Arithmetic and Matricial Calculation

Raoelina Andriambololona; Ravo Tokiniaina Ranaivoson; Wilfrid Chrysante Solofoarisina

doi:doi:10.11648/j.pamj.20160503.14

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Arithmetic and Matricial Calculation

Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Wilfrid Chrysante Solofoarisina

Published in Pure and Applied Mathematics Journal (Volume 5, Issue 3)

Received: 29 April 2016 Accepted: 9 May 2016 Published: 25 May 2016

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Abstract

We present a study on written numeration and arithmetic using matricial formalism for the writing of numeral basis and number. The underlying idea is simple, it consists to consider the numeral representation of number as a matrix representation of an intrinsic number in a basis which represents the numeral system. Then the matrix calculation and linear algebra tools are extensively utilized to simplify arithmetic operations and to remove many inconsistencies existing in arithmetic. Owing to the adopted convention, four dispositions are obtained for the writing of number components according to the disposition in row matrix or column matrix and in decreasing or increasing order. The writing in line from Left handside to the Right handsideby increasing order (called LRi) is shown to be much more logical and coherent with the addition and the multiplication rules than the usual one which starts from the left handside to the right handside by decreasing order (LRd). In the LRi disposition, rules for the addition and multiplication of integers number are derived.

Published in	Pure and Applied Mathematics Journal (Volume 5, Issue 3)
DOI	10.11648/j.pamj.20160503.14
Page(s)	82-86
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Arithmetic, Matricial Calculation, Numeral System, Radix, Basis, Arithmetic Operations

References

[1]	Georges Ifrah, David Bellos, E. F. Harding, Sophie Wood, Ian Monk, “The Universal History of Numbers: From Prehistory to the Invention of the Computer”, John Wiley & Sons, New York, 1999.
[2]	Stephen Chrisomalis, “Numerical Notation: A Comparative History”, Cambridge University Press, 2010.
[3]	Encyclopédie Universalis, "Théorie axiomatique des ensembles. Chapitre 4", Vol. 10 pages 66, 1968.
[4]	Anton Glaser, “History of binary and other nondecimal numeration”, Tomash, 1971.
[5]	M. Morris Mano, Charles Kime. “Logic and computer design fundamentals.” (4th ed.). Pearson, 2014.
[6]	Raoelina Andriambololona, “Algèbre linéaire et multilinéaire”, Collection LIRA, INSTN-Madagascar, Antananarivo, Madagascar, 1986.
[7]	Anton Howard, Chris Rorres, “Elementary Linear Algebra” (10th ed.), John Wiley & Sons, 2010.
[8]	William C. Brown “Matrices and vector spaces”, New York, NY: Marcel Dekker, 1991.
[9]	Raoelina Andriambololona, "Théorie générale des numérations écrite et parlée. II Utilisation du calcul matriciel en arithmétique. Nouvelle proposition d’écriture, d’énoncé des règles d’addition et de multiplication des nombres.". Bull. Acad.Malg LXV/1-2, Antananarivo, Madagascar, 1987.
[10]	Raoelina Andriambololona, “Théorie générale des numérations écrite et parlée”. Bull. Acad. Malg. LXIV./1-2, Antananarivo, Madagascar, 1986.
[11]	Raoelina Andriambololona, “Théorie générale des numérations écrite et parlée. II- Utilisation du calcul matriciel en arithmétique. Application au changement de bases de numération. Bull. Acad. Malg. LXV./1-2, Antananarivo, Madagascar”, 1987 (1989).
[12]	Raoelina Andriambololona, Hanitriarivo Rakotoson “Mpikajy elekronika sy siantifika mampiasa ny fomba fanisana Malagasy (Electronic and scientific calculator based on malagasy counting method)”, communication at the Academie Malgache, Antananarivo Madagascar, 05 June 2008.

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APA Style

Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Wilfrid Chrysante Solofoarisina. (2016). Arithmetic and Matricial Calculation. Pure and Applied Mathematics Journal, 5(3), 82-86. https://doi.org/10.11648/j.pamj.20160503.14

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ACS Style

Raoelina Andriambololona; Ravo Tokiniaina Ranaivoson; Wilfrid Chrysante Solofoarisina. Arithmetic and Matricial Calculation. Pure Appl. Math. J. 2016, 5(3), 82-86. doi: 10.11648/j.pamj.20160503.14

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AMA Style

Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Wilfrid Chrysante Solofoarisina. Arithmetic and Matricial Calculation. Pure Appl Math J. 2016;5(3):82-86. doi: 10.11648/j.pamj.20160503.14

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@article{10.11648/j.pamj.20160503.14,
  author = {Raoelina Andriambololona and Ravo Tokiniaina Ranaivoson and Wilfrid Chrysante Solofoarisina},
  title = {Arithmetic and Matricial Calculation},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {3},
  pages = {82-86},
  doi = {10.11648/j.pamj.20160503.14},
  url = {https://doi.org/10.11648/j.pamj.20160503.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160503.14},
  abstract = {We present a study on written numeration and arithmetic using matricial formalism for the writing of numeral basis and number. The underlying idea is simple, it consists to consider the numeral representation of number as a matrix representation of an intrinsic number in a basis which represents the numeral system. Then the matrix calculation and linear algebra tools are extensively utilized to simplify arithmetic operations and to remove many inconsistencies existing in arithmetic. Owing to the adopted convention, four dispositions are obtained for the writing of number components according to the disposition in row matrix or column matrix and in decreasing or increasing order. The writing in line from Left handside to the Right handsideby increasing order (called LRi) is shown to be much more logical and coherent with the addition and the multiplication rules than the usual one which starts from the left handside to the right handside by decreasing order (LRd). In the LRi disposition, rules for the addition and multiplication of integers number are derived.},
 year = {2016}
}

