Singular

Hi all;
the coefficients of the leading terms of the generators of a reduced Groebner basis should be equal to one (1) as far as I know. Now consider the following code:


Here the leading terms have the coefficients 2 and 16. How comes? What am I missing?

No, that depends on the definition.
Any (skalar) multiples of the elements of a Groebner basis form also
also a Groebner basis.
(see http://www.singular.uni-kl.de/Manual/4-0-3/sing_900.htm)
Some authors divied all elements by the leading coeficient
(and get then a unique Groebner basis, if it is completely reduced)

Thank you for the clarification. For sure it is a matter of definition! Nonetheless I think a few words about the definition of the Reduced Groebner Basis used by the Singular developers would be helpful. It can definitely confuse a few new users.