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A general method of quadrature for uncertainty quantification (UQ) is introduced based on the algebraic method in experimental design. This is a method based on the theory of zero dimensional algebraic varieties. It allows quadrature of polynomials or polynomial approximands for quite general sets of quadrature points, here called 'designs'. The method goes some way to explaining when quadrature weights are non-negative and gives exact quadrature for monomials in the quotient ring defined bydoi:10.1137/140978612 fatcat:ctsfeqpbtndolghxsmsamoirfq