I am looking at a problem of the type
$A^P\equiv A\pmod N$,
where A is a square symmetric integer matrix, and I want to find the minimum value of the power $P$. It seems that the Howell form of $A$ could give some insight into the problem but I am not sure how to calculate it. An algorithm is described in Fast Algorithms for Linear Algebra Modulo N but it is a bit heavy to figure out an implementation from that. Mathematica has a RowReduce function that allows a value for the modulo but it can't calculate the result of any of the two examples listed in the two references.
2026-04-01 11:25:00.1775042700
Howell form for symmetric matrices modulo N
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