Programming and Computer Software最新文献

{"title":"Applying Computer Algebra Systems to Study Chaundy-Bullard Identities for the Vector Partition Function with Weight","authors":"A. B. Leinartene, A. P. Lyapin","doi":"10.1134/s0361768824020105","DOIUrl":"https://doi.org/10.1134/s0361768824020105","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An algorithm for obtaining the Chaundy-Bullard identity for a vector partition function with weight that uses computer algebra methods is proposed. To automate this process in Maple, an algorithm was developed and implemented that calculates the values of the vector partition function with weight by finding non-negative solutions of systems of linear Diophantine equations that are used to form the identities involved. The algorithm’s input data is represented by the set of integer vectors that form a pointed lattice cone and by some point from this cone, and the Chaundy-Bullard identity for the vector partition function with weight is its output. The code involved is stored in the depository and is ready-to-use. An example demonstrating the algorithm’s operation is given.</p>","PeriodicalId":54555,"journal":{"name":"Programming and Computer Software","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solving Rician Data Analysis Problems: Theory and Numerical Modeling Using Computer Algebra Methods in Wolfram Mathematica","authors":"T. V. Yakovleva","doi":"10.1134/s0361768824020154","DOIUrl":"https://doi.org/10.1134/s0361768824020154","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper considers theoretical foundations and mathematical methods of data analysis under the conditions of the Rice statistical distribution. The problem involves joint estimation of the signal and noise parameters. It is shown that this estimation requires the solution of a complex system of essentially nonlinear equations with two unknown variables, which implies significant computational costs. This study is aimed at mathematical optimization of computer algebra methods for numerical solution of the problem of Rician data analysis. As a result of the optimization, the solution of the system of two nonlinear equations is reduced to the solution of one equation with one unknown variable, which significantly simplifies algorithms for the numerical solution of the problem, reduces the amount of necessary computational resources, and enables the use of advanced methods for parameter estimation in information systems with priority of real-time operation. Results of numerical experiments carried out using Wolfram Mathematica confirm the effectiveness of the developed methods for two-parameter analysis of Rician data. The data analysis methods considered in this paper are useful for solving many scientific and applied problems that involve analysis of data described by the Rice statistical model.</p>","PeriodicalId":54555,"journal":{"name":"Programming and Computer Software","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Integration of a Degenerate System of ODEs","authors":"A. D. Bruno, V. F. Edneral","doi":"10.1134/s036176882402004x","DOIUrl":"https://doi.org/10.1134/s036176882402004x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The integrability of a two-dimensional autonomous polynomial system of ordinary differential equations (ODEs) with a degenerate singular point at the origin that depends on six parameters is investigated. The integrability condition for the first quasihomogeneous approximation allows one of these parameters to be fixed on a countable set of values. The further analysis is carried out for this value and five free parameters. Using the power geometry method, the system is reduced to a non-degenerate form through the blowup process. Then, the necessary conditions for its local integrability are calculated using the method of normal forms. In other words, the conditions for the parameters under which the original system is locally integrable near the degenerate stationary point are found. By resolving these conditions, we find seven two-parameter families in the five-dimensional parametric space. For parameter values from these families, the first integrals of the system are found. The cumbersome calculations that occur in the problem under consideration are carried out using computer algebra.</p>","PeriodicalId":54555,"journal":{"name":"Programming and Computer Software","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141145857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Implementation of Analytic Projective Geometry for Computer Graphics","authors":"M. N. Gevorkyan, A. V. Korol’kova, D. S. Kulyabov, L. A. Sevast’yanov","doi":"10.1134/s0361768824020075","DOIUrl":"https://doi.org/10.1134/s0361768824020075","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In their research, the authors actively exploit different branches of geometry. For geometric constructions, computer algebra approaches and systems are used. Currently, we are interested in computer geometry, more specifically, the implementation of computer graphics. The use of the projective space and homogeneous coordinates has actually become a standard in modern computer graphics. In other words, the problem is reduced to the application of analytic projective geometry. The authors failed to find a computer algebra system that could implement projective geometry in its entirety. Therefore, it was decided to partially implement computer algebra for visualization of algebraic relations. For this purpose, the Asymptote system was employed.