Works (102)
Updated: April 15th, 2024 04:33
2024 article
Parametric "non-nested" discriminants for multiplicities of univariate polynomials
Hong, H., & Yang, J. (2024, March 8). SCIENCE CHINA-MATHEMATICS, Vol. 3.
author keywords: parametric polynomial; complex roots; discriminant; multiplicity; resultant
arxiv.org (repository)
UN Sustainable Development Goal Categories
10. Reduced Inequalities
(OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: April 8, 2024
2023 article
Global Identifiability of Differential Models (vol 73, pg 1831, 2020)
Hong, H., Ovchinnikov, A., Pogudin, G., & Yap, C. (2023, September 22). COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, Vol. 9.
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, NC State University Libraries
Added: October 23, 2023
2023 article
Improving Angular Speed Uniformity by Piecewise Radical Reparameterization
ELECTRONIC PROCEEDINGS IN THEORETICAL COMPUTER SCIENCE, Vol. 398, pp. 165–178.
Sources: Web Of Science, NC State University Libraries
Added: April 1, 2024
2021 journal article
A condition for multiplicity structure of univariate polynomials
Journal of Symbolic Computation, 5, 15.
author keywords: Parametric polynomial; Complex roots; Multiplicity structure; Discriminant; Resultant
TL;DR:
This paper gives a novel condition for a univariate polynomial having a given multiplicity structure when the number of distinct roots is given and it is shown that the number and degree of polynomials in the condition are optimal.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
2021 journal article
A condition for multiplicity structure of univariate polynomials
Journal of Symbolic Computation, 104, 523–538.
Source: ORCID
Added: February 15, 2021
2021 journal article
Maximum gap in cyclotomic polynomials
JOURNAL OF NUMBER THEORY, 229, 1–15.
author keywords: Cyclotomic polynomials; Inverse cyclotomic polynomials; Maximum gap
Sources: Web Of Science, NC State University Libraries
Added: August 30, 2021
2020 journal article
Global Identifiability of Differential Models
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 73(9), 1831–1879.
TL;DR:
First, an algebraic criterion for global identifiability is rigorously derived, which yields a deterministic algorithm, which improves the efficiency by randomizing the algorithm while guaranteeing the probability of correctness.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: July 6, 2020
2019 journal article
SIAN: a tool for assessing structural identifiability of parametric ODEs
ACM COMMUNICATIONS IN COMPUTER ALGEBRA, 53(2), 37–40.
TL;DR:
New software SIAN (Structural Identifiability ANalyser) that solves the problem of multiple parameter values that yield the same observed behavior even in the case of continuous noise-free data.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: December 2, 2019
2019 journal article
SIAN: software for structural identifiability analysis of ODE models
BIOINFORMATICS, 35(16), 2873–2874.
Ed(s): J. Wren
MeSH headings : Models, Biological; Software
TL;DR:
A new software SIAN (Structural Identifiability ANalyser) that can tackle problems that could not be tackled by previously developed packages is presented.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: October 28, 2019
2018 journal article
Improving root separation bounds
JOURNAL OF SYMBOLIC COMPUTATION, 84, 25–56.
author keywords: Root separation bounds; Polynomial roots; Polynomial systems
TL;DR:
Two new root separation bounds are presented: one univariate bound, and one multivariate bound that are not harder to compute than the previous bounds.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2018 journal article
Locating and Counting Equilibria of the Kuramoto Model with Rank-One Coupling
SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY, 2(1), 45–71.
author keywords: Kuramoto model; equilibria; univariate solving; homotopy continuation; numerical algebraic geometry
TL;DR:
An algorithm to locate only the real solutions of the Kuramoto model, thereby shortening computation time by several orders of magnitude in certain situations and conjecture an upper bound on the maximum number of equilibria for any number of oscillators which generalizes the known cases and is obtained on a range of explicitly provided natural frequencies.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2018 journal article
Number of common roots and resultant of two tropical univariate polynomials
JOURNAL OF ALGEBRA, 511, 420–439.
author keywords: Tropical semifield; Tropical resultant; Common roots
Sources: Web Of Science, ORCID, NC State University Libraries
Added: October 19, 2018
2018 conference paper
Positive Solutions of Systems of Signed Parametric Polynomial Inequalities
In V. P. Gerdt, W. Koepf, W. M. Seiler, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing - 20th International Workshop, CASC 2018, Lille, France, September 17-21, 2018, Proceedings (Vol. 11077, pp. 238–253).
