Arithmetic and Matricial Calculation
Pure and Applied Mathematics Journal
Volume 5, Issue 3, June 2016, Pages: 82-86
Received: Apr. 29, 2016; Accepted: May 9, 2016; Published: May 25, 2016
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Authors
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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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.
Keywords
Arithmetic, Matricial Calculation, Numeral System, Radix, Basis, Arithmetic Operations
To cite this article
Raoelina Andriambololona, Ravo Tokiniaina Ranaivoson, Wilfrid Chrysante Solofoarisina, Arithmetic and Matricial Calculation, Pure and Applied Mathematics Journal. Vol. 5, No. 3, 2016, pp. 82-86. doi: 10.11648/j.pamj.20160503.14
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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