Frank Sottile

Orcid: 0000-0003-0087-7120

Affiliations:
  • Texas A&M University, College Station, Texas, USA


According to our database1, Frank Sottile authored at least 57 papers between 1996 and 2023.

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Bibliography

2023
Numerical homotopies from Khovanskii bases.
Math. Comput., April, 2023

Numerical Nonlinear Algebra.
CoRR, 2023

2022
Certification for polynomial systems via square subsystems.
J. Symb. Comput., 2022

Euclidean Distance Degree and Mixed Volume.
Found. Comput. Math., 2022

Irrational Toric Varieties and Secondary Polytopes.
Discret. Comput. Geom., 2022

2021
Solving decomposable sparse systems.
Numer. Algorithms, 2021

Numerical Schubert calculus via the Littlewood-Richardson homotopy algorithm.
Math. Comput., 2021

A numerical toolkit for multiprojective varieties.
Math. Comput., 2021

2020
Bivariate semialgebraic splines.
J. Approx. Theory, 2020

Decomposable sparse polynomial systems.
CoRR, 2020

General witness sets for numerical algebraic geometry.
Proceedings of the ISSAC '20: International Symposium on Symbolic and Algebraic Computation, 2020

2018
Numerical Computation of Galois Groups.
Found. Comput. Math., 2018

2017
Semialgebraic splines.
Comput. Aided Geom. Des., 2017

2016
Software for the Gale transform of fewnomial systems and a Descartes rule for fewnomials.
Numer. Algorithms, 2016

A Primal-Dual Formulation for Certifiable Computations in Schubert Calculus.
Found. Comput. Math., 2016

2015
Degenerations of real irrational toric varieties.
J. Lond. Math. Soc., 2015

The Monotone Secant Conjecture in the Real Schubert Calculus.
Exp. Math., 2015

2014
Newton Polytopes and Witness Sets.
Math. Comput. Sci., 2014

2013
Complex Static Skew-Symmetric Output Feedback Control.
SIAM J. Control. Optim., 2013

Lower Bounds in Real Algebraic Geometry and Orientability of Real Toric Varieties.
Discret. Comput. Geom., 2013

2012
Algorithm 921: alphaCertified: Certifying Solutions to Polynomial Systems.
ACM Trans. Math. Softw., 2012

The Secant Conjecture in the Real Schubert Calculus.
Exp. Math., 2012

2011
Toric degenerations of Bézier patches.
ACM Trans. Graph., 2011

Khovanskii-Rolle Continuation for Real Solutions.
Found. Comput. Math., 2011

Injectivity of 2D Toric Bézier Patches.
Proceedings of the 12th International Conference on Computer-Aided Design and Computer Graphics, 2011

Real Solutions to Equations from Geometry.
University lecture series 57, American Mathematical Society, ISBN: 978-0-8218-5331-3, 2011

2010
Hopf Structures on the Multiplihedra.
SIAM J. Discret. Math., 2010

Linear Precision for Toric Surface Patches.
Found. Comput. Math., 2010

Convex Hulls of Orbits and Orientations of a Moving Protein Domain.
Discret. Comput. Geom., 2010

alphaCertified: certifying solutions to polynomial systems
CoRR, 2010

Linear precision for parametric patches.
Adv. Comput. Math., 2010

Solving schubert problems with Littlewood-Richardson homotopies.
Proceedings of the Symbolic and Algebraic Computation, International Symposium, 2010

2009
Galois groups of Schubert problems via homotopy computation.
Math. Comput., 2009

2008
Some Geometrical Aspects of Control Points for Toric Patches.
Proceedings of the Mathematical Methods for Curves and Surfaces, 2008

2007
Irrational proofs for three theorems of Stanley.
Eur. J. Comb., 2007

Lines Tangent to Four Triangles in Three-Dimensional Space.
Discret. Comput. Geom., 2007

Computing monodromy via parallel homotopy continuation.
Proceedings of the Parallel Symbolic Computation, 2007

2006
Experimentation and Conjectures in the Real Schubert Calculus for Flag Manifolds.
Exp. Math., 2006

2005
The Envelope of Lines Meeting a Fixed Line and Tangent to Two Spheres.
Discret. Comput. Geom., 2005

Transversals to Line Segments in Three-Dimensional Space.
Discret. Comput. Geom., 2005

2004
On the number of line tangents to four triangles in three-dimensional space.
Proceedings of the 16th Canadian Conference on Computational Geometry, 2004

2003
Common Transversals and Tangents to Two Lines and Two Quadrics in P.
Discret. Comput. Geom., 2003

The number of transversals to line segments in R^3
CoRR, 2003

The envelope of lines meeting a fixed line that are tangent to two spheres
CoRR, 2003

Transversals to line segments in R<sup>3</sup>.
Proceedings of the 15th Canadian Conference on Computational Geometry, 2003

2002
Shifted quasi-symmetric functions and the Hopf algebra of peak functions.
Discret. Math., 2002

Guest Editors' Foreword.
Discret. Comput. Geom., 2002

Toric ideals, real toric varieties, and the moment map
CoRR, 2002

Common transversals and tangents to two lines and two quadrics in P<sup>3</sup>
CoRR, 2002

2001
Complementary Algorithms for Tableaux.
J. Comb. Theory A, 2001

Enumerative Real Algebraic Geometry.
Proceedings of the Algorithmic and Quantitative Aspects of Real Algebraic Geometry in Mathematics and Computer Science, 2001

2000
Noncommutative Pieri Operators on Posets.
J. Comb. Theory A, 2000

Real Schubert Calculus: Polynomial Systems and a Conjecture of Shapiro and Shapiro.
Exp. Math., 2000

Preface.
Discret. Math., 2000

1999
A Monoid for the Grassmannian Bruhat Order.
Eur. J. Comb., 1999

1998
Numerical Schubert Calculus.
J. Symb. Comput., 1998

1996
Tableau Switching: Algorithms and Applications.
J. Comb. Theory A, 1996


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