Finding all isolated solutions to polynomial systems using HOMPACK. - Alexander P. Morgan; Andrew J. Sommese; Layne T. Watson (ACM Trans. Math. Softw., 1989)

Ideals, Varieties, and Algorithms-An Introduction to Computational Algebraic Geometry and Commutative Algebra (D. Cox, J. Little, and D. O'Shea). - Andrew J. Sommese (SIAM Rev., 1993)

Numerical Homotopies to Compute Generic Points on Positive Dimensional Algebraic Sets. - Andrew J. Sommese; Jan Verschelde (J. Complex., 2000)

Algorithm 801: POLSYS_PLP: a partitioned linear product homotopy code for solving polynomial systems of equations. - Steven M. Wise; Andrew J. Sommese; Layne T. Watson (ACM Trans. Math. Softw., 2000)

Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components. - Andrew J. Sommese; Jan Verschelde; Charles W. Wampler (SIAM J. Numer. Anal., 2001)

Piecewise Linear Approximation of Smooth Compact Fibers. - Eugene L. Allgower; Andrew J. Sommese (J. Complex., 2002)

Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems. - Andrew J. Sommese; Jan Verschelde; Charles W. Wampler (SIAM J. Numer. Anal., 2002)

Numerical Irreducible Decomposition Using PHCpack. - Andrew J. Sommese; Jan Verschelde; Charles W. Wampler (Algebra, Geometry, and Software Systems, 2003)

Homotopies for Intersecting Solution Components of Polynomial Systems. - Andrew J. Sommese; Jan Verschelde; Charles W. Wampler (SIAM J. Numer. Anal., 2004)

Numerical factorization of multivariate complex polynomials. - Andrew J. Sommese; Jan Verschelde; Charles W. Wampler (Theor. Comput. Sci., 2004)

The numerical solution of systems of polynomials - arising in engineering and science. - Andrew J. Sommese; Charles W. Wampler II (World Scientific, 2005)

An intrinsic homotopy for intersecting algebraic varieties. - Andrew J. Sommese; Jan Verschelde; Charles W. Wampler (J. Complex., 2005)

Solution of Polynomial Systems Derived from Differential Equations. - Eugene L. Allgower; Derrick J. Bates; Andrew J. Sommese; Charles W. Wampler (Computing, 2006)

A numerical-symbolic algorithm for computing the multiplicity of a component of an algebraic set. - Daniel J. Bates; Chris Peterson 001; Andrew J. Sommese (J. Complex., 2006)

Exceptional Sets and Fiber Products. - Andrew J. Sommese; Charles W. Wampler (Found. Comput. Math., 2008)

Adaptive Multiprecision Path Tracking. - Daniel J. Bates; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (SIAM J. Numer. Anal., 2008)

A Numerical Local Dimension Test for Points on the Solution Set of a System of Polynomial Equations. - Daniel J. Bates; Jonathan D. Hauenstein; Chris Peterson 001; Andrew J. Sommese (SIAM J. Numer. Anal., 2009)

Witness sets of projections. - Jonathan D. Hauenstein; Andrew J. Sommese (Appl. Math. Comput., 2010)

Algebraic C*-actions and the inverse kinematics of a general 6R manipulator. - Sandra Di Rocco; David Eklund; Andrew J. Sommese; Charles W. Wampler (Appl. Math. Comput., 2010)

Numerical algebraic geometry and algebraic kinematics. - Charles W. Wampler; Andrew J. Sommese (Acta Numer., 2011)

A three-dimensional steady-state tumor system. - Wenrui Hao; Jonathan D. Hauenstein; Bei Hu; Andrew J. Sommese (Appl. Math. Comput., 2011)

Regenerative cascade homotopies for solving polynomial systems. - Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (Appl. Math. Comput., 2011)

Chern numbers of smooth varieties via homotopy continuation and intersection theory. - Sandra Di Rocco; David Eklund; Chris Peterson 001; Andrew J. Sommese (J. Symb. Comput., 2011)

Regeneration homotopies for solving systems of polynomials. - Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (Math. Comput., 2011)

Efficient path tracking methods. - Daniel J. Bates; Jonathan D. Hauenstein; Andrew J. Sommese (Numer. Algorithms, 2011)

