Independent Components of an Indexed Object with Linear Symmetries
| dc.creator | Klioner, Sergei A. | |
| dc.date | 2004-06-04 | |
| dc.date | 2004-06-07 | |
| dc.date.accessioned | 2026-07-07T03:28:45Z | |
| dc.date.available | 2026-07-07T03:28:45Z | |
| dc.description | The problem of finding independent components of an indexed object (e.g., a tensor) with arbitrary number of indices and arbitrary linear symmetries is discussed. It is proved that the number of independent components $f(k)$ is a polynomial of degree not greater than the number of indices $n$, $k$ being the dimension of the space. Several algorithms to compute $f(k)$ for arbitrary $k$ are described and discussed. It is shown that in the worst case finding $f(k)$ for arbitrary $k$ requires solving at most P(n) systems of linear equations with at most $(n!)^2$ equations for at most of $n!$ unknowns, P(n) being the number of partitions of $n$. As a by-product, an efficient algorithm to parametrize all components of the object through its independent components is found and implemented in \Mathematica. | |
| dc.description | 9 pages, Proceedings of the CASC'2004 (Computer Algebra in Scienfic Computing) | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0406019 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0406019 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/34952 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Independent Components of an Indexed Object with Linear Symmetries | |
| dc.type | text |