Software for Polynomials

SLV: Sturmbased 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 ISSAC07
paper.

Sparse resultants by the Incremental Algorithm.
AnsiC library and standalone implementation of the incremental algorithm
for building sparse resultant matrices of Sylvestertype
and for using them in computing all
common roots of a wellconstrained 0dimensional polynomial system.
Optimal Sylvestertype matrices are
constructed for all systems where this is provably possible.
See
README file,
tech.report
on the code, and JSC article
(postscript).
Maple functions for connecting Maple to the program, including conversion of
Maple input to the appropriate format: file
mapl2form and file
maplib.

Sparse Resultants by Mixed Subdivisions
(1)
Maple overall implementation
(mapleV,2002
and
maple9,2004)
of the greedy method
(a CannyPedersen variant of the original algorithm) to construct
a sparse resultant matrix,
including the computation of supports and Newton polytopes;
see J.ACM'00 publication
(dvi,
postscript).
There is the option to apply the d'AndreaEmiris perturbation
for handling degenerate coefficients; see
manuscript.ps.
These are all standalone functions.
The matrix construction is included in the general Maple resultant library:
multires (an
update concerning sparse resultants).
(2)
Maple implementation of the original CannyEmiris 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
(postscript).
(3)
Standalone MapleV code for constructing hybrid matrices of almostSylvester
type (one row expressing the toric Jacobian) for 3 bivariate polynomials whose Newton polygons are scaled copies of a single polygon.
Need 2 files:
bivar.mpl and
hybridJac.mpl.
Joint work with C. D'Andrea
(ISSAC'01).
Code (2) requires Maple functions for converting to the appropriate
format:
mapl2form.
Format conversion is internal to the greedy code (1) but the user gains full
control with the functions in
mapl2mapl.
Additional Maple routines for polynomials and matrices:
maplib.

Sparse Resultants for Multihomogeneous Systems
"scaledmhomo.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.
"mhomo.mpl"
contains Maple V routines for unmixed systems; here is the paper with A. Dickenstein.

MARS
is a Maple/Matlab/C package for resultant matrices and eigensolving.
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)