Related papers: Integer formula encoding SageTeX package
The article describes the advisable ways of the cloud-based systems use to support students collaboration in the process of math disciplines learning. The SageMathCloud-based component that aggregates electronic resources for several math…
We explain the algebra needed to make sense of the log signature of a path, with plenty of examples. We show how the log signature can be calculated numerically, and explain some software tools which demonstrate it.
We present a versatile construction allowing one to obtain pairs of integer sets with infinite symmetric difference, infinite intersection, and identical representation functions.
Integer programming is concerned with solving linear systems of equations over the non-negative integers. The basic question is to find a solution which minimizes a given linear objective function for a fixed right hand side. Here we also…
These lecture notes present a method for symbolic tensor calculus that (i) runs on fully specified smooth manifolds (described by an atlas), (ii) is not limited to a single coordinate chart or vector frame, (iii) runs even on…
We present a notion of geometry encoding suitable for machine learning-based numerical simulation. In particular, we delineate how this notion of encoding is different than other encoding algorithms commonly used in other disciplines such…
The software package developed in the MS thesis research implements functions for the intelligent guessing of polynomial sequence formulas based on user-defined expected sequence factors of the input coefficients. We present a specialized…
In this paper, we examine a ciphertext on the basis of using geometrical objects. Each symbol normative alphabet is determined as a point on the plane. We consider possible ways for presentation of these points.
\noindent Model building in $\mathsf{SO(10)}$, which is the leading grand unification framework, often involves large Higgs representations and their couplings. Explicit calculations of such couplings is a multi-step process that involves…
This paper introduces a sentence to vector encoding framework suitable for advanced natural language processing. Our latent representation is shown to encode sentences with common semantic information with similar vector representations.…
We introduce the package combinatorics for the software CoCoA. This package provides a data structure and the necessary methods for computing several known enumerative combinatorial invariants.
We explore the combination of deterministic and Monte Carlo methods to facilitate efficient automatic numerical computation of multidimensional integrals with singular integrands. Two adaptive algorithms are presented that employ recursion…
The Unigram tokenization algorithm offers a probabilistic alternative to the greedy heuristics of Byte-Pair Encoding. Despite its theoretical elegance, its implementation in practice is complex, limiting its adoption to the SentencePiece…
The new finite state machine package in the mathematics software system SageMath is presented and illustrated by many examples. Several combinatorial problems, in particular digit problems, are introduced, modeled by automata and…
Before we can get the whole potential of employing computers in the process of managing mathematical `knowledge', we have to convert informal knowledge into machine-oriented representations. How exactly to support this process so that it…
Source code summarization of a subroutine is the task of writing a short, natural language description of that subroutine. The description usually serves in documentation aimed at programmers, where even brief phrase (e.g. "compresses data…
In this article, the operator approach to modeling numeral systems is introduced. This approach can be useful for coding information and providing computer protection. Certain examples of such numeral systems are considered. In addition,…
We consider so-called squaring the square-puzzles where a given square (or rectangle) should be dissected into smaller squares. For a specific instance of such problems we demonstrate that a mathematically rigorous solution can be quite…
Integer-forcing source coding has been proposed as a low-complexity method for compression of distributed correlated Gaussian sources. In this scheme, each encoder quantizes its observation using the same fine lattice and reduces the result…
This paper has been accepted for publication in Discrete Optimization.