Efficient incremental algorithms for the sparse resultant and the mixed volume
Journal of Symbolic Computation
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
The projective noether maple package: computing the dimension of a projective variety
Journal of Symbolic Computation
Algorithm 846: MixedVol: a software package for mixed-volume computation
ACM Transactions on Mathematical Software (TOMS)
ACM Transactions on Mathematical Software (TOMS)
Solving Polynominal Systems Using Continuation for Engineering and Scientific Problems
Solving Polynominal Systems Using Continuation for Engineering and Scientific Problems
Interfacing with the numerical homotopy algorithms in PHCpack
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Sampling algebraic sets in local intrinsic coordinates
Computers & Mathematics with Applications
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
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PHCpack is a software package to solve polynomial systems via homotopy continuation methods. In the last twenty years (since the start of the development of PHCpack), the notion of solving a polynomial system by PHCpack evolved from approximating all isolated complex solutions for systems with as many equations as variables into providing tools for a numerical irreducible decomposition. This document provides the outline for a software demonstration highlighting recent additions to the software, such as accepting polynomials with negative exponents and sweeping for real points that lie isolated on complex solution curves.