Proof of Some Properties of the Cross Product of Three Vectors in with Mathematica

Judith Keren Jiménez-Vilcherrez; Josel Antonio Mechato-Durand; Ricardo Velezmoro-León; Robert Ipanaqué-Chero

doi:10.1007/978-3-030-86653-2_18

Proof of Some Properties of the Cross Product of Three Vectors in with Mathematica

Judith Keren Jiménez-Vilcherrez, Josel Antonio Mechato-Durand, Ricardo Velezmoro-León, Robert Ipanaqué-Chero

Academic Department of Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

In this paper, the definition of the cross product of three tangent vectors to at the same point is stated, based on this definition a lemma is stated in which eight properties of said product are proposed and demonstrated. In addition, four theorems and two corollaries are stated and proved. One of the theorems constitutes an extension of the Jacobi identity. In some of the proofs, programs based on the paradigms: functional, rule-based and list-based from the Wolfram language, incorporated in Mathematica, are used.

Original language	English
Title of host publication	Computational Science and Its Applications – ICCSA 2021 - 21st International Conference, Proceedings
Editors	Osvaldo Gervasi, Beniamino Murgante, Sanjay Misra, Chiara Garau, Ivan Blečić, David Taniar, Bernady O. Apduhan, Ana Maria Rocha, Eufemia Tarantino, Carmelo Maria Torre
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	252-260
Number of pages	9
ISBN (Print)	9783030866525
DOIs	https://doi.org/10.1007/978-3-030-86653-2_18
State	Published - 2021
Event	21st International Conference on Computational Science and Its Applications, ICCSA 2021 - Virtual, Online Duration: 13 Sep 2021 → 16 Sep 2021

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	12949 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	21st International Conference on Computational Science and Its Applications, ICCSA 2021
City	Virtual, Online
Period	13/09/21 → 16/09/21

Keywords

Cross product in (Figure Presented)
Demonstrations using mathematica
Hyperparalelepiped
Hypervolume
Jacobi identity in (Figure Presented)

Access to Document

10.1007/978-3-030-86653-2_18

Cite this

Jiménez-Vilcherrez, J. K., Mechato-Durand, J. A., Velezmoro-León, R., & Ipanaqué-Chero, R. (2021). Proof of Some Properties of the Cross Product of Three Vectors in with Mathematica. In O. Gervasi, B. Murgante, S. Misra, C. Garau, I. Blečić, D. Taniar, B. O. Apduhan, A. M. Rocha, E. Tarantino, & C. M. Torre (Eds.), Computational Science and Its Applications – ICCSA 2021 - 21st International Conference, Proceedings (pp. 252-260). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12949 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-030-86653-2_18

Jiménez-Vilcherrez, Judith Keren ; Mechato-Durand, Josel Antonio ; Velezmoro-León, Ricardo et al. / Proof of Some Properties of the Cross Product of Three Vectors in with Mathematica. Computational Science and Its Applications – ICCSA 2021 - 21st International Conference, Proceedings. editor / Osvaldo Gervasi ; Beniamino Murgante ; Sanjay Misra ; Chiara Garau ; Ivan Blečić ; David Taniar ; Bernady O. Apduhan ; Ana Maria Rocha ; Eufemia Tarantino ; Carmelo Maria Torre. Springer Science and Business Media Deutschland GmbH, 2021. pp. 252-260 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Jiménez-Vilcherrez, JK, Mechato-Durand, JA, Velezmoro-León, R & Ipanaqué-Chero, R 2021, Proof of Some Properties of the Cross Product of Three Vectors in with Mathematica. in O Gervasi, B Murgante, S Misra, C Garau, I Blečić, D Taniar, BO Apduhan, AM Rocha, E Tarantino & CM Torre (eds), Computational Science and Its Applications – ICCSA 2021 - 21st International Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12949 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 252-260, 21st International Conference on Computational Science and Its Applications, ICCSA 2021, Virtual, Online, 13/09/21. https://doi.org/10.1007/978-3-030-86653-2_18

Proof of Some Properties of the Cross Product of Three Vectors in with Mathematica. / Jiménez-Vilcherrez, Judith Keren; Mechato-Durand, Josel Antonio; Velezmoro-León, Ricardo et al.
Computational Science and Its Applications – ICCSA 2021 - 21st International Conference, Proceedings. ed. / Osvaldo Gervasi; Beniamino Murgante; Sanjay Misra; Chiara Garau; Ivan Blečić; David Taniar; Bernady O. Apduhan; Ana Maria Rocha; Eufemia Tarantino; Carmelo Maria Torre. Springer Science and Business Media Deutschland GmbH, 2021. p. 252-260 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 12949 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Jiménez-Vilcherrez JK, Mechato-Durand JA, Velezmoro-León R , Ipanaqué-Chero R. Proof of Some Properties of the Cross Product of Three Vectors in with Mathematica. In Gervasi O, Murgante B, Misra S, Garau C, Blečić I, Taniar D, Apduhan BO, Rocha AM, Tarantino E, Torre CM, editors, Computational Science and Its Applications – ICCSA 2021 - 21st International Conference, Proceedings. Springer Science and Business Media Deutschland GmbH. 2021. p. 252-260. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-030-86653-2_18