# Software Installation/Poster Session/Reception

Monday, October 23, 2006 - 4:00pm - 6:00pm

Lind 400

Software developers will offer their software for installation on the laptops of the participants at various booths.

**D-modules for Macaulay2**

Anton Leykin (University of Minnesota, Twin Cities)

The package D-modules for Macaulay 2 implements the

majority of the algorithms in the computational D-module theory.

(http://www.ima.umn.edu/~leykin/Dmodules)**PHCmaple**

Anton Leykin (University of Minnesota, Twin Cities)

This Maple package provides a convenient interface to

the functions of PHCpack, a collection of numerical algorithms for

solving polynomial systems using polynomial homotopy continuation.

(http://www.ima.umn.edu/~leykin/PHCmaple)**The Package CRACK for Solving Large Overdetermined Systems**

Thomas Wolf (Brock University)

The poster gives an overview about recent algorithmic extensions, the interface and visualization aids, the ability to trade speed for safety or memory and other safety enhacing measures.**Some Useful Functions in Risa/Asir**

Nobuki Takayama (Kobe University)

Joint with Masayuki Noro.**KNOPPIX/Math**

Tatsuyoshi Hamada (Fukuoka University)

KNOPPIX/Math is a project to archive free mathematical software and

free mathematical documents and offer them on KNOPPIX.

It provides a desktop for mathematicians that can be

set up easily and quickly.

http://www.knoppix-math.org/

KNOPPIX/Math contains a lot of documents and packages

of mathematical software systems.

Once you run the live system, you can experience a wonderful world of

mathematical software systems without needing to make any installations

yourself.

Our system includes TeX, OpenOffice.org, Firefox, Emacs,

Kile, a KDE based GUI TeX editor, WhizzyTEX

and Active-DVI, a pair of WYSIWYG utilities for TeX documents,

and GNU TeXmacs, an office suite for TeX writing.

The DVD also includes many additional mathematical software systems

or libraries with documents, such as BLAS, Coq, Dynagraph,

GAP, Geomview, ginac, gmp, Gnuplot, Hyplane, jtem, Kali, Kan, KSEG, LAPACK,

Macaulay2, Maxima, NZMATH, Octave, OpenXM, PARI/GP, PHCpack,

polymake, Qhull, R, Risa/Asir, SAGE, Singular, SnapPea,

surf, surfex, Surface Evolver, synaps, Teruaki, XaoS, and Yorick, ...

Computer Algebra System Singular 3-0

Hans Schöenemann (Universität Kaiserslautern)**Symbolic and Numerical Methods for Partial Differential Equations**

Wenyuan Wu (University of Western Ontario)

In this poster both symbolic and numerical methods will be described for

overdetermined systems of Partial Differential Equations.

The symbolic method is the rifsimp package which is available in distributed

Maple. The symbolic-numeric methods are the combination of symbolic differential

elimination (using rifsimp) with numerical homotopy continuation (using phc)

together with Maple programs. Comparison of different methods and examples are

given.

This is joint work with Greg Reid, Jan verschelde and Allan Wittkopf and is a

partner to the talk: Application of Numerical Algebraic Geometry to Partial

Differential Equations given by Greg Reid.**Parallel Implementation of the Polyhedral Homotopy Method**

Jan Verschelde (University of Illinois, Chicago)Yan Zhuang (University of Illinois, Chicago)

Homotopy methods to solve polynomial systems are well suited for parallel computing because the solution paths defined by the homotopy can be tracked independently. For sparse polynomial systems, polyhedral methods give efficient homotopy algorithms. The polyhedral homotopy methods run in three stages: (1)

compute the mixed volume; (2) solve a random coefficient start system; (3) track solution paths to solve the target system. This paper is about how to parallelize the second stage in PHCpack. We use a static workload distribution algorithm and achieve a good speedup on the cyclic n-roots benchmark systems.

Dynamic workload balancing leads to reduced wall times on large polynomial systems which arise in mechanism design.*2000 Mathematics Subject Classification.*Primary 65H10.

Secondary 14Q99, 68W30.*Key words and phrases.*Continuation methods, load balancing,

parallel computation, path following,

polynomial systems, polyhedral homotopies.

This material is based upon work

supported by the National Science Foundation under

Grant No. 0105739 and Grant No. 0134611.**Approximate Groebner Bases - A Backwards Approach**

Robin Scott (University of Western Ontario)

The Grobner basis of a polynomial system is arguably the most fundamental object of exact computational polynomial algebra, as it answers many of the important questions of commutative algebra, such as ideal membership and computation of the Hilbert polynomial. It is traditionally computed using variants of Buchberger's algorithm. Here, we take a backwards approach, and show that a Grobner basis can be computed using the Hilbert polynomial and another important basis from the jet theory of partial differential equations: an involutive basis. This direction, motivated by approximate systems, will allow us to avoid the strict monomial orderings and ordered elimination (reduction) strategies, at the heart of Buchberger-type methods, which are

usually numerically unstable.

For the the computation of exact bases for an ideal near to the one from which we began, we make avid use of structured (numerical) linear algebra. Additionally, we introduce approximate leading terms and an approximate reduced row echelon form. Neither of these require Gaussian elimination, unlike the exact case.**PHClab: A MATLAB/Octave interface to PHCpack**

Yun Guan (University of Illinois, Chicago)Jan Verschelde (University of Illinois, Chicago)

PHCpack is a package for Polynomial Homotopy Continuation,

created to numerically solve systems of polynomial equations.

The executable program phc produced by PHCpack has several

options (the most popular one -b offers a blackbox solver) and

is menu driven. PHClab is a collection of scripts which call phc

from within a MATLAB or Octave session. It provides an interface

to the blackbox solver for finding isolated solutions. PHClab

also interfaces to the numerical irreducible decomposition,

giving access to the tools to represent, factor, and intersect

positive dimensional solution sets.