Ed(s): V. Gerdt, W. Koepf, W. Seiler & E. Vorozhtsov
Source: ORCID
Added: November 6, 2020
2017 journal article
Algorithm for computing mu-bases of univariate polynomials
JOURNAL OF SYMBOLIC COMPUTATION, 80, 844–874.
author keywords: mu-basis; Syzygy module; Polynomial vectors; Rational curves
TL;DR:
A new algorithm for computing a $\mu$-basis of the syzygy module of $n$ polynomials in one variable over an arbitrary field $\mathbb{K}$, based on standard linear algebra and completely self-contained is presented.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2017 journal article
Open weak CAD and its applications
JOURNAL OF SYMBOLIC COMPUTATION, 80, 785–816.
author keywords: Open weak CAD; Open weak delineable; CAD projection; Semi-definiteness; Copositivity
TL;DR:
An algorithm for computing projection polynomials of open weak CADs is proposed to compute the intersection of projection factor sets produced by different projection orders, which significantly improves the efficiency of solving copositive problems.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2017 journal article
Resultants over commutative idempotent semirings I: Algebraic aspect
JOURNAL OF SYMBOLIC COMPUTATION, 79, 285–308.
author keywords: Resultant; Commutative idempotent semiring; Tropical algebra; Sylvester matrix; Permanent
TL;DR:
It is proved that the same property of the resultant (with subtraction replaced with addition) holds over an arbitrary commutative idempotent semiring.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2016 journal article
On using Lazard's projection in CAD construction
JOURNAL OF SYMBOLIC COMPUTATION, 72, 65–81.
author keywords: Cylindrical algebraic decomposition; Projection operation; Theorem of Abhyankar and Jung
TL;DR:
It is shown that Lazard's projection is valid for CAD construction for so-called well-oriented polynomial sets, however his notion of valuation does not make use of it.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2016 journal article
Quality of positive root bounds
JOURNAL OF SYMBOLIC COMPUTATION, 74, 592–602.
author keywords: Polynomial roots; Positive root bounds; Absolute positiveness
TL;DR:
The quality of positive root bounds is studied to find out whether the relative over-estimation of a positive root bound due to Hong is at most linear in the degree, no matter what the coefficient size is.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2016 journal article
Real quantifier elimination for the synthesis of optimal numerical algorithms (Case study: Square root computation)
JOURNAL OF SYMBOLIC COMPUTATION, 75, 110–126.
author keywords: Synthesis; Optimal quadratically convergent algorithm; Square root; Real quantifier elimination
TL;DR:
This work overcame the difficulty of carefully reducing a complicated quantified formula into several simpler ones and automatically eliminating the quantifiers from the resulting ones using the state-of-the-art quantifier elimination software to synthesize semi-automatically an optimal quadratically1 convergent map, which is better than the well known hand-crafted Secant-Newton map.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2015 journal article
An algebraic method for constructing stable and consistent autoregressive filters
JOURNAL OF COMPUTATIONAL PHYSICS, 283, 241–257.
author keywords: Autoregressive filter; Kalman filter; Parameter estimation; Model error
TL;DR:
An algebraic method to construct stable and consistent univariate autoregressive (AR) models of low order for filtering and predicting nonlinear turbulent signals with memory depth finds that the proposed AR models produce significantly more accurate short-term predictive skill and comparable filtering skill relative to the linear regression-based AR models.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
13. Climate Action
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2015 journal article
Explicit formula for optimal ate pairing over cyclotomic family of elliptic curves
FINITE FIELDS AND THEIR APPLICATIONS, 34, 45–74.
author keywords: Pairing-based cryptosystem; Elliptic curve; Cyclotomic polynomial
TL;DR:
This work provides an explicit formula for vectors of polynomials describing optimal pairings over cyclotomic family of elliptic curves by partitioning a certain Cyclotomic polynomial.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2015 journal article
Special algorithm for stability analysis of multistable biological regulatory systems
JOURNAL OF SYMBOLIC COMPUTATION, 70, 112–135.
author keywords: Quantifier elimination; Root classification; Biological regulation system; Stability
TL;DR:
A special algorithm is presented which is much more efficient than the general methods of solving the problem of counting (stable) equilibriums of an important family of algebraic differential equations modeling multistable biological regulatory systems.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2014 chapter
ImUp: A Maple Package for Uniformity-Improved Reparameterization of Plane Curves
In Computer Mathematics (Vol. 10, pp. 437–451).
TL;DR:
It is shown that the quality of plots of plane curves may be effectively improved by means of reparameterization using ImUp, and the capability and performance of the public functions of ImUp are illustrated.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: February 24, 2020
2014 book
Mathematical Software – ICMS 2014: 4th International Congress, Seoul, South Korea, August 5-9, 2014. Proceedings
In H. Hong & C. Yap (Eds.), Lecture Notes in Computer Science (Vol. 8592).
TL;DR:
This talk illustrates the evolution of mathematics towards higher and higher levels of automation of its own problem solving and thinking process by a couple of examples of increasing sophistication starting from calculation with Roman numbers up to the automatic invention of algorithms like the speaker’s algorithm for computing Gröbner bases.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
2014 chapter
Pairing Inversion via Non-degenerate Auxiliary Pairings
In Pairing-Based Cryptography – Pairing 2013 (pp. 77–96).