</p>","PeriodicalId":54555,"journal":{"name":"Programming and Computer Software","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153088","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Interactive Calculation of Light Refraction and Caustics Using a Graphics Processor","authors":"S. I. Vyatkin, B. S. Dolgovesov","doi":"10.1134/s0361768824010122","DOIUrl":"https://doi.org/10.1134/s0361768824010122","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>While modern rendering systems are efficient for modeling complex light paths in complex environments, the rendering of refractive caustics still takes a long time. Caustics are light patterns that occur when light is refracted and reflected from a surface. Due to an irregular density distribution of these specular events, rendering algorithms mainly rely on direct sampling of the bidirectional dispersion distribution function on these surfaces to plot trajectories. This requires a lot of calculations. Photonic maps are also used. However, there are difficulties that limit the applicability of caustic maps. Since each photon in the photon buffer must be processed, one has to choose between a strongly underestimated caustic sampling and a large decrease in speed in order to use a sufficient number of photons for caustics in order to obtain high-quality images. Complex specular interactions cause oversampling in bright focal areas, while other areas of the caustic map remain undersampled and noisy. At the same time, speed takes precedence over realism in most interactive applications. However, the desire to improve the quality of graphics prompted the development of various fast approximations for realistic lighting. This paper presents a combined method for rendering refraction of light and caustics using backward integration for illumination and direct integration for viewing rays. An approach for simultaneous propagation of light and for tracking rays in a volume is used; therefore, it does not require storing data of an intermediate volume of illumination. In the implementation of this method, the distance between the light planes is set to one voxel, which provides at least one sample per voxel for all orientations. The method does not use preliminary calculations, and all rendering parameters can be changed interactively. As a result, using the proposed method, it is possible to create plausible approximations of complex phenomena, such as refractions and caustics. The effect of refraction on the shadow is shown. Complex light patterns occurring due to the curved geometry of objects are demonstrated. The visualization results show the importance of refraction for the appearance of transparent objects, e.g., the effect distortions caused by refraction in the medium and refraction on the interfaces between media. The difference in refractive indices between different media causes a complex interaction between light and shadow areas. It is shown how refraction and caustics improve rendering of functionally defined objects by providing additional information about their shape and location.</p>","PeriodicalId":54555,"journal":{"name":"Programming and Computer Software","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Software Implementation of an Algorithm for Automatic Detection of Lineaments and Their Properties in Open-Pit Dumps","authors":"S. E. Popov, V. P. Potapov, R. Y. Zamaraev","doi":"10.1134/s0361768824010080","DOIUrl":"https://doi.org/10.1134/s0361768824010080","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper presents an algorithm and description of its software implementation for detection of lineaments (ground erosions or cracks) in aerial images of open pits. The proposed approach is based on the apparatus of convolutional neural networks for semantic classification of binarized images of lineament objects, as well as graph theory for determining the geometric location of linearized lineament objects with subsequent calculation of their lengths and areas. As source data, three-channel RGB images of high-resolution aerial photography (10×10 cm) are used. The software module of the model is logically divided into three levels: preprocessing, detection, and post-processing. The first level implements the preprocessing of input data to form a training sample based on successive transformations of RGB images into binary images by using the OpenCV library. A neural network of the U-Net type, which includes convolutional (Encoder) and scanning (Decoder) blocks, represents the second level of the information model. At this level, automatic detection of objects is implemented. The third level of the model is responsible for calculating their areas and lengths. The result provided by the convolutional neural network is passed to it as input data. The lineament area is calculated by summing the total number of points and multiplying by the pixel size. The lineament length is calculated by linearizing the areal object into a segmented object with node pixels and, then, calculating the lengths between them while taking into account the resolution of the source image. The software module can work with fragments of the source image by combining them. The module is implemented in Python and its source code is available at https://gitlab.ict.sbras.ru/popov/lineaments/-/tree/master/lineaments-cnn.