**Up:** *Directory of Computational Geometry Software*

## Numerical and algebraic computation

### Robust floating-point predicates

C subroutines to compute orientation and in-circle tests
on floating-point inputs.
Adaptive floating point arithmatic evaluates only to the
precision required to return the correct yes or no answer.
For an explaination of the predicates and the software
itself, see the
Web page. Also contains pointers to the papers explaining
how they work.

Developed by Jonathan Shewchuck for the
Triangle program.

### Real/Expr

Exact arithmetic computation package.
Implementation of C++ classes for real numbers and expressions.
Automatically evaluates comparisons to the precision required to
get it right, or allows the user to specify the level of
precision in expression evaluation.
Handles +,-,*,/,sqrt on regular floats,
BigInts, Rationals and BigFloats,
with some smarts for efficiency.
By Chee Yap, Tom Dube, and Kouji Ouchi.

See their homepage
for more info and links to the code.

### Exact determinant testing

C++ libraries to find the exact sign of 2x2 and
3x3 integer matrix determinants.
By F. Avnaim,J-D. Boissonnat,O. Devillers, F. Preparata, and M. Yvinec,
INRIA.

See the Web page for more information and the code.

The Detri
program includes a long-integer arithmatic package (+,-,*)
and the *Simulation of Simplicity* library.
This is the closest thing I know of to an (implemented) ``black box'' for
removing degeneracies from a point set by
symbolic perturbation.
Both in C.

### Toolkit for Algebra and Geometry

Resultants, sub-resultants and Sturm-Habicht sequences
for multivariate polynomials
over floating-point numbers, integers modulo a prime,
straight-line programs or mixed-arithmetic.
Use to solve systems of polynomial equalities.
Take a look at the
paper for an overview.
There is also documentation and the text of the relevant papers
at the ftp site.

By Ashu Rege
and John Canny, U.C. Berkeley.

Get the toolkit by
ftp
from Berkeley.

### Sparse resultants and mixed volumes

Sparse polynomial system solver based on the Newton resultant, which
finds all common solutions for a system of polynomials.
This is apparently more efficient than Gröbner bases for
polynomials of high degree with few terms.
Also programs to compute the mixed volume and mixed subdivision of
sets of polytopes.
These can be used to count the roots of
polynomials.
Mostly by Ioannis Z. Emiris, now at INRIA, and John F. Canny, UC Berkeley.

Documentation, papers and code
are
here.

**Up:** *Directory of Computational Geometry Software*

*The Geometry Center Home Page*
Comments to: nina@geom.umn.edu

Created: May 31 1995 ---
Last modified: Thu Jun 1 14:24:44 1995