Optimal method to invert symbolic matrix

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If I read the source code correctly, a matrix defined over SR is inverted by the Moore-Penrose pseudo-inversion. For a real, symmetric, symbolic, full-rank matrix, is this algorithm optimal? Or is there another algorithm that would be a) less memory intensive, and/or b) less time-consuming. [In my particular case, the attempted inversion of a 4x4 matrix runs out of memory (8 GB) after approximately 15 hours.]