}{x}{+}{i}{}{y}{+}{y}{}{x}{+}{1}$
See Also
Ore_algebra/skew_product
Ore_algebra/Weyl_algebra
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