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

Departamento Académico de Matemática

Producción científica: Capítulo del libro/informe/acta de congreso › Contribución a la conferencia › revisión exhaustiva

Resumen

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.

Idioma original	Inglés
Título de la publicación alojada	Computational Science and Its Applications – ICCSA 2021 - 21st International Conference, Proceedings
Editores	Osvaldo Gervasi, Beniamino Murgante, Sanjay Misra, Chiara Garau, Ivan Blečić, David Taniar, Bernady O. Apduhan, Ana Maria Rocha, Eufemia Tarantino, Carmelo Maria Torre
Editorial	Springer Science and Business Media Deutschland GmbH
Páginas	252-260
Número de páginas	9
ISBN (versión impresa)	9783030866525
DOI	https://doi.org/10.1007/978-3-030-86653-2_18
Estado	Publicada - 2021
Evento	21st International Conference on Computational Science and Its Applications, ICCSA 2021 - Virtual, Online Duración: 13 set. 2021 → 16 set. 2021

Serie de la publicación

Nombre	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volumen	12949 LNCS
ISSN (versión impresa)	0302-9743
ISSN (versión digital)	1611-3349

Conferencia

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

Acceder al documento

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

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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. En 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. En 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).

Producción científica: Capítulo del libro/informe/acta de congreso › Contribución a la conferencia › revisión exhaustiva

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AU - Mechato-Durand, Josel Antonio

AU - Velezmoro-León, Ricardo

AU - Ipanaqué-Chero, Robert

PY - 2021

Y1 - 2021

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AB - 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.

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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. En Gervasi O, Murgante B, Misra S, Garau C, Blečić I, Taniar D, Apduhan BO, Rocha AM, Tarantino E, Torre CM, editores, 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