TL;DR:
This paper provides a simpler approach for PI by generalizing and simplifying Kanayama-Okamoto's approach, and defines an infinite set of curve parameters, which includes those of typical pairing friendly curves, and shows that PI of arbitrarily given generalized ate pairing can be reduced to modified EI in polynomial time.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: February 24, 2020
2014 conference paper
Synthesis of Optimal Numerical Algorithms Using Real Quantifier Elimination (Case Study: Square Root Computation)
In K. Nabeshima, K. Nagasaka, F. Winkler, & Á. Szántó (Eds.), Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation (pp. 162–169).
Ed(s): K. Nabeshima, K. Nagasaka, F. Winkler & Á. Szántó
Event: at New York, NY, USA
TL;DR:
The on-going efforts to apply real quantifier elimination to the synthesis of optimal numerical algorithms were able to synthesize semi-automatically, under mild assumptions, a class of optimal maps, which are significantly better than the well known hand-crafted Secant-Newton map.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
2013 journal article
A framework for improving uniformity of parameterizations of curves
SCIENCE CHINA-INFORMATION SCIENCES, 56(10).
author keywords: parametric curve; framework; quasi-speed; uniform parameterization; uniformity-improved reparameterization; optimal Mobius transformation
TL;DR:
A general framework is developed for studying uniformity behaviors under reparameterization via proper parameter transformation and for computingReparameterizations with improved uniformity of quasispeed by means of optimal single-piece, C0 piecewise, and C1 piecewise Möbius transformations.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2013 chapter
Improving Angular Speed Uniformity by C 1 Piecewise Reparameterization
In Automated Deduction in Geometry (pp. 33–47).
TL;DR:
A C 1 piecewise-rational reparameterization is shown that closely approximates to the arc-angle parameterization of any plane curve by C 1 pieceswise Mobius transformation by making use of the first derivative of the angular speed function.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: February 24, 2020
2013 journal article
Improving angular speed uniformity by reparameterization
Computer Aided Geometric Design, 30(7), 636–652.
TL;DR:
The notion of angular speed uniformity as a quality measure for parameter-izations of plane curves and an algorithm to compute uniform reparameterizations for quadratic and cubic curves are introduced and it is proved that only straight lines have uniform rational parameterizations.
(via Semantic Scholar)
Sources: NC State University Libraries, ORCID, NC State University Libraries
Added: August 6, 2018
2013 journal article
Object-Image Correspondence for Algebraic Curves under Projections
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 9.
author keywords: central and parallel projections; finite and affine cameras; camera decomposition; curves; classifying differential invariants; projective and affine transformations; signatures; machine vision
UN Sustainable Development Goal Categories
14. Life Below Water
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2013 conference paper
Pairing Inversion via Non-degenerate Auxiliary Pairings
In Z. Cao & F. Zhang (Eds.), Pairing-Based Cryptography - Pairing 2013 - 6th International Conference, Beijing, China, November 22-24, 2013, Revised Selected Papers (Vol. 8365, pp. 77–96).
Ed(s): Z. Cao & F. Zhang
Source: ORCID
Added: November 6, 2020
2013 journal article
Reducing Pairing Inversion to Exponentiation Inversion using Non-degenerate Auxiliary Pairing
IACR Cryptol. EPrint Arch., 2013, 313. http://eprint.iacr.org/2013/313
Source: ORCID
Added: November 6, 2020
2013 journal article
Simple and exact formula for minimum loop length in Ate (i) pairing based on Brezing-Weng curves
DESIGNS CODES AND CRYPTOGRAPHY, 67(2), 271–292.
author keywords: Pairing-based cryptosystem; Elliptic curves; Miller algorithm
TL;DR:
It will turn out that the formula depends only on essentially two parameters, providing freedom to choose the other parameters to address the design issues other than minimizing the loop length.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions
(OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2013 journal article
The Secant-Newton Map is Optimal Among Contracting Quadratic Maps for Square Root Computation
Reliab. Comput., 18, 73–81. http://interval.louisiana.edu/reliable-computing-journal/volume-18/reliable-computing-18-pp-073-081.pdf
Source: ORCID
Added: November 6, 2020
2012 chapter
Improving Angular Speed Uniformity by Optimal C 0 Piecewise Reparameterization
In Computer Algebra in Scientific Computing (pp. 349–360).
TL;DR:
The C0 piecewise Mobius transformation is adapted to compute a C0 pieceswise-rational reparameterization of any plane curve that approximates to the arc-angle parameterization of the curve.
