The article describes one of the methods for computing determinants without using fractions proposed by Bareiss. This problem has a clear algorithmic character in nature and refers to the field of computer algebra. The implementation of this algorithm is proposed in the known Maxima system of symbolic computations. In addition, this method makes it possible to get enough convenient formula for the calculation of the matrix of unitriangular transformation of a quadratic form to a canonical one.
It is shown that heat energy transfer from the source to the medium is accompanied by rheological transitions. Physical parameters of the medium change in the rheological transition zone due to heat energy flow transfer at a certain speed. It is shown that use of linear gradient laws during description of heat energy transfer processes leads to great differences between theoretical and experimental results, as well as the paradox of infinite spreading speed of disturbances of temperature fields. For mathematical description of heat energy transfer processes in mediums, it is proposed to use the method of irreversible rheological transitions and zero gradient, thus providing solutions of nonlinear differential equations in analytical form.