Bibliographic Details
| Title: |
Simultaneous direct sum decompositions of several multivariate polynomials. |
| Authors: |
Fang, Lishan1 (AUTHOR) fanglishan@hqu.edu.cn, Huang, Hua-Lin1 (AUTHOR) hualin.huang@hqu.edu.cn, Liao, Lili1 (AUTHOR) lili.liao@hqu.edu.cn |
| Source: |
Linear Algebra & its Applications. Nov2025, Vol. 724, p320-335. 16p. |
| Subjects: |
Homogeneous polynomials, Orthogonalization, Set theory, Idempotents, Polynomials |
| 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. • Extend Harrison's center theory to a set of multivariate polynomials. • Discover the connection between simultaneous direct sum decompositions and centers. • Provide an algorithm for simultaneously decomposing multivariate polynomials. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
