Abstract
We revisit fraction-free Gaussian elimination as a method for finding exact solutions of linear systems over integral domains, specifically integers and univariate polynomials. We conducted several experiments regarding common folklore about these methods such as pivoting strategies. Moreover, we find that the classical algorithms produce a unsettlingly high amount of common factors in the rows of the resulting matrices which they seem unable to detect let alone remove. We present preliminary results on remedying this fact. Finally, we apply fraction-free elimination to compute matrix inverses and to solve linear systems, and compare that to the use of fractional methods.
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