A mathematical definition of Gröbner bases is beyond the
scope of this document. Interested readers are referred
to, e.g., Gröbner bases: a computational approach to
commutative algebra, Thomas Becker and Volker
Weispfenning, Springer-Verlag, NY, 1993. A more detailed
explanation about the Gröbner commands in ALG48
and a large number of examples can also be found in the
``Grobner'' document that is distributed with ALG48.
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