### 5.1.145 slimgb

`Syntax:`
  `slimgb (` ideal_expression`)`
  `slimgb (` module_expression`)`
`Type:`
  ideal or module
`Purpose:`
  slim Groebner bases

  Returns a Groebner basis of an ideal or module with respect to the monomial ordering of the basering (which has to be global).

`Note:`
  The algorithm is designed to keep polynomials slim (short with small coefficients). For details see `https://www.singular.uni-kl.de/reports/35/paper_35_full.ps.gz`. A reduced Groebner basis is returned if option(redSB) is set (see option(redSB)). To view the progress of long running computations, use option(prot) (see option(prot)).

`Warning:`
  Groebner basis computations with inexact coefficients can not be trusted due to rounding errors.

`Example:`

        ring r=2,(x,y,z),lp;
        poly s1=z*(x*y+1);
        poly s2=x2+x;
        poly s3=y2+y;
        ideal i=s1,s2,s3;
        slimgb(i);
      ==> _[1]=y2+y
      ==> _[2]=x2+x
      ==> _[3]=yz+z
      ==> _[4]=xz+z

See degBound; groebner; ideal; option; ring; std.

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