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Abstract— This paper describes the synthesis of a numerical method, to compute Modular Inverse Matrices and so, Modular Linear Equations Systems (with one, infinite or no-solution set), with no theoretical limit, in 𝒁𝒏; considering polynomial and logarithmic time computational complexity. The geometric interpretation of this, implies that elements, such as planes, lines and vectors of these spaces, interact in the n-dimensional grid. The interaction in the Grid, can only be possible in a discrete way; from one point to another, like digital states. On the other hand, this work also considers applied mathematics solving the ‘Gauss-Jacques’ function obtaining quaternionic linear equation in fields such as Modular Linear Algebra and Modular Multilinear Algebra. Based on research, it was concluded that this method is a math function, because its attributes described in this work. Furthermore, it can be coded in any computer language making libraries. The equation as a logic entity is validated using logic systems witnessing ‘Inverse Migration Field’ transport. This work constitutes a deep analysis in numerical methods, for modular inverse matrix computation as well as a prolegomenon to Modular Linear Algebra. Technological & Scientific uses and applications of this work are numerous.
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Aug 2, 2024, 11:38 PM
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Declaration Date:
Aug 2, 2024, 11:38 PM
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Title A Digital Frontier Composition - Extended Author's Edition
Abstract— This paper describes the synthesis of a numerical method, to compute Modular Inverse Matrices and so, Modular Linear Equations Systems (with one, infinite or no-solution set), with no theoretical limit, in 𝒁𝒏; considering polynomial and logarithmic time computational complexity. The geometric interpretation of this, implies that elements, such as planes, lines and vectors of these spaces, interact in the n-dimensional grid. The interaction in the Grid, can only be possible in a discrete way; from one point to another, like digital states. On the other hand, this work also considers applied mathematics solving the ‘Gauss-Jacques’ function obtaining quaternionic linear equation in fields such as Modular Linear Algebra and Modular Multilinear Algebra. Based on research, it was concluded that this method is a math function, because its attributes described in this work. Furthermore, it can be coded in any computer language making libraries. The equation as a logic entity is validated using logic systems witnessing ‘Inverse Migration Field’ transport. This work constitutes a deep analysis in numerical methods, for modular inverse matrix computation as well as a prolegomenon to Modular Linear Algebra. Technological & Scientific uses and applications of this work are numerous.
Work type Technical
Tags numerical analysis, inverse migration field., modular inverse matrices, gauss-jacques, the jacques equation
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Identifier 2408028973067
Entry date Aug 2, 2024, 11:38 PM UTC
License Creative Commons Attribution-NonCommercial-ShareAlike 4.0
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Author. Holder Fausto Abraham Jacques García. Date Aug 2, 2024.
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