poly_algebra - Maple Help

Ore_algebra

 poly_algebra
 create an algebra of commutative polynomials

 Calling Sequence poly_algebra(x_1,..., x_n)

Parameters

 x_i - indeterminates (variable names)

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Ore_algebra}\right):$
 > $A≔\mathrm{poly_algebra}\left(a,b,x,y\right)$
 ${A}{≔}{\mathrm{Ore_algebra}}$ (1)
 > $\mathrm{skew_product}\left(\left(a+1\right)x,by,A\right)$
 ${a}{}{b}{}{x}{}{y}{+}{b}{}{x}{}{y}$ (2)
 > $A≔\mathrm{poly_algebra}\left(i,x,y,\mathrm{alg_relations}=\left\{{i}^{2}+1\right\}\right):$
 > $\mathrm{skew_product}\left(x+i,y-i,A\right)$
 ${-}{i}{}{x}{+}{i}{}{y}{+}{y}{}{x}{+}{1}$ (3)