Gröbner bases and primary decomposition of polynomial ideals
نویسندگان
چکیده
منابع مشابه
Gröbner Bases and Primary Decomposition of Polynomial Ideals
We present an algorithm to compute the primary decomposition of any ideal in a polynomial ring over a factorially closed algorithmic principal ideal domain R. This means that the ring R is a constructive PID and that we are given an algorithm to factor polynomials over fields which are finitely generated over R or residue fields of R. We show how basic ideal theoretic operations can be performe...
متن کاملPolynomial ideals for sandpiles and their Gröbner bases
A polynomial ideal encoding topplings in the abelian sandpile model on a graph is introduced. A Gröbner basis of this ideal is interpreted combinatorially in terms of well-connected subgraphs. This gives rise to algorithms to determine the identity and the operation in the group of recurrent configurations.
متن کاملExploiting chordal structure in polynomial ideals: a Gröbner bases approach
Chordal structure and bounded treewidth allow for efficient computation in numerical linear algebra, graphical models, constraint satisfaction and many other areas. In this paper, we begin the study of how to exploit chordal structure in computational algebraic geometry, and in particular, for solving polynomial systems. The structure of a system of polynomial equations can be described in term...
متن کاملGRÖBNER BASES AND DETERMINANTAL IDEALS -- An Introduction
We give an introduction to the theory of determinantal ideals and rings, their Gröbner bases, initial ideals and algebras, respectively. The approach is based on the straightening law and the Knuth-Robinson-Schensted correspondence. The article contains a section treating the basic results about the passage to initial ideals and algebras. Let K be a field and X an m × n matrix of indeterminates...
متن کاملGröbner bases of ideals invariant under endomorphisms
We introduce the notion of Gröbner S-basis of an ideal of the free associative algebra K〈X〉 over a field K invariant under the action of a semigroup S of endomorphisms of the algebra. We calculate the Gröbner S-bases of the ideal corresponding to the universal enveloping algebra of the free nilpotent of class 2 Lie algebra and of the T-ideal generated by the polynomial identity [x, y, z] = 0, w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1988
ISSN: 0747-7171
DOI: 10.1016/s0747-7171(88)80040-3