Starting from our previous papers [AGMO] and [ABC], we prove the existence of a non-empty Euclidean open subset whose elements are polynomial vectors with 4 components, in 3 variables, degrees, respectively, 2,3,3,3 and rank 6, which are not identifiable over $ mathbbC $ but are identifiable over $ mathbbR $. This result has been obtained via computer-aided procedures suitably adapted to investigate the number of Waring decompositions for general polynomial vectors over the fields of complex and real numbers. Furthermore, by means of the Hessian criterion ([COV]), we prove identifiability over $ mathbbC $ for polynomial vectors in many cases of sub-generic rank.
Angelini, E. (2019). Waring decompositions and identifiability via Bertini and Macaulay2 software. JOURNAL OF SYMBOLIC COMPUTATION, 91, 200-212 [10.1016/j.jsc.2018.06.021].
Waring decompositions and identifiability via Bertini and Macaulay2 software
Elena Angelini
2019-01-01
Abstract
Starting from our previous papers [AGMO] and [ABC], we prove the existence of a non-empty Euclidean open subset whose elements are polynomial vectors with 4 components, in 3 variables, degrees, respectively, 2,3,3,3 and rank 6, which are not identifiable over $ mathbbC $ but are identifiable over $ mathbbR $. This result has been obtained via computer-aided procedures suitably adapted to investigate the number of Waring decompositions for general polynomial vectors over the fields of complex and real numbers. Furthermore, by means of the Hessian criterion ([COV]), we prove identifiability over $ mathbbC $ for polynomial vectors in many cases of sub-generic rank.File | Dimensione | Formato | |
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https://hdl.handle.net/11365/1035909