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Fast Symbolic Linear Algebra CAS?

I am a regular user of Mathematica, Julia, and MATLAB but I am looking for something different. The problem I am trying to solve in Mathematica only requires (dense) linear algebra to specify but is of a size such that Mathematica takes too long (and seems to automatically halt the computation after like 18 hours, when it should finish in a week or so). I am looking for a symbolic solution and not a numeric solution (to then use a machine learning approach on the resulting equations). I was wondering if anyone knew if there are more efficient symbolic packages. Checking around it looks like Singularity or Machaly2 may be what's right for this problem?