(via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: February 24, 2020
2012 conference paper
Improving Angular Speed Uniformity by Optimal C 0 Piecewise Reparameterization
In V. P. Gerdt, W. Koepf, E. W. Mayr, & E. V. Vorozhtsov (Eds.), Computer Algebra in Scientific Computing - 14th International Workshop, CASC 2012, Maribor, Slovenia, September 3-6, 2012. Proceedings (Vol. 7442, pp. 349–360).
Ed(s): V. Gerdt, W. Koepf, E. Mayr & E. Vorozhtsov
Source: ORCID
Added: November 6, 2020
2012 journal article
Maximum gap in (inverse) cyclotomic polynomial
JOURNAL OF NUMBER THEORY, 132(10), 2297–2315.
author keywords: Cyclotomic polynomial; Inverse cyclotomic polynomial; Pairing-based cryptosystem
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2012 conference paper
Real solution formulas of cubic and quartic equations applied to generate dynamic diagrams with inequality constraints
In S. Ossowski & P. Lecca (Eds.), Proceedings of the 27th Annual ACM Symposium on Applied Computing - SAC '12 (pp. 94–101).
Ed(s): S. Ossowski & P. Lecca
TL;DR:
It is shown that for generating dynamic diagrams automatically the performance of this approach can be enhanced, in terms of stability of numeric computation and quality of generated diagrams, when the used solution formulas of cubic and quartic equations are replaced by newly introduced real solution formulas with inequality constraints.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
2012 journal article
Variant quantifier elimination
Journal of Symbolic Computation, 47(7), 883–901.
TL;DR:
The main idea underlying the algorithm is to substitute the repeated projection step of CAD by a single projection without carrying out a parametric existential decision over the reals, and it is found that the algorithm can tackle important and challenging problems, such as numerical stability analysis of the widely-used MacCormack's scheme.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
16. Peace, Justice and Strong Institutions
(OpenAlex)
Sources: NC State University Libraries, ORCID, NC State University Libraries
Added: August 6, 2018
2011 journal article
Solution formulas for cubic equations without or with constraints
JOURNAL OF SYMBOLIC COMPUTATION, 46(8), 904–918.
author keywords: Cubic polynomial; Solution formula; Root convention; Constraint
TL;DR:
A convention is presented (for square/cubic root) which provides correct interpretations of the Lagrange formula for all cubic polynomial equations with real coefficients under equality and inequality constraints.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2011 conference paper
WTHD optimization for single phase multilevel converters with step modulation
IECON 2011 - 37th Annual Conference of the IEEE Industrial Electronics Society.
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy
(OpenAlex)
Source: ORCID
Added: November 6, 2020
2010 conference paper
Connectivity in Semi-algebraic Sets
In T. Ida, V. Negru, T. Jebelean, D. Petcu, S. M. Watt, & D. Zaharie (Eds.), 2010 12th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (pp. 4–7).
Ed(s): T. Ida, V. Negru, T. Jebelean, D. Petcu, S. Watt & D. Zaharie
author keywords: connectivity; road map; semi-algebraic sets; gradient fields; Morse-Smale complex
Source: ORCID
Added: November 6, 2020
2009 journal article
Real-Time Algorithm for Minimizing THD in Multilevel Inverters With Unequal or Varying Voltage Steps Under Staircase Modulation
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, 56(6), 2249–2258.
author keywords: Multilevel inverter; multilevel pulsewidth modulation (PWM); power conversion; staircase modulation
TL;DR:
A real-time algorithm for multilevel inverters with unequal or varying voltage steps under the staircase modulation results in the minimal total harmonic distortion of the output voltage of the inverter, which is proved by rigorous mathematical derivations in this paper.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2009 journal article
Real-Time Calculation of Switching Angles Minimizing THD for Multilevel Inverters With Step Modulation
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, 56(2), 285–293.
author keywords: Multilevel inverter; optimal pulsewidth modulation (PWM); power conversion
TL;DR:
A novel real-time algorithm for calculating switching angles that minimizes total harmonic distortion (THD) for step modulation is proposed and a mathematical proof that the output voltage has the minimum THD is given.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2009 journal article
Sylvester’s double sums: The general case
Journal of Symbolic Computation, 44(9), 1164–1175.
author keywords: Subresultants; Double sums; Vandermonde determinants
TL;DR:
The technique developed to answer the question of what are the other members of the Sylvester family turns out to be general enough to characterize allMembers of the family, providing a uniform method.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries, Crossref
Added: August 6, 2018
2009 conference paper
Variant real quantifier elimination
In J. R. Johnson, H. Park, & E. Kaltofen (Eds.), Proceedings of the 2009 international symposium on Symbolic and algebraic computation - ISSAC '09 (pp. 183–190).
