Presents a systematic study of the common zeros of polynomials in
several variables which are related to higher dimensional
quadrature. The author uses a new approach which is based on the
recent development of orthogonal polynomials in several variables
and differs significantly from the previous ones based on algebraic
ideal theory. Featuring a great deal of new work, new theorems and,
in many cases, new proofs, this self-contained work will be of
great interest to researchers in numerical analysis, the theory of
orthogonal polynomials and related subjects.
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