Computation of Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford Algebras
Clifford algebras are an active area of mathematical research having numerous applications in mathematical physics and computer graphics, among many others. This paper demonstrates algorithms for the computation of characteristic polynomials, inverses, and minimal polynomials of general multivectors...
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MDPI AG
2025-03-01
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| author | Dimiter Prodanov |
| author_facet | Dimiter Prodanov |
| author_sort | Dimiter Prodanov |
| collection | DOAJ |
| description | Clifford algebras are an active area of mathematical research having numerous applications in mathematical physics and computer graphics, among many others. This paper demonstrates algorithms for the computation of characteristic polynomials, inverses, and minimal polynomials of general multivectors residing in a non-degenerate Clifford algebra of an arbitrary dimension. The characteristic polynomial and inverse computation are achieved by a translation of the classical Faddeev–LeVerrier–Souriau (FVS) algorithm in the language of Clifford algebra. The demonstrated algorithms are implemented in the Clifford package of the open source computer algebra system Maxima. Symbolic and numerical examples residing in different Clifford algebras are presented. |
| format | Article |
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| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-5c4c84a337c040bda7a6019079fcb0fa2025-08-20T02:09:17ZengMDPI AGMathematics2227-73902025-03-01137110610.3390/math13071106Computation of Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford AlgebrasDimiter Prodanov0PAML-LN, Institute for Information and Communication Technologies (IICT), Bulgarian Academy of Sciences, 1113 Sofia, BulgariaClifford algebras are an active area of mathematical research having numerous applications in mathematical physics and computer graphics, among many others. This paper demonstrates algorithms for the computation of characteristic polynomials, inverses, and minimal polynomials of general multivectors residing in a non-degenerate Clifford algebra of an arbitrary dimension. The characteristic polynomial and inverse computation are achieved by a translation of the classical Faddeev–LeVerrier–Souriau (FVS) algorithm in the language of Clifford algebra. The demonstrated algorithms are implemented in the Clifford package of the open source computer algebra system Maxima. Symbolic and numerical examples residing in different Clifford algebras are presented.https://www.mdpi.com/2227-7390/13/7/1106multivectorcharacteristic polynomialClifford algebracomputer algebra |
| spellingShingle | Dimiter Prodanov Computation of Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford Algebras Mathematics multivector characteristic polynomial Clifford algebra computer algebra |
| title | Computation of Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford Algebras |
| title_full | Computation of Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford Algebras |
| title_fullStr | Computation of Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford Algebras |
| title_full_unstemmed | Computation of Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford Algebras |
| title_short | Computation of Minimal Polynomials and Multivector Inverses in Non-Degenerate Clifford Algebras |
| title_sort | computation of minimal polynomials and multivector inverses in non degenerate clifford algebras |
| topic | multivector characteristic polynomial Clifford algebra computer algebra |
| url | https://www.mdpi.com/2227-7390/13/7/1106 |
| work_keys_str_mv | AT dimiterprodanov computationofminimalpolynomialsandmultivectorinversesinnondegeneratecliffordalgebras |