Singular

7.8.9 twostd (letterplace)

Syntax:

twostd( ideal_expression); twostd( module_expression);

Type:

ideal

Purpose:

returns a two-sided Groebner basis of the two-sided ideal, generated by the input, which is treated as a set of two-sided generators.

Example:

LIB "freegb.lib"; ring r = 3,(x,d),dp; // notice: we work over Z/3Z ring R = freeAlgebra(r,5); ideal I = x^4, d^3, d*x - x*d - 1; twostd(I); // a proper ideal, note x^3 as a generator ==> _[1]=d*x-x*d-1 ==> _[2]=d*d*d ==> _[3]=x*x*x ideal J = x^2, d^3, d*x - x*d - 1; twostd(J); // the whole ring ==> _[1]=1 ideal T = twostd(ideal(d*x - x*d - 1)); T; ==> T[1]=d*x-x*d-1 qring Q = T; // thus Q is the Weyl algebra over Z/3z ideal I = x^4, d^3; twostd(I); ==> _[1]=d*d*d ==> _[2]=x*x*x ideal J = x^2, d^3; twostd(J); ==> _[1]=1