Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition

Zongyan Huang, Matthew England, David Wilson, James H. Davenport, Lawrence Paulson, James Bridge

Research output: Chapter in Book/Report/Conference proceedingChapter

  • 15 Citations

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.
LanguageEnglish
Title of host publicationIntelligent Computer Mathematics
EditorsStephen M. Watt, James H. Davenport, Alan P. Sexton, Petr Sojka, Joesf Urban
PublisherSpringer
Pages92-107
Number of pages16
Volume8543
ISBN (Electronic)9783319084343
ISBN (Print)9783319084336
DOIs
StatusPublished - 2014

Publication series

NameLecture Notes in Artificial Intelligence
PublisherSpringer

Fingerprint

Learning systems
Decomposition
Computational geometry
Support vector machines

Keywords

  • machine learning
  • support vector machine
  • symbolic computation
  • cylindrical algebraic decomposition
  • problem formulation

Cite this

Huang, Z., England, M., Wilson, D., Davenport, J. H., Paulson, L., & Bridge, J. (2014). Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition. In S. M. Watt, J. H. Davenport, A. P. Sexton, P. Sojka, & J. Urban (Eds.), Intelligent Computer Mathematics (Vol. 8543, pp. 92-107). (Lecture Notes in Artificial Intelligence). Springer. https://doi.org/10.1007/978-3-319-08434-3_8

Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition. / Huang, Zongyan; England, Matthew; Wilson, David; Davenport, James H.; Paulson, Lawrence; Bridge, James.

Intelligent Computer Mathematics. ed. / Stephen M. Watt; James H. Davenport; Alan P. Sexton; Petr Sojka; Joesf Urban. Vol. 8543 Springer, 2014. p. 92-107 (Lecture Notes in Artificial Intelligence).

Research output: Chapter in Book/Report/Conference proceedingChapter

Huang, Z, England, M, Wilson, D, Davenport, JH, Paulson, L & Bridge, J 2014, Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition. in SM Watt, JH Davenport, AP Sexton, P Sojka & J Urban (eds), Intelligent Computer Mathematics. vol. 8543, Lecture Notes in Artificial Intelligence, Springer, pp. 92-107. https://doi.org/10.1007/978-3-319-08434-3_8
Huang Z, England M, Wilson D, Davenport JH, Paulson L, Bridge J. Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition. In Watt SM, Davenport JH, Sexton AP, Sojka P, Urban J, editors, Intelligent Computer Mathematics. Vol. 8543. Springer. 2014. p. 92-107. (Lecture Notes in Artificial Intelligence). https://doi.org/10.1007/978-3-319-08434-3_8
Huang, Zongyan ; England, Matthew ; Wilson, David ; Davenport, James H. ; Paulson, Lawrence ; Bridge, James. / Applying machine learning to the problem of choosing a heuristic to select the variable ordering for cylindrical algebraic decomposition. Intelligent Computer Mathematics. editor / Stephen M. Watt ; James H. Davenport ; Alan P. Sexton ; Petr Sojka ; Joesf Urban. Vol. 8543 Springer, 2014. pp. 92-107 (Lecture Notes in Artificial Intelligence).
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