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Decomposition of multihomogeneous polynomials: minimal number of variables

Jérémy Berthomieu 1, *
* Corresponding author
1 PolSys - Polynomial Systems
Inria Paris-Rocquencourt, LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : In this paper, we generalize Hironaka's invariants, the ridge and the directrix, of homogeneous ideals, to multihomogeneous ideals. These invariants are the minimal number of additive polynomials or linear forms to write a given ideal. We design algorithms to compute both these invariants which make use of the multihomogeneous structure of the ideal and study their complexities depending on the number of blocks of variables, the number of variables in each block and the degree of the polynomials spanning the considered ideal. We report our implementation in Maple using FGb library.
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Contributor : Jérémy Berthomieu <>
Submitted on : Monday, January 21, 2013 - 12:02:17 PM
Last modification on : Friday, January 8, 2021 - 5:42:02 PM
Long-term archiving on: : Monday, April 22, 2013 - 3:52:50 AM


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  • HAL Id : hal-00778659, version 1


Jérémy Berthomieu. Decomposition of multihomogeneous polynomials: minimal number of variables. 2013. ⟨hal-00778659⟩



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