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위키데이터

• ID : Q1551631

말뭉치

1. Gröbner basis theory for parametric polynomial ideals is explored with the main objective of mimicking the Gröbner basis theory for ideals.
2. (iv) S-polynomials among parametric polynomials, (v) completion algorithm for directly computing a comprehensive Gröbner basis from a given basis of a parametric ideal.
3. in this Gröbner basis form can be easily solved.
4. Later, we will give another characterization of Gröbner bases by which it can be checked in finitely many steps whether a given basis is a Gröbner basis.
5. In analogy to systems of linear equations, a Gröbner basis with respect to lexicographic ordering is also called a triangular system.
6. an equivalent Gröbner basis \(G\) can be found constructively by Buchberger's Algorithm.
7. The time and memory required to calculate a Gröbner basis depend very much on the variable ordering, monomial ordering, and on which variables are regarded as constants.
8. K. A Gröbner basis allows many important properties of the ideal and the associated algebraic variety to be deduced easily, such as the dimension and the number of zeros when it is finite.
9. Gröbner basis theory was initially introduced for the lexicographical ordering.
10. The concept of reduction, also called multivariate division or normal form computation, is central to Gröbner basis theory.
11. Degree reverse lexicographic order typically provides for the fastest Gröbner basis computations.
12. In the first part of the lecture we will introduce the Gröbner basis of an ideal in a polynomial ring.
13. The notion of the Gröbner basis and the Buchberger’s algorithm for computing it was proposed by Bruno Buchberger in 1965.
14. In this chapter, we will give a short introduction on Gröbner basis theory, and then we will present some applications of Gröbner bases.
15. Every ideal has a reduced Gröbner basis.
16. Thus we are guaranteed that for arbitrary set of polynomials we can compute a corresponding Gröbner basis in finite time.
17. F, where G will be the desired Gröbner basis of F at the and of this procedure.
18. Next apply the Buchberger criterion to see if G is already a Gröbner basis.
19. All reductions resulted in zero reminders, so the extended F is a Gröbner basis.

메타데이터

위키데이터

• ID : Q1551631