Book contents
- Frontmatter
- Contents
- Preface
- Programme Committee
- Tutorials
- Research Papers
- The Fractal Walk
- Gröbner Bases Property on Elimination Ideal in the Noncommutative Case
- 17 The CoCoA 3 Framework for a Family of Buchberger-like Algorithms
- 18 Newton Identities in the Multivariate Case: Pham Systems
- 19 Gröbner Bases in Rings of Differential Operators
- 20 Canonical Curves and the Petri Scheme
- 21 The Buchberger Algorithm as a Tool for Ideal Theory of Polynomial Rings in Constructive Mathematics
- 22 Gröbner Bases in Non-Commutative Reduction Rings
- 23 Effective Algorithms for Intrinsically Computing SAGBI-Gröbner Bases in a Polynomial Ring over a Field
- 24 De Nugis Groebnerialium 1: Eagon, Northcott, Gröbner
- 25 An application of Gröbner Bases to the Decomposition of Rational Mappings
- 26 On some Basic Applications of Gröbner Bases in Non-commutative Polynomial Rings
- 27 Full Factorial Designs and Distracted Fractions
- 28 Polynomial interpolation of Minimal Degree and Gröbner Bases
- 29 Inversion of Birational Maps with Gröbner Bases
- 30 Reverse Lexicographic Initial Ideals of Generic Ideals are Finitely Generated
- 31 Parallel Computation and Gröbner Bases: An Application for Converting Bases with the Gröbner Walk
- Appendix An Algorithmic Criterion for the Solvability of a System of Algebraic Equations (translated by Michael Abramson and Robert Lumbert)
- Index of Tutorials
27 - Full Factorial Designs and Distracted Fractions
Published online by Cambridge University Press: 05 July 2011
- Frontmatter
- Contents
- Preface
- Programme Committee
- Tutorials
- Research Papers
- The Fractal Walk
- Gröbner Bases Property on Elimination Ideal in the Noncommutative Case
- 17 The CoCoA 3 Framework for a Family of Buchberger-like Algorithms
- 18 Newton Identities in the Multivariate Case: Pham Systems
- 19 Gröbner Bases in Rings of Differential Operators
- 20 Canonical Curves and the Petri Scheme
- 21 The Buchberger Algorithm as a Tool for Ideal Theory of Polynomial Rings in Constructive Mathematics
- 22 Gröbner Bases in Non-Commutative Reduction Rings
- 23 Effective Algorithms for Intrinsically Computing SAGBI-Gröbner Bases in a Polynomial Ring over a Field
- 24 De Nugis Groebnerialium 1: Eagon, Northcott, Gröbner
- 25 An application of Gröbner Bases to the Decomposition of Rational Mappings
- 26 On some Basic Applications of Gröbner Bases in Non-commutative Polynomial Rings
- 27 Full Factorial Designs and Distracted Fractions
- 28 Polynomial interpolation of Minimal Degree and Gröbner Bases
- 29 Inversion of Birational Maps with Gröbner Bases
- 30 Reverse Lexicographic Initial Ideals of Generic Ideals are Finitely Generated
- 31 Parallel Computation and Gröbner Bases: An Application for Converting Bases with the Gröbner Walk
- Appendix An Algorithmic Criterion for the Solvability of a System of Algebraic Equations (translated by Michael Abramson and Robert Lumbert)
- Index of Tutorials
Summary
Abstract
Design of Experiments is an important branch of Statistics. One of its key problems is to find minimal Fractions of a Full Factorial Design, which identify a Complete Polynomial Model. This paper shows how to use Computer Algebra and Commutative Algebra techniques and results to produce good classes of solutions to the problem. It is known that most of them can be obtained by means of Gröbner bases, hence they generally depend on the term-order chosen; here we show how to use the Distracted Fractions to yield solutions independent of the term-order.
Introduction
Design of Experiments (DoE) is a branch of Statistics, which has a long tradition in the use of algebraic methods (see for example Box et al. 1978 and Collombier 1996). In general all these methods were developed in the case of binary experiments, with coding levels either {0,1} or {-1,1} and some generalizations to the non-binary case were also developed (see Collombier 1996).
More recently some connections were discovered between classical problems in Statistics and the methods of Computer Algebra. For instance in their recent work Pistone and Wynn (1996) address the problem of identifying polynomial models in general designs. In particular they point out the connection between DoE and Gröbner bases.
- Type
- Chapter
- Information
- Gröbner Bases and Applications , pp. 473 - 482Publisher: Cambridge University PressPrint publication year: 1998
- 2
- Cited by