Ed(s): J. Johnson, H. Park & E. Kaltofen
TL;DR:
The main idea underlying the algorithm VQE is to substitute the repeated projection step of CAD by a single projection without carrying out a parametric existential decision over the reals, which can tackle important and challenging problems, such as numerical stability analysis of the widely-used MacCormack's scheme.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
2008 article
Are Buchberger's criteria necessary for the chain condition? (vol 42, pg 717, 2007)
Journal of Symbolic Computation, Vol. 43, pp. 233–233.
Source: NC State University Libraries
Added: August 6, 2018
2008 journal article
Connectivity in semialgebraic sets (abstract only)
ACM Commun. Comput. Algebra, 42(1-2), 86.
TL;DR:
This talk considers the problem of deciding whether two given points in a semialgebraic set are connected, that is, whether the two points lie in the same connected component.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
2008 journal article
Corrigendum to “Are Buchberger’s criteria necessary for the chain condition?” [J. Symbolic Comput. 42 (2007) 717–732]
Journal of Symbolic Computation, 43(3), 233.
Sources: Crossref, NC State University Libraries
Added: August 28, 2020
2007 journal article
An elementary proof of Sylvester's double sums for subresultants
JOURNAL OF SYMBOLIC COMPUTATION, 42(3), 290–297.
author keywords: subresultants; double-sum formula; Vandermonde determinant
TL;DR:
An elementary proof that uses only basic properties of matrix multiplication and Vandermonde determinants to express the polynomial subresultants in terms of the roots of the input polynomials is provided.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2007 journal article
Are Buchberger’s criteria necessary for the chain condition?
Journal of Symbolic Computation, 42(7), 717–732.
author keywords: Grobner bases; S-polynomials; Buchberger criteria
TL;DR:
This paper has found an extension to Buchberger's criteria that is necessary as well as sufficient for skipping S-polynomial reductions, but not necessary when there are exactly three polynomials.
(via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020
2007 journal article
Foreword
Mathematics in Computer Science, 1(1), 3–7.
Source: ORCID
Added: November 6, 2020
2006 book
Automated Deduction in Geometry, 5th International Workshop, ADG 2004, Gainesville, FL, USA, September 16-18, 2004, Revised Papers
In H. Hong & D. Wang (Eds.), Springer Berlin Heidelberg (Vol. 3763).
Source: ORCID
Added: November 6, 2020
2006 article
Bruno Buchberger - A life devoted to symbolic computation
JOURNAL OF SYMBOLIC COMPUTATION, Vol. 41, pp. 255–258.
TL;DR:
This special issue contains polished and refereed versions of many lectures presented at the symposium “LMCS 2002 – Logic, Mathematics and Computer Science: Interactions”, held in honor of Prof. Bruno Buchberger on the occasion of his 60th birthday in October 2002.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2006 chapter
Solving Dynamic Geometric Constraints Involving Inequalities
In Artificial Intelligence and Symbolic Computation (pp. 181–195).
TL;DR:
The method works by decomposing the system of constraints into finitely many explicit solution representations in terms of parameters with radicals using triangular decomposition and real quantifier elimination to solve dynamic geometric constraints involving equalities and inequalities.
(via Semantic Scholar)
Source: Crossref
Added: February 24, 2020
2006 conference paper
Solving Dynamic Geometric Constraints Involving Inequalities
In J. Calmet, T. Ida, & D. Wang (Eds.), Artificial Intelligence and Symbolic Computation (pp. 181–195). Berlin, Heidelberg: Springer Berlin Heidelberg.
Ed(s): J. Calmet, T. Ida & D. Wang
Event: at Berlin, Heidelberg
Source: ORCID
Added: November 6, 2020
2004 journal article
Note on Jacobi's method for approximating dominant roots
JOURNAL OF SYMBOLIC COMPUTATION, 37(4), 449–453.
author keywords: dominant roots; root bounds
TL;DR:
It is shown that Jacobi’s method can still be useful even when the dominant roots are not simple, if the authors use it for approximating the “distinct” dominant roots.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
4. Quality Education
(Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2002 journal article
Sparse resultant of composed polynomials I* mixed-unmixed case
JOURNAL OF SYMBOLIC COMPUTATION, 33(4), 447–465.
TL;DR:
The main contribution of this paper is to provide an answer for the case when g1,…,gn are unmixed and the above expression can be applied to compute sparse resultants of composed polynomials with improved efficience.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2001 journal article
Ore principal subresultant coefficients in solutions
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 11(3), 227–237.
author keywords: ore polynomials; resultants; subresultants; elimination theory
TL;DR:
This expression can be viewed as a generalization of the well known expression for resultants of two commutative polynomials: the product of the pair-wise differences of their roots.
(via Semantic Scholar)
Sources: ORCID, Web Of Science
Added: August 6, 2018
2001 journal article
Ore subresultant coefficients in solutions
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 12(5), 421–428.
author keywords: ore polynomials; resultants; subresultants
TL;DR:
This paper gives expressions for the principal (formal leading) coefficients of subresultants and all the other coefficients in terms of the solutions of Ore polynomials.
