Related papers: Integer formula encoding SageTeX package
Arithmetic Coding is an efficient lossless compression scheme applied for many multimedia standards such as JPEG, JPEG2000, H.263, H.264 and H.265. Due to nonlinearity, high error propagation and high error sensitivity of arithmetic coders,…
Superdense coding is a paradigmatic protocol in quantum information science, employing a quantum communication channel to send classical information more efficiently. As we show here, it can be understood as a particular case of a prepare…
In this note we try to bring out the ideas of Hamming's classic paper on coding theory in a form understandable by undergraduate students of mathematics.
Algorithms like those for differentiating functional expressions manipulate the syntactic structure of mathematical expressions in a mathematically meaningful way. A formalization of such an algorithm should include a specification of its…
While neural network approaches are achieving breakthrough performance in the natural language related fields, there have been few similar attempts at mathematical language related tasks. In this study, we explore the potential of applying…
The present work includes some of the author's original researches on integer solutions of Diophantine liner equations and systems. The notion of "general integer solution" of a Diophantine linear equation with two unknowns is extended to…
A introduction to the syntax and Semantics of Answer Set Programming intended as an handout to [under]graduate students taking Artificial Intlligence or Logic Programming classes.
In the domain of Software Engineering, program analysis and understanding has been considered to be a very challenging task since decade, as it demands dedicated time and efforts. The analysis of source code may occasionally be…
The concept of a universal algorithm is discussed. Examples of this kind of algorithms are presented. Software implementations of such algorithms in C++ type languages are discussed together with means that provide for computations with an…
The notion of symmetry is defined in the context of Linear and Integer Programming. Symmetric integer programs are studied from a group theoretical viewpoint. We investigate the structure of integer solutions of integer programs and show…
The majority of text is stored in UTF-8, which must be validated on ingestion. We present the lookup algorithm, which outperforms UTF-8 validation routines used in many libraries and languages by more than 10 times using commonly available…
We demonstrate how methods in Functional Programming can be used to implement a computer algebra system. As a proof-of-concept, we present the computational-algebra package. It is a computer algebra system implemented as an embedded…
It is possible to interpret text as numbers (and vice versa) if one interpret letters and other characters as digits and assume that they have an inherent immutable ordering. This is demonstrated by the conventional digit set of the…
With dramatic improvements in optimization software, the solution of large-scale problems that seemed intractable decades ago are now a routine task. This puts even more real-world applications into the reach of optimizers. At the same…
This paper gives a brief description of the author's database of integer sequences, now over 35 years old, together with a selection of a few of the most interesting sequences in the table. Many unsolved problems are mentioned.
This work present the main encryption's algorithm of the PASME tool. This software allows encrypt and hide an information in various types of files. The algorithm uses the fact that factoring large numbers is a difficult issue in terms of…
This paper discusses new analytic algorithms and software for the enumeration of all integer flows inside a network. Concrete applications abound in graph theory \cite{Jaeger}, representation theory \cite{kirillov}, and statistics…
Transformer-based large language models exhibit groundbreaking capabilities, but their storage and computational costs are prohibitively high, limiting their application in resource-constrained scenarios. An effective approach is to…
Numerous methods have been considered to create a fast integer factorization algorithm. Despite its apparent simplicity, the difficulty to find such an algorithm plays a crucial role in modern cryptography, notably, in the security of RSA…
Nowadays interactive digital scientific environments have become an integral part of scientific computing in solving various scientific tasks in research, but also STEM education. We introduce SageMath or shortly Sage -- a free open…