Abstract
H-bases are bases for polynomial ideals, characterized by the fact that their homogeneous leading terms are a basis for the associated homogeneous ideal. In the computation ofH-bases without term orders, an important task is to determine the orthogonal projection of a homogeneous polynomial to certain subspaces of homogeneous polynomials with respect to a given inner product. One way of doing so is to use an orthogonal basis of the subspace. In this paper, we present and study a method to efficiently compute such a basis for a particular but important inner product.
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Communicated by T. Lyche
Dedicated to Mariano Gasca, a very special friend and collaborator, on the occasion of his sixtieth birthday
Mathematics subject classification (2000)
13P10
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Peña, J.M., Sauer, T. Efficient polynomial reduction. Adv Comput Math 26, 323–336 (2007). https://doi.org/10.1007/s10444-004-7208-0
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DOI: https://doi.org/10.1007/s10444-004-7208-0