Shimura subvarieties in the Prym locus of ramified Galois coverings

We study Shimura (special) subvarieties in the moduli space $$A_{p,D}$$ A p , D of complex abelian varieties of dimension p and polarization type D. These subvarieties arise from families of covers compatible with a fixed group action on the base curve such that the quotient of the base curve by the group is isomorphic to $${{\mathbb {P}}}^1$$ P 1 . We give a criterion for the image of these families under the Prym map to be a special subvariety and, using computer algebra, obtain 210 Shimura subvarieties contained in the Prym locus.

Investigation of the existence domain for Dyakonov surface waves in the Sage computer algebra system

Surface electromagnetic waves (Dyakonov waves) propagating along a plane interface between an isotropic substance with a constant dielectric constant and an anisotropic crystal, whose dielectric tensor has a symmetry axis directed along the interface, are considered. It is well known that the question of the existence of such surface waves is reduced to the question of the existence of a solution to a certain system of algebraic equations and inequalities. In the present work, this system is investigated in the Sage computer algebra system. The built-in technique of exceptional ideals in Sage made it possible to describe the solution of a system of algebraic equations parametrically using a single parameter, with all the original quantities expressed in terms of this parameter using radicals. The remaining inequalities were only partially investigated analytically. For a complete study of the solvability of the system of equations and inequalities, a symbolic-numerical algorithm is proposed and implemented in Sage, and the results of computer experiments are presented. Based on these results, conclusions were drawn that require further theoretical substantiation.

In Memory of Vladimir Gerdt

Center for Computational Methods in Applied Mathematics of RUDN, Professor V.P. Gerdt, whose passing was a great loss to the scientific center and the computer algebra community. The article provides biographical information about V.P. Gerdt, talks about his contribution to the development of computer algebra in Russia and the world. At the end there are the authors personal memories of V.P. Gerdt.

Tonality analysis in Wolfram Mathematica 12 computer algebra system

Sentiment analysis is a class of methods that are used to automatically determine the tonality of statements in the text. There are many solutions and technologies to define of text tonality at the moment and the choice depends on task. With the release of Wolfram Mathematica 12 versions, it became possible to use included nlp methods for determination of text tonality. This article is about definition of text tonality in the wolfram Mathematica 12 using nlp and compare nlp methods with standard definition function.

Automated generation of turbulence shell models by the methods of computer algebra

Описана разработанная методика генерации уравнений каскадных моделей турбулентности с помощью систем компьютерной алгебры. Методика позволяет варьировать размер масштабной нелокальности модели, вид квадратичных законов сохранения и спектральных законов, знаменатель геометрической прогрессии масштабов. Ее использование позволяет быстро и безошибочно генерировать целые классы моделей. Может использоваться для разработки каскадных моделей гидродинамических, магнитогидродинамических и конвективных турбулентных систем. There is a great variety of shell turbulence models. Such models reproduce certain characteristics of turbulence. A model that could reproduce all turbulence regimes does not exist at the moment. Information about a particular model is contained in a set of persistent quantities, which are some quadratic forms of turbulent fields. These quadratic forms should be formal analogs of the exact conserved quantities. It is important to note that the main idea of Shell models presupposes a refusal to describe the geometric structure of movements. At the same time, it is well known that turbulent processes in spaces of two and three dimensions behave differently. Therefore, the provision of certain combinations of conserved quantities allows indirect introducing into the shell model the information about the dimension of the physical space in which the turbulent process develops. Purpose. The aim of this work was to create software tools that would quickly generate classes of models that satisfy one or another set of conservation laws. The choice of a specific model within these classes can then be specified using additional physical considerations, for example, the existence of a given probability distribution for the interaction of certain shells. Methods. The developed technique for generating equations of shell turbulence models is carried out using symbolic computation systems (computer algebra systems - CAS). Note that symbolic packages are used not for studying ready-made shell models, but for the automated generation of the equations of these models themselves. The technique allows varying the value of the scale nonlocality of the model, the form of the quadratic conservation laws and spectral laws, the denominator of the geometric progression of scales. It allows quickly and accurately generating the entire set of classes of the models. It can be used to develop shell models of hydrodynamic, magnetohydrodynamic and convective turbulent systems. Findings. It seems that the proposed technique will be useful for studying the properties of turbulence in the framework of cascade models

Mathematical logic: construction of logic circuits from logical elements in Maple

В статье рассматриваются возможности применения библиотеки Logic системы компьютерной алгебры Maple в аспекте компьютерного моделирования логических схем в различных базисах. Смоделированы основные логические элементы в Maple. На конкретном примере детально представлен алгоритм построения логической схемы в различных базисах. The article discusses the possibilities of using the Logic library of the Maple computer algebra system in the aspect of computer modeling of logic circuits in various bases. Basic logic gates are modeled in Maple. On a specific example, an algorithm for constructing a logical circuit in various bases is presented in detail.

SMIS: A Stepwise Multiple Integration Solver Using a CAS

Multiple Integration is a very important topic in different applications in Engineering and other Sciences. Using numerical software to get an approximation to the solution is a normal procedure. Another approach is working in an algebraic form to obtain an exact solution or to get general solutions depending on different parameters. Computer Algebra Systems (CAS) are needed for this last approach. In this paper, we introduce SMIS, a new stepwise solver for multiple integration developed in a CAS. The two main objectives of SMIS are: (1) to increase the capabilities of CAS to help the user to deal with this topic and (2) to be used in Math Education providing an important tool for helping with the teaching and learning process of this topic. SMIS can provide just the final solution or an optional stepwise solution (even including some theoretical comments). The optional stepwise solutions provided by SMIS are of great help for (2). Although SMIS has been developed in the specific CAS Derive, since the code is provided, it can be easily migrated to any CAS which deals with integrals and text management that allow us to display comments for intermediate steps.

Shimura curves in the Prym loci of ramified double covers

We study Shimura curves of PEL type in the space of polarized abelian varieties [Formula: see text] generically contained in the ramified Prym locus. We generalize to ramified double covers, the construction done in [E. Colombo, P. Frediani, A. Ghigi and M. Penegini, Shimura curves in the Prym locus, Commun. Contemp. Math. 21(2) (2019) 1850009] in the unramified case and in the case of two ramification points. Namely, we construct families of double covers which are compatible with a fixed group action on the base curve. We only consider the case of one-dimensional families and where the quotient of the base curve by the group is [Formula: see text]. Using computer algebra we obtain 184 Shimura curves contained in the (ramified) Prym loci.