Geometric algebra is currently considered as a universal mathematical apparatus of computer graphics. Active research, both academic and applied, is being conducted in this area. …
For describing specialized mathematical structures, it is preferable to use a special formalism rather than a general one. However, tradition often prevails in this case. For …
Tensor formalism (and its special case—vector formalism) is a mathematical technique that is widely used in physical and engineering problems. Even though this formalism is fairy …
Calculations of optical devices in the geometrized Maxwell’s theory use well-known formalisms of general theory of relativity and differential geometry. In particular, for such …
Geometric algebra is based on the works by Grassmann and Clifford. Its main objects of research are polyvectors (p-vectors) and multivectors. Polyvectors, together with the …
Recently, the place of the main programming language for scientific and engineering computations has been little by little taken by Julia. Some users want to work completely within …
In research problems that involve the use of numerical methods for solving systems of ordinary differential equations (ODEs), it is often required to select the most efficient …
This paper has a practical aim. For a long time, implementations of pseudorandom number generators in standard libraries of programming languages had poor quality. The situation …
Computer algebra systems are complex software systems that cover a wide range of scientific and practical problems. However, the absolute coverage cannot be achieved. Often, it is …
In certain scientific domains, there is a need for tensor operations. To facilitate tensor computations, computer algebra systems are employed. In our research, we have been using …
In this paper we compare the performance of classical Runge–Kutta methods implemented in Fortran and Julia languages. We use the technique described in technical report by Tomas …
To construct realistic mathematical models from the first principles, the authors suggest using the stochastization method. In a number of works different approaches to …
When modeling such phenomena as population dynamics, controllable flows, etc., a problem arises of adapting the existing models to a phenomenon under study. For this purpose, we …
To synthesize Maxwell optics systems, the mathematical apparatus of tensor and vector analysis is generally employed. This mathematical apparatus implies executing a great number …
This paper considers three types of tensor computations. On their basis, we attempt to formulate criteria that must be satisfied by a computer algebra system dealing with tensors. …