Solution: 2022-20 4 by 4 symmetric integral matrices

Let \(S\) be the set of all 4 by 4 integral positive-definite symmetric unimodular matrices. Define an equivalence relation \( \sim \) on \(S\) such that for any \( A,B \in S\), we have \(A \sim B\) if and only if \(PAP^\top = B\) for some integral unimodular matrix \(P\). Determine \(S ~/\sim \).

The best solution was submitted by 김기수 (KAIST 수리과학과 18학번, +4). Congratulations!

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