Updated: April 15th, 2024 04:33

2024 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

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

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

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.

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.

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

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).

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).

Ed(s): ^{ n} & C. Yap ^{*}

Source: ORCID

Added: November 6, 2020

2014 chapter

Pairing Inversion via Non-degenerate Auxiliary Pairings

In *Pairing-Based Cryptography – Pairing 2013* (pp. 77–96).

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

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).

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.

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*.

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

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).

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

Source: ORCID

Added: November 6, 2020

2012 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

2012 journal article

Variant quantifier elimination

*Journal of Symbolic Computation*, *47*(7), 883–901.

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

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.

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.

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).

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

2005 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

Source: ORCID

Added: November 6, 2020

2005 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

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.

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.

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.

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.

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.

Source: ORCID

Added: November 6, 2020

1997 journal article

Implicitization of Nested Circular Curves

*Journal of Symbolic Computation*, *23*(2-3), 177–189.

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.

Source: ORCID

Added: November 6, 2020

1997 journal article

Testing Stability by Quantifier Elimination

*Journal of Symbolic Computation*, *24*(2), 161–187.

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

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.

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.

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.

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

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

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 journal article

Programming in PACLIB

*SIGSAM Bull.*, *26*(4), 1–6.

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

Source: ORCID

Added: November 6, 2020

1991 journal article

Partial Cylindrical Algebraic Decomposition for quantifier elimination

*Journal of Symbolic Computation*, *12*(3), 299–328.

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*.

Source: ORCID

Added: November 6, 2020

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

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