A method of separative monomials is presented for constructing a partition of a set of monomials associated with a certain involutive division.
INTRODUCTION. A general algorithmic approach to construction of involutive polynomial Gröbner bases can be developed.
A method of separative monomials is presented for constructing a partition of a set of monomials associated with a certain involutive division. Given a ...
Method of Separative Monomials for Involutive Divisions · Y. A. Blinkov. Computer Science, Mathematics. Programming and computer software. 2004. TLDR. A method ...
As this takes place, for a nonglobally defined division one has to recompute the separation into multiplicative and nonmultiplicative variables for all ...
People also ask
What are the rules for monomials?
When dividing a polynomial by a monomial, each term of the polynomial is divided by what?
What are the operations of a monomial?
What is the formula for dividing monomials?
Oct 22, 2024 · In the paper, two classes of involutive divisions related to admissible monomial orderings—≻-divisions and ≺-divisions—are considered.
[PDF] Involutive Division Technique: Some Generalizations and Optimizations
arxiv.org › pdf › math.SC
Therefore, for a pairwise division L and a monomial set U the correction of the separation due to enlargement of U by an element v is performed by formula.
Involutive bases of polynomial ideals - ScienceDirect.com
www.sciencedirect.com › article › abs › pii
In this paper we consider an algorithmic technique more general than that proposed by Zharkov and Blinkov for the involutive analysis of polynomial ideals.
Let K be a field and K[x] the ring of polynomials in x. If f1,...,fk ∈ K[x] then hf1,...,fki = hgcd(f1,...,fk)i. K[x] is a PID, e.g. hx − 1,x2 − 1i = hx − ...
Abstract. We consider computational and implementation issues for the completion of monomial sets to involution using different involutive divisions.