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TY  - JOUR
T1  - Arithmetic and Matricial Calculation
AU  - Raoelina Andriambololona
AU  - Ravo Tokiniaina Ranaivoson
AU  - Wilfrid Chrysante Solofoarisina
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PY  - 2016
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DO  - 10.11648/j.pamj.20160503.14
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AB  - We present a study on written numeration and arithmetic using matricial formalism for the writing of numeral basis and number. The underlying idea is simple, it consists to consider the numeral representation of number as a matrix representation of an intrinsic number in a basis which represents the numeral system. Then the matrix calculation and linear algebra tools are extensively utilized to simplify arithmetic operations and to remove many inconsistencies existing in arithmetic. Owing to the adopted convention, four dispositions are obtained for the writing of number components according to the disposition in row matrix or column matrix and in decreasing or increasing order. The writing in line from Left handside to the Right handsideby increasing order (called LRi) is shown to be much more logical and coherent with the addition and the multiplication rules than the usual one which starts from the left handside to the right handside by decreasing order (LRd). In the LRi disposition, rules for the addition and multiplication of integers number are derived.
VL  - 5
IS  - 3
ER  -

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Author Information

Raoelina Andriambololona

Theoretical Physics Department, Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar
Ravo Tokiniaina Ranaivoson

Theoretical Physics Department, Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar
Wilfrid Chrysante Solofoarisina

Theoretical Physics Department, Institut National des Sciences et Techniques Nucléaires (INSTN-Madagascar), Antananarivo, Madagascar

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APA Style

Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Wilfrid Chrysante Solofoarisina. (2016). Arithmetic and Matricial Calculation. Pure and Applied Mathematics Journal, 5(3), 82-86. https://doi.org/10.11648/j.pamj.20160503.14

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ACS Style

Raoelina Andriambololona; Ravo Tokiniaina Ranaivoson; Wilfrid Chrysante Solofoarisina. Arithmetic and Matricial Calculation. Pure Appl. Math. J. 2016, 5(3), 82-86. doi: 10.11648/j.pamj.20160503.14

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AMA Style

Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Wilfrid Chrysante Solofoarisina. Arithmetic and Matricial Calculation. Pure Appl Math J. 2016;5(3):82-86. doi: 10.11648/j.pamj.20160503.14

Copy | Download

@article{10.11648/j.pamj.20160503.14,
  author = {Raoelina Andriambololona and Ravo Tokiniaina Ranaivoson and Wilfrid Chrysante Solofoarisina},
  title = {Arithmetic and Matricial Calculation},
  journal = {Pure and Applied Mathematics Journal},
  volume = {5},
  number = {3},
  pages = {82-86},
  doi = {10.11648/j.pamj.20160503.14},
  url = {https://doi.org/10.11648/j.pamj.20160503.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20160503.14},
  abstract = {We present a study on written numeration and arithmetic using matricial formalism for the writing of numeral basis and number. The underlying idea is simple, it consists to consider the numeral representation of number as a matrix representation of an intrinsic number in a basis which represents the numeral system. Then the matrix calculation and linear algebra tools are extensively utilized to simplify arithmetic operations and to remove many inconsistencies existing in arithmetic. Owing to the adopted convention, four dispositions are obtained for the writing of number components according to the disposition in row matrix or column matrix and in decreasing or increasing order. The writing in line from Left handside to the Right handsideby increasing order (called LRi) is shown to be much more logical and coherent with the addition and the multiplication rules than the usual one which starts from the left handside to the right handside by decreasing order (LRd). In the LRi disposition, rules for the addition and multiplication of integers number are derived.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Arithmetic and Matricial Calculation
AU  - Raoelina Andriambololona
AU  - Ravo Tokiniaina Ranaivoson
AU  - Wilfrid Chrysante Solofoarisina
Y1  - 2016/05/25
PY  - 2016
N1  - https://doi.org/10.11648/j.pamj.20160503.14
DO  - 10.11648/j.pamj.20160503.14
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 82
EP  - 86
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20160503.14
AB  - We present a study on written numeration and arithmetic using matricial formalism for the writing of numeral basis and number. The underlying idea is simple, it consists to consider the numeral representation of number as a matrix representation of an intrinsic number in a basis which represents the numeral system. Then the matrix calculation and linear algebra tools are extensively utilized to simplify arithmetic operations and to remove many inconsistencies existing in arithmetic. Owing to the adopted convention, four dispositions are obtained for the writing of number components according to the disposition in row matrix or column matrix and in decreasing or increasing order. The writing in line from Left handside to the Right handsideby increasing order (called LRi) is shown to be much more logical and coherent with the addition and the multiplication rules than the usual one which starts from the left handside to the right handside by decreasing order (LRd). In the LRi disposition, rules for the addition and multiplication of integers number are derived.
VL  - 5
IS  - 3
ER  -

Copy | Download