Computational Commutative Algebra has been applied to the Design of Experiments by defining a design as a 0-dimensional variety in an affine space. Responses over the design are modeled by polynomials, while fractional designs are represented by indicator polynomials. A special choice of the coding of factor levels leads, via the application of discrete Fourier transforms, to a neat presentation of key concept like confounding and regular designs. This framework is extended in the present paper to a generic field with any characteristic and a coherent presentation of the various cases is given, i.e. complex coding and Galois field coding of levels. The computational issue of complex coding is considered. The meaning of the coefficients of an indicator polynomial is discussed for both the complex and Galois fields cases. The methodology is applied to regular fractions in both frameworks.
Regular Fractions and Indicator Polynomials
ROGANTIN, MARIA PIERA
2010-01-01
Abstract
Computational Commutative Algebra has been applied to the Design of Experiments by defining a design as a 0-dimensional variety in an affine space. Responses over the design are modeled by polynomials, while fractional designs are represented by indicator polynomials. A special choice of the coding of factor levels leads, via the application of discrete Fourier transforms, to a neat presentation of key concept like confounding and regular designs. This framework is extended in the present paper to a generic field with any characteristic and a coherent presentation of the various cases is given, i.e. complex coding and Galois field coding of levels. The computational issue of complex coding is considered. The meaning of the coefficients of an indicator polynomial is discussed for both the complex and Galois fields cases. The methodology is applied to regular fractions in both frameworks.
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