The reduction of a polynomial by other polynomials with respect to a monomial ordering is central to Gröbner basis theory. It is a generalization of both row reduction occurring in Gaussian elimination and division steps of the Euclidean division of univariate polynomials.
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Nov 28, 2012 · A Gröbner basis is a set of multivariate nonlinear polynomials enjoying certain properties that allow simple algorithmic solutions for many fundamental ...
May 12, 2011 · The Gröbner basis is used to convert from the initial four variables needed to define a binary function to six "symmetrized variables" that are ...
An Introduction to Grobner Bases - American Mathematical Society
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In this book we give a leisurely introduction to the subject and its applications suitable for students with a little knowledge of abstract and linear algebra.
A Gröbner basis is equivalent to Gaussian elimination. The algorithm for computing Gröbner bases is known as Buchberger's algorithm.
Apr 12, 2011 · I would like to present an application of Gröbner bases. The audience is a class of first year graduate students who are taking first year algebra.
Sep 27, 2016 · Not every theorem in Euclidean geometry can be proven by Gröbner basis methods, because the connection between Gröbner bases and geometry only goes through for ...
The method of Gröbner bases is a powerful technique for solving problems in commutative algebra (polynomial ideal theory, algebraic geometry)
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As the primary tool for doing explicit computations in polynomial rings in many variables, Gröbner bases are an important component of all computer algebra ...
In this paper we study the relationship between Buchberger's Gröbner basis method and the straightening algorithm in the bracket algebra.