## RISC-Linz Basic Research Projects |

This page describes basic research projects funded by various national and international organizations.

**Effective Projects in Algebraic Geometry (2001-2002)**- A joint project with the University of Sevilla.
**The Theorema Project (1996-)**- The Theorema project aims at combining general predicate logic proof methods and special proof methods for special areas of mathematics in one coherent system.
**Computation of Adjoints for Surfaces (1998-1999)**- The goal of this project is to devise an efficient algorithm for computing the adjoints of a surface in 3-space, an important geometrical problem with many applications.
**SFB Numerical and Symbolic Scientific Computing (1998-)**- The SFB ("Sonderforschungsbereich", special research area) Numerical and Symbolic Scientific Computing of the Johannes Kepler University in Linz will start operation in 1998.
**Distributed Constraint Solving for Functional Logic Programming (1997-1999)**- The goal of this project is to develop a distributed software system consisting of a functional logic language interpreter and a number of constraint solving engines.
**HySaX -- Hybrid Software for Algebraic Geometry in X-windows Environment (1996-1998)**- This project aims at the implementation of hybrid symbolic-numerical algorithms for approximation and representation of algebraic sets in two and three dimensions.
**HPGP -- High-Performance Generic Programming (1996-1998)**- This project aims at the development of a programming environment for the construction of generic software based on the concept of higher-order functors.

**COOPERATE Meeting Minutes Generator (1998)**- In the frame of the COOPERATE initiative, we are developing a component of a software system for the support of distributed meetings.
**CGAL -- Computational Geometry Algorithms Library (1996-1998)**- The goal of the project is to design and implement a robust, easy to use, and efficient C++ software library of geometric algorithms. The library is developed in close collaboration with 10 companies in Europe.
**SAC Network -- A Network for Symbolic and Algebraic Computation (1995-1998)**- The purpose of the SAC Network project is to create a platform on which the various activities of Symbolic and Algebraic Computation can be successfully integrated; information related to SAC is disseminated through a network of WWW-based information servers.
**VRÖIG -- Virtual Reality for the Austrian Information Society (1997-1998)**- This is a preparatory project to develop and to establish a center of expertise for methods and applications in Distributed Multiuser Virtual Environments.
**ACCLAIM -- Constraint Logic Programming (1992-1996)**- This project aims to elaborate a general, coherent and applicabe theoretical framework of constraint logic programming, directly usable by systems designers, and to utilize the results of computer algebra in dealing with non-linear constraints.
**Parallel Symbolic Computation on Shared Memory Machine (1992-1996)**- The overall goal of this project is the development of algorithms and languages for parallel symbolic computation.
**MEDLAR-II (1992-1995)**- The goals of this project are: synthesis of specific reasoning capabilities in a given combination of logics; development of the general framework to produce the specific reasoning capabilities; exploration of the architecture for specialisation, implementation and integration of these higher-level reasoning capabilities in a generic practical reasoning agent.
**PARAGRAPH -- Parallel Computer Graphics and Geometry (1993-1995)**- This project resulted in the development of parallel algorithms for computer graphics including geometric modeling, computational geometry and applications to robot programming.
**Hybrid Evolutionary Programming Techniques (1993-1995)**- The main goal is to develop "hybrid evolutionary programming techniques" for selected application areas of real world computing.
**POSSO -- Polynomial System Solving (1992-1995)**- A software package CARDANO is to be developed for solving systems of algebraic equations by the currently best known methods.
**Quantifier Elimination (1992-1994)**- Ideas for the continued practical improvement of the method of cylindrical algebraic decomposition for quantifier elimination will be pursued and the improvements will be continually incorporated into Hong's recent implementation of the method, evaluated and tested on numerous application areas.
**Collision Detection (1992-1994)**- In the frame of the project different methods for collision detection between various kinds of objects are investigated.
**Symbolic Geometric Computation (1992-1993)**- The goal of SGC is to increase the computational power of CASA.
**Robot Vision (1991-1993)**- The main goal is to incorporate geometric modeling techniques into vision systems for technical objects.
**Algebraic and Computational Combinatorics (1989-1992)**-
Symbolic methods for the treatment of formulae (binomial identies,
formal power series,
**q**-hypergeometric functions, closed form solutions of difference equations, etc.) in the area of combinatorics are studied. **MEDLAR -- Mechanizing Deduction in the Logics of Practical Reasoning (1989-1992)**- The main goal of this project is to study and improve various approaches to automated theorem proving.
**Methodologies of Design and Implementation of Symbolic Computation Systems (1990-1991)**- The main goal of this project is to pursue research on the methodologies of design and implementation of computation and deduction methods for manipulating mathematical objects.
**Solution of Algebraic Equations by Puiseux Series (1989-1991)**- The method of Puiseux series is generalized to algebraic equations in more than two variables. Applications to symbolic integration and the solution of linear differential equations is studied
**Algorithmic Algebraic Geometry (1988-1991)**- This research project continues the traditional research emphasis of RISC-Linz during the past ten years, in particular, research on the method of Gr" obner bases developed at RISC-Linz.
**Computer-Aided Molecular Synthesis (1986-1991)**- The goal of the project is to investigate algorithms for the problem of synthesizing chemical molecules from information on initial molecules and chemical reactions. The algorithms are embedded into a new software system for molecular synthesis.
**Functional and Logic Programming (1989-1990)**- A common framework for functional and logic programming is developed both on the level of formal semantics and on the level of implementation.

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Last Modification: September 12, 2001

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