Singular Manual: twostd (letterplace)

  | ### 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).

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