Year: 2025
Type: preprint
Abstract: We consider the problem of simultaneous direct sum decomposition of a set of multivariate polynomials. To this end, we extend Harrison's center theory for a single homogeneous polynomial to this broader setting. It is shown that the center of a set of polynomials is a special Jordan algebra, and simultaneous direct sum decompositions of the given polynomials are in bijection with complete sets of orthogonal idempotents of their center algebra. Several examples are provided to illustrate the performance of this method.
Source: arXiv (Cornell University)
Authors: Fang, Lishan, Huang, Hua-Lin, Liao, Lili
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G2387255867, G5592559879
OpenAlex ID: W6979381292
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