• Study Resource
  • Explore
    • Arts & Humanities
    • Business
    • Engineering & Technology
    • Foreign Language
    • History
    • Math
    • Science
    • Social Science

    Top subcategories

    • Advanced Math
    • Algebra
    • Basic Math
    • Calculus
    • Geometry
    • Linear Algebra
    • Pre-Algebra
    • Pre-Calculus
    • Statistics And Probability
    • Trigonometry
    • other →

    Top subcategories

    • Astronomy
    • Astrophysics
    • Biology
    • Chemistry
    • Earth Science
    • Environmental Science
    • Health Science
    • Physics
    • other →

    Top subcategories

    • Anthropology
    • Law
    • Political Science
    • Psychology
    • Sociology
    • other →

    Top subcategories

    • Accounting
    • Economics
    • Finance
    • Management
    • other →

    Top subcategories

    • Aerospace Engineering
    • Bioengineering
    • Chemical Engineering
    • Civil Engineering
    • Computer Science
    • Electrical Engineering
    • Industrial Engineering
    • Mechanical Engineering
    • Web Design
    • other →

    Top subcategories

    • Architecture
    • Communications
    • English
    • Gender Studies
    • Music
    • Performing Arts
    • Philosophy
    • Religious Studies
    • Writing
    • other →

    Top subcategories

    • Ancient History
    • European History
    • US History
    • World History
    • other →

    Top subcategories

    • Croatian
    • Czech
    • Finnish
    • Greek
    • Hindi
    • Japanese
    • Korean
    • Persian
    • Swedish
    • Turkish
    • other →
 
Profile Documents Logout
Upload
MONOMIAL IDEALS, ALMOST COMPLETE INTERSECTIONS AND
MONOMIAL IDEALS, ALMOST COMPLETE INTERSECTIONS AND

7-6 - FJAHAlg1Geo
7-6 - FJAHAlg1Geo

Minimal ideals and minimal idempotents
Minimal ideals and minimal idempotents

@comment -*-texinfo-*- @comment $Id: plumath,v 1.18 2004
@comment -*-texinfo-*- @comment $Id: plumath,v 1.18 2004

... \subseteq N^n$. We call $\ell(S)$ a \textbf{monoid of leading exponents}. There exist $\alpha_1, \ldots, \alpha_m \in N^n$, such that $\ell(S) :=\langle \alpha_1, \ldots, \alpha_m \rangle$. We define a \textbf{set of leading monomials of $S$} be $L(S) := \{ x^{\alpha} \mid \alpha \in \ell(S) \}\subs ...
Chapter 1 PLANE CURVES
Chapter 1 PLANE CURVES

Mathematics Course 111: Algebra I Part III: Rings
Mathematics Course 111: Algebra I Part III: Rings

4. Rings 4.1. Basic properties. Definition 4.1. A ring is a set R with
4. Rings 4.1. Basic properties. Definition 4.1. A ring is a set R with

MA3A6 Algebraic Number Theory
MA3A6 Algebraic Number Theory

Solving Problems with Magma
Solving Problems with Magma

Section 3-2 Finding Rational Zeros of Polynomials
Section 3-2 Finding Rational Zeros of Polynomials

EXAMPLES OF REFINABLE COMPONENTWISE POLYNOMIALS
EXAMPLES OF REFINABLE COMPONENTWISE POLYNOMIALS

Ring Theory
Ring Theory

Commutative Algebra Notes Introduction to Commutative Algebra
Commutative Algebra Notes Introduction to Commutative Algebra

Subfield-Compatible Polynomials over Finite Fields - Rose
Subfield-Compatible Polynomials over Finite Fields - Rose

The support of local cohomology modules
The support of local cohomology modules

... theory of local cohomology is to determine for which values of i does the local cohomology module HiI (M ) vanish. This question is both useful and difficult even in the case where R is a regular local ring and M = R, and this case has been studied intensely since the introduction of local cohomolog ...
Polynomial Maps of Modules
Polynomial Maps of Modules

Full text
Full text

Aurifeuillian factorizations - American Mathematical Society
Aurifeuillian factorizations - American Mathematical Society

PM 464
PM 464

Toric Varieties
Toric Varieties

contributions to the theory of finite fields
contributions to the theory of finite fields

Change log for Magma V2.11-3 - Magma Computational Algebra
Change log for Magma V2.11-3 - Magma Computational Algebra

On the Lower Central Series of PI-Algebras
On the Lower Central Series of PI-Algebras

Dedekind Domains
Dedekind Domains

FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASS 19
FOUNDATIONS OF ALGEBRAIC GEOMETRY CLASS 19

< 1 2 3 4 5 6 7 8 9 10 ... 30 >

Gröbner basis

In mathematics, and more specifically in computer algebra, computational algebraic geometry, and computational commutative algebra, a Gröbner basis is a particular kind of generating set of an ideal in a polynomial ring over a field K[x1, ..,xn]. 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. Gröbner basis computation is one of the main practical tools for solving systems of polynomial equations and computing the images of algebraic varieties under projections or rational maps.Gröbner basis computation can be seen as a multivariate, non-linear generalization of both Euclid's algorithm for computing polynomial greatest common divisors, andGaussian elimination for linear systems.Gröbner bases were introduced in 1965, together with an algorithm to compute them (Buchberger's algorithm), by Bruno Buchberger in his Ph.D. thesis. He named them after his advisor Wolfgang Gröbner. In 2007, Buchberger received the Association for Computing Machinery's Paris Kanellakis Theory and Practice Award for this work.However, the Russian mathematician N. M. Gjunter had introduced a similar notion in 1913, published in various Russian mathematical journals. These papers were largely ignored by the mathematical community until their rediscovery in 1987 by Bodo Renschuch et al. An analogous concept for local rings was developed independently by Heisuke Hironaka in 1964, who named them standard bases.The theory of Gröbner bases has been extended by many authors in various directions. It has been generalized to other structures such as polynomials over principal ideal rings or polynomial rings, and also some classes of non-commutative rings and algebras, like Ore algebras.
  • studyres.com © 2025
  • DMCA
  • Privacy
  • Terms
  • Report