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The Gröbner Basis Algorithm requires that we have
imposed an ordering
(a ``term order'') on
the monic monomials in the ring of polynomials in several variables
over a field *K* as in
§.
Once a term order is defined, one can define the notion
of a leading term, leading monomial and leading coefficient
of a nonzero polynomial *p*. If *p* is a polynomial,
and is a monic monomial,
then is the leading term of *p*
if appears as a term of *p* and for every
term *c M* of *p* (with
and *M* a monic monomial), is greater than
or equal to *M* in the term order. In this case,
is called the leading coefficient of *p* and
is called the leading monomial of *p*.
For a nonzero polynomial *f*, let *lt*(*f*)
denote the leading term of *f* (with
respect
to the given ordering),
*lc*(*f*) denote the leading
coefficient of *f* and
*lm*(*f*) denote the leading monomial of *f*.
Note that *lt*(*f*)=*lc*(*f*) *lm*(*f*).

*Helton *

Wed Jul 3 10:27:42 PDT 1996