# Software for Polynomials

• SLV: Sturm-based solver on Maple. Real solving of univariate equations and bivariate systems, operations on real algebraic numbers, based on our paper at ACM ISSAC 2007.
• Sparse resultants by the Incremental Algorithm. Ansi-C library and stand-alone implementation of the incremental algorithm for building sparse resultant matrices of Sylvester-type and for using them in computing all common roots of a well-constrained 0-dimensional polynomial system. Optimal Sylvester-type matrices are constructed for all systems where this is provably possible. See a tech. report on the code, and the JSC article.

Maple functions for connecting Maple to the program, including conversion of Maple input to the appropriate format: file "mapl2form" and file "maplib".

Recent C++ code by Dr Clement Laroche here.
• Sparse Resultants by Mixed Subdivisions
Maple overall implementation (spares9,2004) of the greedy method (a Canny-Pedersen variant of the original algorithm) to construct a sparse resultant matrix, including the computation of supports and Newton polytopes; see our article (J.ACM'00). There is the option to apply the D'Andrea-Emiris perturbation for handling degenerate coefficients (paper). These are all stand-alone functions. The matrix construction is included in the general Maple resultant library (1998): multires.

Here are the relevant Maple functions. Maple functions for format conversion: mapl2form. The user gains further / full control with functions in "mapl2mapl". Additional Maple routines for polynomials and matrices: maplib.
• Sparse Resultants for Multihomogeneous Systems
"scaled-mhomo.mpl" contains Maple routines for testing the existence, computing the dimension, and constructing sparse resultant matrices of Sylvester, Bezout, or hybrid type, either determinantal or not, for systems whose Newton polytopes are scale copies of a single polytope. Here is the paper with A. Mantzaflaris and an example worksheet; based on the paper with A. Dickenstein.
• MARS is a Maple/Matlab/C package for resultant matrices and eigen-solving. Jointly with A. Wallack and D. Manocha.
• Mixed Volume, Mixed Subdivisions, Convex Hulls, and more: see software in Discrete and Computational Geometry.