I have a certain 7x7 matrix whose elements are all symbolic, and I want to know the eigenvalues. I have to solve a septic equation, but it is generally impossible. However, I am only interested in the eigenvalues that are all integers, so I am attempting to find some constrains on the matrix elements (coefficient of the septic) so that its solutions are integers. I have never studied group theory before so I might be saying something wrong, but according to my poor knowledge, a polynomial is solvable if the Galois group of the equation is a solvable group. Does this mean that there are certain criteria for the coefficients so that it can be solved analytically?
2026-04-04 00:45:05.1775263505
Criteria for a solvable septic equation
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