</p>","PeriodicalId":54555,"journal":{"name":"Programming and Computer Software","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An Extendable Essay on the Sage Computer Algebra System and an Editor for Creating Extendable Essays","authors":"E. A. Bordachenkova, V. N. Zubareva, A. A. Panferov","doi":"10.1134/s0361768824020038","DOIUrl":"https://doi.org/10.1134/s0361768824020038","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An extendable essay is a special format of electronic texts that is more convenient for reading than hypertext. To facilitate the creation and editing of extendable essays, an editor program implemented as a web application is proposed. Using this editor, an extendable essay on the Sage computer algebra system is written. Sage seems to be a good choice for the users who are not familiar with computer algebra systems.</p>","PeriodicalId":54555,"journal":{"name":"Programming and Computer Software","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153086","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Linear Cellular Automata","authors":"V. R. Kulikov, A. A. Kytmanov, A. O. Poroshin, I. V. Timofeev, D. P. Fedchenko","doi":"10.1134/s0361768824010067","DOIUrl":"https://doi.org/10.1134/s0361768824010067","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>wolfram cellular automata are considered and their operation is demonstrated using an example of traffic flow simulation. For the class of one-dimensional elementary cellular automata, the concept of linearity is introduced in the language of Zhegalkin operators. An algorithm for finding linear Zhegalkin operators with multipliers of three variables is presented. The algorithm is implemented in Python.</p>","PeriodicalId":54555,"journal":{"name":"Programming and Computer Software","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fuzzy Measure on p-Adic Balls Defined on a Finite Number Set","authors":"V. P. Bocharnikov, S. V. Sveshnikov","doi":"10.1134/s036176882401002x","DOIUrl":"https://doi.org/10.1134/s036176882401002x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>An approach to constructing a fuzzy measure on <i>p</i>-adic balls is considered that does not require the measure density to be directly specified. Relationships for determining this measure for an arbitrary subset of a bounded number set represented as a set of <i>p</i>-adic balls have been proven. Uniform and nonuniform fuzzy measures are considered. An algorithm for determining a fuzzy measure on <i>p</i>-adic balls is proposed. Examples of calculating this measure are given.</p>","PeriodicalId":54555,"journal":{"name":"Programming and Computer Software","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153078","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lower Bounds for the Rank of a Matrix with Zeros and Ones outside the Leading Diagonal","authors":"A. V. Seliverstov, O. A. Zverkov","doi":"10.1134/s0361768824020142","DOIUrl":"https://doi.org/10.1134/s0361768824020142","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>We found a lower bound on the rank of a square matrix where every entry in the leading diagonal is neither zero nor one and every entry outside the leading diagonal is either zero or one. The rank of this matrix is at least half its order. Under an additional condition, the lower bound is higher by one. This condition means that some auxiliary system of linear equations has no binary solution. Some examples are provided that show that the lower bound can be achieved. This lower bound on the matrix rank allows the problem of finding a binary solution to a system of linear equations with a sufficiently large number of linearly independent equations to be reduced to a similar problem in a smaller number of variables. Restrictions on the existence of a large set of solutions are found, each differing from the binary one by the value of one variable. In addition, we discuss the possibility of certifying the absence of a binary solution to a large system of linear algebraic equations. Estimates of the time required for calculating the matrix rank in the SymPy computer algebra system are also provided. It is shown that the rank of a matrix over the field of residues modulo prime number is calculated faster than it generally takes to calculate the rank of a matrix of the same order over the field of rational numbers.</p>","PeriodicalId":54555,"journal":{"name":"Programming and Computer Software","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141153120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}