A new technique is introduced here, which enables exact integration of

monomials of any order, without requiring any integration points or weights.

The greedy add method is slower than the methods described in [3, 14], but this is due to the use of a more general basis than the

monomial basis.

n](0), for any field F, by constructing another basis for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] which consists of certain polynomials whose leading terms are the descent

monomials.

There are many characterizations for a Grobner basis for a given ideal I and

monomial ordering >.

Wolna, The stability of

monomials on a restricted domain, Aequationes Math.

2 and rather discuss its consequences: Since the polynomial Q1,0,0 contains

monomials [x.

Sargos, Three-dimensional exponential sums with

monomials, J.

A P1P (Potential polynomial of degree 1 in each variable) will consist of a finite sum of

monomials in the variables

0], the first m + 1 polynomials of the sequence [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] can uniquely be generated by linear combinations of the first m+1

monomials of the sequence [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

We define a total order on

monomials by comparing their shape w.

ij] to be the complex vector space of polynomials generated by the

monomials in the variables from [S.

We begin by introducing the usual lexicographical order among

monomials in [H.