Left GB's
Quantum Algebra
Maximal Ideal
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