Computer algebra systems typically drop some degenerate cases when
evaluating expressions, e.g., x/x becomes 1 dropping the case x=0. We
claim that it is feasible in practice to compute also the degenerate
cases yielding guarded expressions. We work over real closed fields
but our ideas about handling guarded expression can be easily
transferred to other situations. Using formulas as guards provides a
powerful tool for heuristically reducing the combinatorial explosion
of cases: equivalent, redundant, tautological, and contradictive cases
can be detected by simplification and quantifier elimination. Our
approach allows to simplify the expressions on the basis of
simplification knowledge on the logical side. Our method is
implemented in the REDUCE package GUARDIAN based on REDLOG.
Andreas Dolzmann and Thomas Sturm. Guarded expressions in practice. In
Wolfgang W. Küchlin, editor, Proceedings of the 1997
International Symposium on Symbolic and Algebraic Computation (ISSAC
97), pages 376-383, New York, July 1997. ACM, ACM Press.
