I am solving a computer materials science problem in the MAPLE software package. Solving this problem requires calculating the eigenvalues ​​of matrices of sufficiently large sizes (16×16 or more) and further plotting of graphs using these eigenvalues. The elements of these matrices are trigonometric functions of fairly curved angles. I encountered the problem that when the matrix reaches 24×24 or more in size, MAPLE simply freezes and stops producing any results. I am confident in the correctness of my code, because when working with matrices whose dimensions are smaller than 24×24, MAPLE produces correct results. I calculate the eigenvalues ​​of matrices using the eigenvals() function.

I thought that the problem could be solved by reducing the accuracy of the calculations by decreasing the Digits value. However, in this case, the eigenvalues ​​of the matrices began to be output in the form of RootOf(), despite the fact that at the beginning of the entire code I wrote _EnvExplicit := true. This option does not suit me, since MAPLE does not build graphs based on the eigenvalues ​​of matrices output in the RootOf() format. Using the allvalues() function also does not help get rid of RootOf(). Please tell me how to solve this problem?