Continuation Along Bifurcation Branches for a Tumor Model with a Necrotic Core. - Wenrui Hao; Jonathan D. Hauenstein; Bei Hu; Yuan Liu 018; Andrew J. Sommese; Yong-Tao Zhang (J. Sci. Comput., 2012)

Numerically Solving Polynomial Systems with Bertini. - Daniel J. Bates; Andrew J. Sommese; Jonathan D. Hauenstein; Charles W. Wampler (SIAM, 2013)

Membership tests for images of algebraic sets by linear projections. - Jonathan D. Hauenstein; Andrew J. Sommese (Appl. Math. Comput., 2013)

Recovering Exact Results from Inexact Numerical Data in Algebraic Geometry. - Daniel J. Bates; Jonathan D. Hauenstein; Timothy M. McCoy; Chris Peterson 001; Andrew J. Sommese (Exp. Math., 2013)

Computing steady-state solutions for a free boundary problem modeling tumor growth by Stokes equation. - Wenrui Hao; Jonathan D. Hauenstein; Bei Hu; Timothy M. McCoy; Andrew J. Sommese (J. Comput. Appl. Math., 2013)

A homotopy method based on WENO schemes for solving steady state problems of hyperbolic conservation laws. - Wenrui Hao; Jonathan D. Hauenstein; Chi-Wang Shu; Andrew J. Sommese; Zhiliang Xu; Yong-Tao Zhang (J. Comput. Phys., 2013)

Cell Cycle Control and Bifurcation for a Free Boundary Problem Modeling Tissue Growth. - Wenrui Hao; Bei Hu; Andrew J. Sommese (J. Sci. Comput., 2013)

Cell decomposition of almost smooth real algebraic surfaces. - GianMario Besana; Sandra Di Rocco; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (Numer. Algorithms, 2013)

Algorithm 931: An algorithm and software for computing multiplicity structures at zeros of nonlinear systems. - Wenrui Hao; Andrew J. Sommese; Zhonggang Zeng (ACM Trans. Math. Softw., 2013)

On Computing a Cell Decomposition of a Real Surface Containing Infinitely Many Singularities. - Daniel J. Bates; Daniel A. Brake; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (ICMS, 2014)

Bertini_real: Software for One- and Two-Dimensional Real Algebraic Sets. - Daniel A. Brake; Daniel J. Bates; Wenrui Hao; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (ICMS, 2014)

Comparison of probabilistic algorithms for analyzing the components of an affine algebraic variety. - Daniel J. Bates; Wolfram Decker; Jonathan D. Hauenstein; Chris Peterson 001; Gerhard Pfister; Frank-Olaf Schreyer; Andrew J. Sommese; Charles W. Wampler (Appl. Math. Comput., 2014)

A bootstrapping approach for computing multiple solutions of differential equations. - Wenrui Hao; Jonathan D. Hauenstein; Bei Hu; Andrew J. Sommese (J. Comput. Appl. Math., 2014)

Numerical Local Irreducible Decomposition. - Daniel A. Brake; Jonathan D. Hauenstein; Andrew J. Sommese (MACIS, 2015)

Homotopies for Connected Components of Algebraic Sets with Application to Computing Critical Sets. - Daniel J. Bates; Daniel A. Brake; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (MACIS, 2017)

Perturbation results on the zero-locus of a polynomial. - Maria-Laura Torrente; Mauro Carlo Beltrametti; Andrew J. Sommese (J. Symb. Comput., 2017)

Algorithm 976: Bertini_real: Numerical Decomposition of Real Algebraic Curves and Surfaces. - Daniel A. Brake; Daniel J. Bates; Wenrui Hao; Jonathan D. Hauenstein; Andrew J. Sommese; Charles W. Wampler (ACM Trans. Math. Softw., 2017)

Polynomial Systems Arising From Discretizing Systems of Nonlinear Differential Equations. - Andrew J. Sommese (ISSAC, 2018)

Singular Value Decomposition of Complexes. - Danielle A. Brake; Jonathan D. Hauenstein; Frank-Olaf Schreyer; Andrew J. Sommese; Michael Eugene Stillman (SIAM J. Appl. Algebra Geom., 2019)

Branch points of homotopies: Distribution and probability of failure. - Jonathan D. Hauenstein; Caroline Hills; Andrew J. Sommese; Charles W. Wampler (Appl. Math. Comput., 2025)