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Ideal Interpolation, H-Bases and Symmetry

Erick Rodriguez Bazan 1 Evelyne Hubert 1 
1 AROMATH - AlgebRe, geOmetrie, Modelisation et AlgoriTHmes
CRISAM - Inria Sophia Antipolis - Méditerranée , NKUA - National and Kapodistrian University of Athens
Abstract : Multivariate Lagrange and Hermite interpolation are examples of ideal interpolation. More generally an ideal interpolation problem is defined by a set of linear forms, on the polynomial ring, whose kernels intersect into an ideal. For an ideal interpolation problem with symmetry, we address the simultaneous computation of a symmetry adapted basis of the least interpolation space and the symmetry adapted H-basis of the ideal. Beside its manifest presence in the output, symmetry is exploited computationally at all stages of the algorithm.
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Submitted on : Tuesday, July 7, 2020 - 11:38:48 AM
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Erick Rodriguez Bazan, Evelyne Hubert. Ideal Interpolation, H-Bases and Symmetry. ISSAC 2020 - International Symposium on Symbolic and Algebraic Computation, Jul 2020, Kalamata, Greece. ⟨10.1145/3373207.3404057⟩. ⟨hal-02482098v2⟩



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