SINGULAR Examples

Left GB's

Gröbner Bases for Left and Two-Sided Ideals - (2)


ideal I3=e3,f3,h3-4h;

ideal L3=std(I3);

L3; // GB of left ideal

==> L3[1]=h3-4h L3[2]=fh2-2fh L3[3]=f3 L3[4]=eh2+2eh L3[5]=6efh-h3-3h2-2h L3[6]=e3


ideal T3=system("twostd",I3);

T3; // GB of two-sided ideal

==> T3[1]=h3-4h T3[2]=fh2-2fh T3[3]=f2h-2f2 T3[4]=f3 T3[5]=eh2+2eh T3[6]=4efh-h3-2h2 T3[7]=ef2-fh T3[8]=e2h+2e2 T3[9]=e2f-eh-2e T3[10]=e3

We see that I₃ is not a two-sided ideal.

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Sao Carlos, 08/02 http://www.singular.uni-kl.de