Experience with FORMAC algorithm design
Communications of the ACM
The application of symbolic mathematics to a singular perturbation problem
ACM '72 Proceedings of the ACM annual conference - Volume 2
REDUCE 2: A system and language for algebraic manipulation
SYMSAC '71 Proceedings of the second ACM symposium on Symbolic and algebraic manipulation
The exact analysis of sparse rectangular linear systems
ACM Transactions on Mathematical Software (TOMS)
The Algebraic Solution of Sparse Linear Systems via Minor Expansion
ACM Transactions on Mathematical Software (TOMS)
The Exact Solution of Linear Equations with Rational Function Coefficients
ACM Transactions on Mathematical Software (TOMS)
A Comparison of Algorithms for the Exact Solution of Linear Equations
ACM Transactions on Mathematical Software (TOMS)
The REDUCE system for computer algebra
ACM '75 Proceedings of the 1975 annual conference
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This paper discusses some of the problems encountered during the solution of a large system of sparse linear equations with algebraic coefficients, using REDUCE 2. Of particular importance is intermediate expression swell, which ultimately uses up all the available storage, and produces voluminous unreadable output. By optimally ordering the equations (optimal pivoting algorithms), and decomposing the intermediate expressions, so as to share common sub-expressions (“hash coded CONS”), a considerable saving in storage is achieved. By suitably renaming frequently used common sub-expressions, using the table built up above, and outputting these first, followed by the more complex expressions, a simplification in the output occurs. These techniques are general, and may be useful in any problem with large expressions to store and output.