(via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018
2000 journal article
Editorial
J. Symb. Comput., 29(1), 3–4.
Source: ORCID
Added: November 6, 2020
1998 journal article
Algorithms for trigonometric curves (simplification, implicitization, parameterization)
JOURNAL OF SYMBOLIC COMPUTATION, 26(3), 279–300.
TL;DR:
Algorithms for (a) simplifying a given parametric representation, (b) computing an implicit representation from a givenparametrically by a truncated Fourier series, and (c) computing a parametric representations from aGiven implicit representation are given.
(via Semantic Scholar)
Sources: ORCID, Web Of Science
Added: August 6, 2018
1998 chapter
An Improvement of the Projection Operator in Cylindrical Algebraic Decomposition
In Texts and Monographs in Symbolic Computation (pp. 166–173).
Source: ORCID
Added: November 6, 2020
1998 journal article
Bounds for Absolute Positiveness of Multivariate Polynomials
J. Symb. Comput., 25(5), 571–585.
TL;DR:
A simple formula for computing bounds for the absolute positiveness of P, a multivariate polynomial with real coefficients, is provided and it is proved that the resulting bounds are guaranteed to be close to the optimal ones.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1998 conference paper
Computation of Variant Resultants
In B. F. Caviness & J. R. Johnson (Eds.), Quantifier Elimination and Cylindrical Algebraic Decomposition (pp. 327–340). Vienna: Springer Vienna.
Ed(s): B. Caviness & J. Johnson
Event: at Vienna
Source: ORCID
Added: November 6, 2020
1998 journal article
Editorial
Mathematics and Computers in Simulation.
Source: ORCID
Added: November 6, 2020
1998 journal article
Groebner Basis Under Composition I
Journal of Symbolic Computation, 25(5), 643–663.
TL;DR:
It is proved that this happens iff the composition is compatible with the term ordering and the nondivisibility of Groebner basis computation.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1998 journal article
Testing Positiveness of Polynomials
Journal of Automated Reasoning, 21(1), 23–38.
author keywords: positiveness of polynomials; termination proofs; term rewrite systems
TL;DR:
This paper exactly determines how partial several partial methods in the field of term rewriting systems are, and proposes simpler and/or more efficient methods with the same power.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
16. Peace, Justice and Strong Institutions
(OpenAlex)
Source: ORCID
Added: November 6, 2020
1997 journal article
Comparison of Several Decision Algorithms for the Existential Theory of the Reals
5.
Source: ORCID
Added: November 6, 2020
1997 journal article
Heuristic Search and Pruning in Polynomial Constraints Satisfaction.
Ann. Math. Artif. Intell., 19(3-4), 319–334.
TL;DR:
How certain AI techniques can be used to speed up an algebraic algorithm for deciding the satisfiability of a system of polynomial equations, dis-equations, and inequalities is reported.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1997 journal article
Implicitization of Nested Circular Curves
Journal of Symbolic Computation, 23(2-3), 177–189.
TL;DR:
This paper gives an efficient method for obtaining an implicit equation of a nested circular curve, a real plane curve traced by a point on a circle that rotates around another circle that again rotatesaround still another circle, and so on.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1997 journal article
Multivariate Resultants Under Composition
4.
Source: ORCID
Added: November 6, 2020
1997 journal article
Special Issue on Application of Quantifier Elimination. Foreword of the Guest Editors
Journal of Symbolic Computation, 24(2), 123.
Source: ORCID
Added: November 6, 2020
1997 journal article
Subresultants Under Composition
Journal of Symbolic Computation, 23(4), 355–365.
TL;DR:
The main contribution of the paper is to show that the subresultants ``almost'' commute with composition, which generalizes the well-known fact that the resultant is invariant under translation.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1997 journal article
Testing Stability by Quantifier Elimination
Journal of Symbolic Computation, 24(2), 161–187.
TL;DR:
This paper shows how to write all common stability problems as quantifier-elimination problems, and develops a set of computer-algebra tools that allows us to find analytic solutions to simple stability problems in a few seconds, and to solve some interesting problems in from a few minutes to a few hours.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1996 journal article
An efficient method for analyzing the topology of plane real algebraic curves
Mathematics and Computers in Simulation, 42(4-6), 571–582.
author keywords: topology; algebraic curve; real roots; isolation; counting
TL;DR:
A practically efficient algorithm for analyzing the topology of plane real algebraic curves is given, which produces a planar graph which is topologically equivalent to the real variety of the polynomial on the Euclidean plane.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1996 conference paper
Groebner basis under composition II
In E. Engeler, B. F. Caviness, & Y. N. Lakshman (Eds.), Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC '96 (pp. 79–85).
