scholarly journals Computation of Hilbert Polynomials in Two Variables

1999 ◽  
Vol 28 (4-5) ◽  
pp. 681-710 ◽  
Author(s):  
Alexander Levin
Keyword(s):  
Hilbert Polynomials

scholarly journals Hilbert polynomials over artinian rings

1999 ◽  
Vol 43 (2) ◽  
pp. 338-349
Author(s):  
Cristina Blancafort ◽  
Scott Nollet
Keyword(s):  
Hilbert Polynomials ◽  
Artinian Rings

Reduction numbers and Hilbert polynomials of ideals in higher dimensional CohenMacaulay local rings

1992 ◽  
Vol 111 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Yinghwa Wu
Keyword(s):  
Local Ring ◽  
Residue Field ◽  
Primary Ideal ◽  
Local Rings ◽  
Hilbert Polynomials ◽  
Higher Dimensional ◽  
Reduction Number ◽  
Minimal Reduction ◽  
System Of Parameters

Throughout, (R, m) will denote a d-dimensional CohenMacaulay (CM for short) local ring having an infinite residue field and I an m-primary ideal in R. Recall that an ideal J I is said to be a reduction of I if Ir+1 = JIr for some r 0, and a reduction J of I is called a minimal reduction of I if J is generated by a system of parameters. The concepts of reduction and minimal reduction were first introduced by Northcott and Rees12. If J is a reduction of I, define the reduction number of I with respect to J, denoted by rj(I), to be min {r 0 Ir+1 = JIr}. The reduction number of I is defined as r(I) = min {rj(I)J is a minimal reduction of I}. The reduction number r(I) is said to be independent if r(I) = rj(I) for every minimal reduction J of I.

Computing Polynomials of the Ramanujan tn Class Invariants

2009 ◽  
Vol 52 (4) ◽  
pp. 583-597 ◽  
Author(s):  
Elisavet Konstantinou ◽  
Aristides Kontogeorgis
Keyword(s):  
Quadratic Field ◽  
Imaginary Quadratic Field ◽  
Class Field ◽  
Minimal Polynomials ◽  
Hilbert Polynomials ◽  
Reciprocity Law ◽  
Class Invariants ◽  
Hilbert Class Field

AbstractWe compute the minimal polynomials of the Ramanujan values tn, where n ≡ 11 mod 24, using the Shimura reciprocity law. These polynomials can be used for defining the Hilbert class field of the imaginary quadratic field and have much smaller coefficients than the Hilbert polynomials.

scholarly journals Hilbert polynomials of non-standard bigraded algebras

2003 ◽  
Vol 245 (2) ◽  
pp. 309-334 ◽  
Author(s):  
Nguy�n Duc Hoang ◽  
Ng� Vi�t Trung
Keyword(s):  
Hilbert Polynomials

scholarly journals On the set of Hilbert polynomials

2001 ◽  
Vol 64 (2) ◽  
pp. 291-305 ◽  
Author(s):  
Alexander B. Levin
Keyword(s):  
Chromatic Polynomial ◽  
Hilbert Polynomial ◽  
Graded Algebra ◽  
Open Problems ◽  
Graded Algebras ◽  
Hilbert Polynomials

We characterise the set of all Hilbert polynomials of standard graded algebras over a field and give solutions of some open problems on Hilbert polynomials. In particular, we prove that a chromatic polynomial of a graph is a Hilbert polynomial of some standard graded algebra.

scholarly journals Mora’s holy graal: Algorithms for computing in localizations at prime ideals

2015 ◽  
Vol 25 (07) ◽  
pp. 1125-1143 ◽  
Author(s):  
Magdaleen S. Marais ◽  
Yue Ren
Keyword(s):  
Computer Algebra ◽  
Computer Algebra System ◽  
Computational Approach ◽  
Prime Ideals ◽  
Graded Algebra ◽  
Coordinate Ring ◽  
Localization Formula ◽  
Hilbert Polynomials ◽  
Systems Of Parameters ◽  
Appl Math

This paper discusses a computational treatment of the localization [Formula: see text] of an affine coordinate ring [Formula: see text] at a prime ideal [Formula: see text] and its associated graded algebra [Formula: see text] with the means of computer algebra. Building on Mora’s paper [T. Mora, La queste del Saint [Formula: see text]: A computational approach to local algebra, Discrete Appl. Math. 33 (1991) 161–190], we present shorter proofs on two of the central statements and expand on the applications touched by Mora: resolutions of ideals, systems of parameters and Hilbert polynomials, as well as dimension and regularity of [Formula: see text]. All algorithms are implemented in the library graal.lib for the computer algebra system Singular.

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