Singular

5.1.141 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 http://www.mathematik.uni-kl.de/~zca/Reports_on_ca/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 groebner; ideal; option; ring; std.