Information om | Engelska ordet MONOMIALS

Exempel på hur man kan använda MONOMIALS i en mening

• A linear Diophantine equation equates to a constant the sum of two or more monomials, each of degree one.
• Formal powers series in several indeterminates are defined similarly by replacing the powers of a single indeterminate by monomials in several indeterminates.
• The number of the common zeros of the polynomials in a Gröbner basis is strongly related to the number of monomials that are irreducibles by the basis.
• All minimal Gröbner bases of a given ideal (for a fixed monomial ordering) have the same number of elements, and the same leading monomials, and the non-minimal Gröbner bases have more elements than the minimal ones.
• In mathematics, a monomial order (sometimes called a term order or an admissible order) is a total order on the set of all (monic) monomials in a given polynomial ring, satisfying the property of respecting multiplication, i.
• This fact, modulo an inductive argument on the degree of (non-canonical) monomials, shows one can always achieve products where the factors are ordered in a non-decreasing fashion.
• For problems which require choosing a total order, such as Gröbner basis computations, one generally chooses an admissible monomial order – that is, a total order on the set of monomials such that.
• A simple example shows that normal ordering cannot be extended by linearity from the monomials to all operators in a self-consistent way.
• Expressing that one has a syzygy provides a system of linear equations whose unknowns are the coefficients of these monomials.
• The Zhegalkin monomials are naturally ordered by divisibility, whereas the Boolean minterms do not so naturally order themselves; each one represents an exclusive eighth of the three-variable Venn diagram.
• Ward's research interests included the study of recurrence relations and the divisibility properties of their solutions, diophantine equations including Euler's sum of powers conjecture and equations between monomials, abstract algebra, lattice theory and residuated lattices, functional equations and functional iteration, and numerical analysis.

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