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Symbolic Computation of Divided Differences
, 1999
"... Divided differences are enormously useful in developing stable and accurate numerical formulas. For example, programs to compute f(x)  f(y) as might occur in integration, can be notoriously inaccurate. Such problems can be cured by approaching these computations through divided difference formulati ..."
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Divided differences are enormously useful in developing stable and accurate numerical formulas. For example, programs to compute f(x)  f(y) as might occur in integration, can be notoriously inaccurate. Such problems can be cured by approaching these computations through divided difference formulations. This paper provides a guide to divided difference theory and practice, with a special eye toward the needs of computer algebra systems that should be programmed to deal with these oftenmessy formulas.
DRAFT: Comments on Sets in Computer Algebra Systems, especially including Infinite Indexed Sets
, 2012
"... Computing with “sets ” is wellexplored in the programminglanguage and datastructure literature. Many languages have one or more set representations as well as operations for these sets. Unfortunately, the notion of set in mathematics is far more powerful than the notional support offered by ordin ..."
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Computing with “sets ” is wellexplored in the programminglanguage and datastructure literature. Many languages have one or more set representations as well as operations for these sets. Unfortunately, the notion of set in mathematics is far more powerful than the notional support offered by ordinary programming languages. The programming languages ’ notations and operations work for explicit finite sets only, not (for