Software for Polynomials
SLV: Sturm-based solver on Maple.
Real solving of univariate equations and bivariate systems, operations on real algebraic numbers.
Jointly with D. Diochnos and E. Tsigaridas, based on ISSAC-07
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.
on the code, and JSC article
Maple functions for connecting Maple to the program, including conversion of
Maple input to the appropriate format: file
mapl2form and file
Sparse Resultants by Mixed Subdivisions
Maple overall implementation
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 J.ACM'00 publication
There is the option to apply the d'Andrea-Emiris perturbation
for handling degenerate coefficients; see
These are all stand-alone functions.
The matrix construction is included in the general Maple resultant library:
update concerning sparse resultants).
Maple implementation of the original Canny-Emiris algorithm to construct
a sparse resultant matrix, as well as the denominator which is conjectured to
lead to an exact expression for the resultant;
see J.ACM'00 publication
Stand-alone MapleV code for constructing hybrid matrices of almost-Sylvester
type (one row expressing the toric Jacobian) for 3 bivariate polynomials whose Newton polygons are scaled copies of a single polygon.
Need 2 files:
Joint work with C. D'Andrea
Code (2) requires Maple functions for converting to the appropriate
Format conversion is internal to the greedy code (1) but the user gains full
control with the functions in
Additional Maple routines for polynomials and matrices:
Sparse Resultants for Multihomogeneous Systems
"scaled-mhomo.mpl" contains Maple routines for testing the existence, computing the dimension,
and constructing sparse (or toric) 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 an example worksheet and the paper with A. Mantzaflaris.
contains Maple V routines for unmixed systems; here is the paper with A. Dickenstein.
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.
Ioannis Z. Emiris, 2016
(this page is hardly maintained anymore)