Ed(s): E. Engeler, B. Caviness & Y. Lakshman
TL;DR:
It is proved that this happens i the composition is ‘compatible’ with the term ordering and the nondivisibility of Groebner basis computation.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1996 journal article
The exact region of stability for MacCormack scheme
Computing, 56(4), 371–383.
author keywords: stability; MacCormack scheme; advection equation
TL;DR:
It is proved that the stability region of the MacCormack scheme for this equation is exactly given.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1996 journal article
The exact stability region of the MacCormack scheme for the scalar advection equation
Applied Mathematics Letters, 9(4), 99–101.
TL;DR:
This note announces that the stability region of the MacCormack scheme for the scalar advection equation ut = aux + buy is exactly given by a Δt Δx 2 3 + b ΔT Δy 2 3 ≥ 1 where Δt, Δx and Δy are the grid distances.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1995 journal article
Bernstein form is inclusion monotone
Computing, 55(1), 43–53.
author keywords: INTERVAL ANALYSIS; RANGE COMPUTATION; INCLUSION MONOTONICITY; BERNSTEIN COEFFICIENTS
TL;DR:
This paper shows that the bernstein form is inclusion monotone, i.e. the Bernstein Form inklusionsmonoton, which defines an interval extensionF off, which is called Bernstein form.
(via Semantic Scholar)
UN Sustainable Development Goal Categories
10. Reduced Inequalities
(OpenAlex)
Source: ORCID
Added: November 6, 2020
1995 conference paper
Implicitization of Curves Parameterized by Generalized Trigonometric Polynomials
In G. D. Cohen, M. Giusti, & T. Mora (Eds.), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 11th International Symposium, AAECC-11, Paris, France, July 17-22, 1995, Proceedings (Vol. 948, pp. 285–296).
Ed(s): G. Cohen, M. Giusti & T. Mora
Source: ORCID
Added: November 6, 2020
1995 journal article
Preface
Annals of Mathematics and Artificial Intelligence, 13(1-2), I-II.
Source: ORCID
Added: November 6, 2020
1995 journal article
The Design of the SACLIB/PACLIB Kernels
Journal of Symbolic Computation, 19(1-3), 111–132.
TL;DR:
The design of the kernels of two variants of the SAC-2 computer algebra library: Saclib and Paclib are described, supporting lightweight concurrency, non-determinism, and parallel garbage collection.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1994 conference paper
Parallel Computation of Modular Multivariate Polynominal Resultants on a Shared Memory Machine
In B. Buchberger & J. Volkert (Eds.), Parallel Processing: CONPAR 94 - VAPP VI, Third Joint International Conference on Vector and Parallel Processing, Linz, Austria, September 6-8, 1994, Proceedings (Vol. 854, pp. 325–336).
Ed(s): B. Buchberger & J. Volkert
Source: ORCID
Added: November 6, 2020
1994 conference paper
RISC-CLP(CF) Constraint Logic Programming over Complex Functions
In F. Pfenning (Ed.), Logic Programming and Automated Reasoning, 5th International Conference, LPAR'94, Kiev, Ukraine, July 16-22, 1994, Proceedings (Vol. 822, pp. 99–113).
Ed(s): F. Pfenning
Source: ORCID
Added: November 6, 2020
1994 journal article
Safe starting regions by fixed points and tightening
Computing, 53(3-4), 323–335.
author keywords: NONLINEAR EQUATION SYSTEMS; INTERVAL ARITHMETIC; SAFE STARTING REGIONS; TIGHTENING
TL;DR:
A method for finding safe starting regions for a given system of non-linear equations by enclosing the components of the equation system by univariante interval polynomials whose zero sets are found.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1993 conference paper
A New Library for Parallel Algebraic Computation
In R. F. Sincovec, D. E. Keyes, M. R. Leuze, L. R. Petzold, & D. A. Reed (Eds.), Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, PPSC 1993, Norfolk, Virginia, USA, March 22-24, 1993 (pp. 776–783). SIAM.
Ed(s): R. Sincovec, D. Keyes, M. Leuze, L. Petzold & D. Reed
Source: ORCID
Added: November 6, 2020
1993 conference paper
Parallelization of Quantifier Elimination on a Workstation Network
In G. D. Cohen, T. Mora, & O. Moreno (Eds.), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, 10th International Symposium, AAECC-10, San Juan de Puerto Rico, Puerto Rico, May 10-14, 1993, Proceedings (Vol. 673, pp. 170–179).
Ed(s): G. Cohen, T. Mora & O. Moreno
Source: ORCID
Added: November 6, 2020
1993 journal article
Quantifier Elimination for Formulas Constrained by Quadratic Equations via Slope Resultants
The Computer Journal, 36(5), 439–449.
