منابع مشابه
When does a Polynomial Ideal Contain a Positive Polynomial?
We use Gröbner bases and a theorem of Handelman to show that an ideal I of R[x1, . . . , xk] contains a polynomial with positive coefficients if and only if no initial ideal inv(I), v ∈ R, has a positive zero. Let R = R[x1, . . . , xk], R = R[x1, . . . , xk] and, considering Laurent polynomials, let R̃ = R[x1 , . . . , xk ], R̃ = R[x ± 1 , . . . , x ± k ]. For a = (a1, . . . , ak) ∈ Z, write x = ...
متن کاملComputing the Dimension of a Polynomial Ideal
Following ideas from [Hei83, DFGS91, MT97] and applying the techniques proposed in [May89, KM96, Küh98], we present a deterministic algorithm for computing the dimension of a polynomial ideal requiring polynomial working space.
متن کاملWhen is a polynomial ideal binomial after an ambient automorphism?
Can an ideal I in a polynomial ring k[x] over a field be moved by a change of coordinates into a position where it is generated by binomials x − λx with λ ∈ k, or by unital binomials (i.e., with λ = 0 or 1)? Can a variety be moved into a position where it is toric? By fibering the G-translates of I over an algebraic group G acting on affine space, these problems are special cases of questions a...
متن کاملHilbert Polynomial of a Certain Ladder-Determinantal Ideal
A ladder-shaped array is a subset of a rectangular array which looks like a Ferrers diagram corresponding to a partition of a positive integer. The ideals generated by the p-by-p minors of a ladder-type array of indeterminates in the corresponding polynomial ring have been shown to be hilbertian (i.e., their Hilbert functions coincide with Hilbert polynomials for all nonnegative integers) by Ab...
متن کاملTypes of Generalized Open Sets with Ideal
The aim of this paper is to introduce and study the notions of (resp., pre, semi, )-open sets in terms of an ideal I. These concepts generalize the usual notions of (resp., pre, semi, ) open sets. Also, several of their topological properties are investigated.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1979
ISSN: 0002-9939
DOI: 10.2307/2042739