### 7.8.14 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

See ideal; lift (letterplace); liftstd (letterplace); module; ncgen; option; rightstd (letterplace); syz (letterplace).

User manual for Singular version 4.4.1, 2025, generated by texi2html.