TL;DR:
An algorithm is given for eliminating the quantifier from a formula such that the system has no solution in R r and the output formulas are made of resultants and their variants, which the authors call slope resultants.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1993 conference paper
Quantifier elimination for formulas constrained by quadratic equations
In M. Bronstein (Ed.), Proceedings of the 1993 international symposium on Symbolic and algebraic computation - ISSAC '93 (pp. 264–274).
Ed(s): M. Bronstein
TL;DR:
An algorithm is given for constructing a quantifier free formula (a boolean expression of polynomial equations and inequalities) equivalent to a given formula of the form: (% c R)[azzz + alz + a. = O A F], where F is a quantifiers free formula in Z1, Z~, z, and az, al, ao are polynomials in z 1, Xr with real coefficients such that the system has no solution in Rr.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1993 chapter
RISC-CLP (Real): Logic Programming with Non-Linear Constraints over the Reals
In Constraint Logic Programming: Selected Research (pp. 133–159). Cambridge, MA, USA: MIT Press.
Event: at Cambridge, MA, USA
Source: ORCID
Added: November 6, 2020
1993 journal article
Special Issue Editorial: Computational Quantifier Elimination
Comput. J., 36(5), 399.
Source: ORCID
Added: November 6, 2020
1993 conference paper
The Design of the PACLIB Kernel for Parallel Algebraic Computation
In J. Volkert (Ed.), Parallel Computation, Second International ACPC Conference, Gmunden, Austria, October 4-6, 1993, Proceedings (Vol. 734, pp. 204–218).
Ed(s): J. Volkert
Source: ORCID
Added: November 6, 2020
1993 conference paper
The Design of the SACLIB/PACLIB Kernels
In A. Miola (Ed.), Design and Implementation of Symbolic Computation Systems, International Symposium, DISCO '93, Gmunden, Austria, September 15-17, 1993, Proceedings (Vol. 722, pp. 288–302).
Ed(s): A. Miola
Source: ORCID
Added: November 6, 2020
1992 conference paper
Heuristic Search Strategies for Cylindrical Algebraic Decomposion
In J. Calmet & J. A. Campbell (Eds.), Artificial Intelligence and Symbolic Mathematical Computation, International Conference, AISMC-1, Karlsruhe, Germany, August 3-6, 1992, Proceedings (Vol. 737, pp. 152–165).
Ed(s): J. Calmet & J. Campbell
Source: ORCID
Added: November 6, 2020
1992 conference paper
Non-linear Real Constraints in Constraint Logic Programming
In H. Kirchner & G. Levi (Eds.), Algebraic and Logic Programming, Third International Conference, Volterra, Italy, September 2-4, 1992, Proceedings (Vol. 632, pp. 201–212).
Ed(s): H. Kirchner & G. Levi
TL;DR:
This work reports the initial effort in tackling the problem with two methods developed in computer algebra during last three decades: Partial Cylindrical Algebraic Decomposition and Grobner basis to provide a full support of non-linear constraints over real numbers.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1992 journal article
Programming in PACLIB
SIGSAM Bull., 26(4), 1–6.
TL;DR:
This paper gives a short overview on PACLIB, a new system for parallel algebraic computation on shared memory computers that provides concurrency, shared memory communication, non-determinism, speculative parallelism, streams and pipelining and a parallelized garbage collection.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1992 conference paper
Simple Solution Formula Construction in Cylindrical Algebraic Decomposition Based Quantifier Elimination
In P. S. Wang (Ed.), Proceedings of the 1992 International Symposium on Symbolic and Algebraic Computation, ISSAC '92, Berkeley, CA, USA, July 27-29, 1992 (pp. 177–188).
Ed(s): P. Wang
TL;DR:
Since Tarski (1951) gave the first quantifier elimination algorithm for real closed fields, various improvements and new methods have been devised and analyzed.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1991 journal article
Partial Cylindrical Algebraic Decomposition for quantifier elimination
Journal of Symbolic Computation, 12(3), 299–328.
TL;DR:
This paper presents a method which intermingles CAD construction with truth evaluation so that parts of the CAD are constructed only as needed to further truth evaluation and aborts CAD construction as soon as no more truth evaluation is needed.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
1990 conference paper
An improvement of the projection operator in cylindrical algebraic decomposition
Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '90.
TL;DR:
By generalizing a lemma on which the proof of the original projection operation is based, this paper is able to find another projection operation which produces a smaller number of polynomials.
(via Semantic Scholar)
Source: ORCID
Added: November 6, 2020
Citation Index includes data from a number of different sources. If you have questions about the sources of data in the Citation Index or need a set of data which is free to re-distribute, please contact us.
Certain data included herein are derived from the Web of Science© and InCites© (2024) of Clarivate Analytics. All rights reserved. You may not copy or re-distribute this material in whole or in part without the prior written consent of Clarivate Analytics.