Under this correspondence, Dickson's lemma may be seen as a special case of Hilbert's basis theorem stating that every ideal has a finite basis, for the ideals generated by monomials.
42.
This follows from the one-to-one correspondence between the monomials of degree in variables and the monomials of degree at most in variables, which consists in substituting by 1 the extra variable.
43.
This follows from the one-to-one correspondence between the monomials of degree in variables and the monomials of degree at most in variables, which consists in substituting by 1 the extra variable.
44.
For example, consider the monomials xy ^ 2z, z ^ 2, x ^ 3, and x ^ 2z ^ 2; the monomial orders above would order these four monomials as follows:
45.
For example, consider the monomials xy ^ 2z, z ^ 2, x ^ 3, and x ^ 2z ^ 2; the monomial orders above would order these four monomials as follows:
46.
Once a monomial ordering is fixed, the " terms " of a polynomial ( product of a monomial with its nonzero coefficient ) are naturally ordered by decreasing monomials ( for this order ).
47.
In mathematics, a "'quadratic-linear algebra "'is an algebra over a field with a presentation such that all relations are sums of monomials of degrees 1 or 2 in the generators.
48.
Many of the main algorithms for multivariate polynomials are related with Gr�bner bases, concept that requires the choice of a monomial order, that is a total order, which is compatible with the monoid structure of the monomials.
49.
Thus, the number of monomials that appear in the partial Bell polynomial is equal to the number of ways the integer " n " can be expressed as a summation of " k " positive integers.
50.
Thus, given a complete Bell polynomial " B n ", we can separate the partial Bell polynomial " B n, k " by collecting all those monomials with degree " k ".
