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We study a prey-predator model based on the classical Lotka–Volterra system with Leslie–Gower and Holling IV schemes and a constant-effort harvesting. Our goal is twofold: to present the model proposed by Cheng and Zhang in 2021, pointing out some inconsistencies; to analyse the number and type of equilibrium points of the model. We end by proving the stability of the meaningful equilibrium point, according to the distribution of the eigenvalues. published

Runge-Kutta schemes play a very important role in solving ordinary differential equations numerically. At first we want to present the Sage routine for calculation of Butcher matrix, we call it an rk package. We tested our Sage routine in several numerical experiments with standard and symplectic schemes and verified our result by corporation with results of the calculations made by hand.Second, in Sage there are the excellent tools for investigation of algebraic sets, based on Gröbner basis technique. As we all known, the choice of parameters in Runge- Kutta scheme is free. By the help of these tools we study the algebraic properties of the manifolds in affine space, coordinates of whose are Butcher coefficients in Runge-Kutta scheme. Results are given both for explicit Runge-Kutta scheme and implicit Runge-Kutta scheme by using our rk package. Examples are carried out to justify our results. All calculation are executed in the computer algebra system Sage.

Darbā "Aptuvenu kopīgu dalītāju atrašana ar režģiem" tiek realizēts prototips, kas aprēķina aptuvenu kopīgu dalītāju nejauši uzģenerētam skaitļu komplektam. Prototips ļauj eksperimentālā veidā aprēķināt parametrus, pie kuriem dalītājs ir aprēķināms/neaprēķināms Prototips tiek veidots lietojot matemātisko programmatūru SageMath., In the work "Finding approximate common divisors via lattices" prototype is implemented that finds approximate common divisor of randomly generated set of integers. Prototype supports determining parameters for which it is possible/impossible to find such divisor. Prototype is implemented using mathematical software system SageMath.