Abstract
The possibilities of modern packages of symbolic mathematics for the scientific work of novice researchers in mathematics are discussed. Counterexamples for Schwartz theorem on the equality of mixed derivatives are considered. It is shown how you can use the graphical and computational capabilities of symbolic mathematics packages for their analysis so that novice researchers with the traditional engineering background in mathematics understand them. The article focuses on the problems of ambiguous perception of the PC user of three-dimensional graphic images on the monitor screen. This is important for operators who make decisions based on information obtained in a mixed virtuality or mixed reality environment. The analysis of counterexamples for the Schwartz theorem is carried out using both classical mathematics and possibilities of symbolic mathematics packages. It is shown that this assertion is not necessary. During the virtual demonstration of three-dimensional graphic objects, recommendations on their perception in terms of information environments are provided.
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