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Flat matching
 Journal of Symbolic Computation
"... We study matching in flat theories both from theoretical and practical points of view. A flat theory is defined by the axiom f(x, f(y), z). = f(x, y, z) that indicates that nested occurrences of the function symbol f can be flattened out. From the theoretical side, we design a procedure to solve a s ..."
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We study matching in flat theories both from theoretical and practical points of view. A flat theory is defined by the axiom f(x, f(y), z). = f(x, y, z) that indicates that nested occurrences of the function symbol f can be flattened out. From the theoretical side, we design a procedure to solve a system of flat matching equations and prove its soundness, completeness, and minimality. The minimal complete set of matchers for such a system can be infinite. The procedure enumerates this set and stops if it is finite. We identify a class of problems on which the procedure stops. From the practical point of view, we look into restrictions of the procedure that give an incomplete terminating algorithm. From this perspective, we give a set of rules that, in our opinion, describes the precise semantics for the flat matching algorithm implemented in the Mathematica system. 1.
Symbolic Mathematics System Evaluators
 In Proceedings of the 1996 International Symposium on Symbolic and Algebraic Computation
, 1996
"... “Evaluation ” of expressions and programs in a computer algebra system is central to every system, but inevitably fails to provide complete satisfaction. Here we explain the conflicting requirements, describe some solutions from current systems, and propose alternatives that might be preferable some ..."
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“Evaluation ” of expressions and programs in a computer algebra system is central to every system, but inevitably fails to provide complete satisfaction. Here we explain the conflicting requirements, describe some solutions from current systems, and propose alternatives that might be preferable sometimes. We give examples primarily from Axiom, Macsyma, Maple, Mathematica, with passing mention of a few other systems. 1
Matching and Unification for the ObjectOriented Symbolic Computation System AlgBench
 In Proc. of the 3rd Intern. Symposium on Design and Implementation of Symbolic Computation Systems (DISCO'93), SpringerVerlag, LNCS 722
, 1993
"... . Term matching has become one of the most important primitive operations for symbolic computation. This paper describes the extension of the objectoriented symbolic computation system AlgBench with pattern matching and unification facilities. The various pattern objects are organized in subclasses ..."
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. Term matching has become one of the most important primitive operations for symbolic computation. This paper describes the extension of the objectoriented symbolic computation system AlgBench with pattern matching and unification facilities. The various pattern objects are organized in subclasses of the class of the composite expressions. This leads to a clear design and to a distributed implementation of the pattern matcher in the subclasses. New pattern object classes can consequently be added easily to the system. Huet's and our simple mark and retract algorithm for standard unification as well as Stickel's algorithm for associative commutative unification have been implemented in an objectoriented style. Unifiers are selected at runtime. We extend Mathematica's typeconstrained pattern matching by taking into account inheritance information from a userdefined hierarchy of object types. The argument unification is basically instance variable unification. The improvement of the ...
By Ian Gregory,
"... Deviance critical values for finite sample size when testing the reduction of (G)ARCH(1,1) to a ..."
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Deviance critical values for finite sample size when testing the reduction of (G)ARCH(1,1) to a
Excerpts from a proposal to the National Science Foundation on Programming Environments and Tools for Advanced Scientific Computation
"... "by hand" mathematical models whose consequences can be simulated by running computer programs. These programs are typically written in Fortran, but are increasingly being written in C, C++, or other languages that have better tools for abstraction and data structures. In part, the computa ..."
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"by hand" mathematical models whose consequences can be simulated by running computer programs. These programs are typically written in Fortran, but are increasingly being written in C, C++, or other languages that have better tools for abstraction and data structures. In part, the computational approach we advocate involves the use of computers in that earlier "by hand" stage of model formulation, using symbolic mathematics. The blossoming of this area via commercial programs typified by Mathematica and Maple, as well as some less widely used but still viable competitors (Axiom, Macsyma, MuPAD) might suggests that this approach is (a) successful and (b) needs no more academic research. Actually, the relatively higher level of activity (and funding) in Europe has demonstrated that important results remain to be found in advancement of algorithms and building systems. Work at RISCLinz (Austria), ETH (Zurich), CAN (Netherlands), INRIA (France) and the multinational POSSO project are ju