# Generic Gram-Schmidt orthogonalization by exact division

@inproceedings{Erlingsson1996GenericGO, title={Generic Gram-Schmidt orthogonalization by exact division}, author={{\'U}lfar Erlingsson and Erich L. Kaltofen and David R. Musser}, booktitle={ISSAC '96}, year={1996} }

Given a vector space basis with integral domain coefficients, a variant of the Gram-Schmidt process produces an orthogonal basis using exact divisions, so that all arithmetic is within the integral domain. Zero-division is avoided by the assumption that in the domain a sum of squares of nonzero elements is always nonzero. In this paper we fully develop this method and use it to illustrate and compare a variety of means for implementing generic algorithms. Previous generic programming methods…

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