Binomial Canonical Decompositions of Binomial Ideals
نویسندگان
چکیده
منابع مشابه
Decompositions of Binomial Ideals
A binomial ideal in a polynomial ring is an ideal which can be generated by binomials. We present Binomials, a package for the computer algebra system Macaulay 2 (Eisenbud et al (2001)), which specializes well known algorithms to binomial ideals, allowing for a significant speedup of common computations like primary decomposition. Central parts of the implemented algorithms go back to the found...
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We prove that the log canonical thresholds of a large class of binomial ideals, such as complete intersection binomial ideals and the defining ideals of space monomial curves, are computable by linear programming.
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We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and it has numerous applications within and beyond pure mathematics. The ideals defining toric varieties are precisely the binomial prime ideals. Our main result...
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It is known that algorithms exist which compute primary decompositions of polynomial ideals (Gianni et al., 1988; Eisenbud et al., 1992; Becker and Weispfenning, 1993; and more recently Shimoyama and Yokoyama, 1996). However, in case the ideal is binomial, binomiality of its primary components is not assured, that is, the above algorithms do not necessarily compute a decomposition into binomial...
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In this paper, binomial difference ideals are studied. Three canonical representations for Laurent binomial difference ideals are given in terms of the reduced Gröbner basis of Z[x]-lattices, regular and coherent difference ascending chains, and partial characters over Z[x]-lattices, respectively. Criteria for a Laurent binomial difference ideal to be reflexive, prime, well-mixed, and perfect a...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2011
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927872.2010.511923