2019/03/29 by Dimiter Prodanov, Prodanov, Dimiter
Mathematics · #11E88 #15A66 #Advanced Algebra and Geometry #Algebraic and Geometric Analysis #F.2.2 #FOS: Mathematics #I.1.2 #Mathematical Analysis and Transform Methods #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1904.00084
openalex publication_date 2019/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Modern advances in general-purpose computer algebra systems offer solutions\nto a variety of problems, which in the past required substantial time\ninvestments by trained mathematicians. An excellent example of such development\nare the Clifford algebras. The main objective of the paper is to demonstrate an\nutterly algorithmic construction of a Clifford algebra matrix algebra\nrepresentation of a non-degenerate signature (p, q). While this is not the most\neconomical way of implementation, it offers a transparent mechanism of\ntranslation between a Clifford algebra and its faithful real-valued matrix\nrepresentation and can be used for automated proof checking. This\nrepresentation is used to derive an algorithm for the computation of an\narbitrary multivector inverse as a proof certificate. The proposed algorithm is\na mapping of the Faddeev--LeVerrier--Souriau algorithm for computation of the\ncharacteristic polynomial of matrices.\n