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2. 06271 Abstracts Collection ��� Challenges in Symbolic Computation Software

Author

Decker, Wolfram, Dewar, Mike, Kaltofen, Erich, and Watt, Stephen M.

Subjects
Symbolic computation, hybrid, systems and user interfaces, symbolic computation languages, combinatorial methods in algebra, symbolic-numerical methods, computer algebra, computational algebraic geometry, algorithm design
Abstract

From 02.07.06 to 07.07.06, the Dagstuhl Seminar 06271 ``Challenges in Symbolic Computation Software'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

Published
2006
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3. 06271 Executive Summary - Challenges in Symbolic Computation Software

Author

Decker, Wolfram, Dewar, Mike, Kaltofen, Erich, and Watt, Stephen M.

Subjects
Symbolic computation, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, hybrid symbolic-numerical methods, Computer Science::Symbolic Computation, combinatorial methods in algebra, computer algebra, algori, computational algebraic geometry
Abstract

Symbolic computation software allows mathematicians, scientists, engineers, or educators to deal with elaborate calculations using a computer. The applications range from introducing the experimental method in fields of pure mathematics to practical applications, for instance, in cryptology, robotics, or signal theory. The software includes mainstream commercial products such as Maple or Mathematica and highly specialized, public domain systems such as CoCoa, Macaulay2, or Singular. Symbolic computation software implements a variety of sophisticated algorithms on polynomials, matrices, combinatorial structures, and other mathematical objects in a multitude of different dense, sparse, or implicit (black box) representations. The subject of the seminar was innovation in algorithms and software, bringing algorithm designers, software builders, and software users together.

Published
2006
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4. Applying Machine Learning to the Problem of Choosing a Heuristic to Select the Variable Ordering for Cylindrical Algebraic Decomposition

Author

Huang, Zongyan, England, Matthew, Wilson, David, Davenport, James H., Paulson, Lawrence C., Bridge, James, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Goebel, Randy, editor, Tanaka, Yuzuru, editor, Wahlster, Wolfgang, editor, Siekmann, Jörg, editor, Watt, Stephen M., editor, Davenport, James H., editor, Sexton, Alan P., editor, Sojka, Petr, editor, and Urban, Josef, editor

Published
2014
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7. Applying Machine Learning to the Problem of Choosing a Heuristic to Select the Variable Ordering for Cylindrical Algebraic Decomposition

Author

James H. Davenport, Matthew England, Zongyan Huang, David Wilson, Lawrence C. Paulson, James P. Bridge, Watt, Stephen M., Davenport, James H., Sexton, Alan P., Sojka, Petr, and Urban, Joesf

Subjects
problem formulation, business.industry, Computer science, Heuristic, 010102 general mathematics, 0102 computer and information sciences, Algebraic geometry, cylindrical algebraic decomposition, Machine learning, computer.software_genre, Symbolic computation, 01 natural sciences, symbolic computation, Cylindrical algebraic decomposition, Support vector machine, machine learning, 010201 computation theory & mathematics, Quantifier elimination, support vector machine, Artificial intelligence, 0101 mathematics, Heuristics, business, computer, Variable (mathematics)
Abstract

Cylindrical algebraic decomposition(CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. When using CAD, there is often a choice for the ordering placed on the variables. This can be important, with some problems infeasible with one variable ordering but easy with another. Machine learning is the process of fitting a computer model to a complex function based on properties learned from measured data. In this paper we use machine learning (specifically a support vector machine) to select between heuristics for choosing a variable ordering, outperforming each of the separate heuristics.

Published
2014

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