Scratchpad II: An Abstract Datatype System for Mathematical Computation

Jenks, Richard D.; Sutor, Robert S.; Watt, Stephen M.

doi:10.1007/978-1-4684-7074-1_7

Cited by 3 publications

(3 citation statements)

References 2 publications

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“…A number of computer algebra systems with object-oriented features have been developed during recent years. One of the best known is the AXI0.\1 system [22J, a descendant of SCRATCH-PAD [23], which has a type system that in some sense is object-oriented, even though the language constructs provided are different from the ones usually found in object-oriented languages. Another example is the Mathematiea-inspired system AlgBench [24], which extends the pattern matching of Mathematica to inheritance-based unification.…”

Section: Related Workmentioning

confidence: 99%

ObjectMath – An Object‐Oriented Language and Environment for Symbolic and Numerical Processing in Scientific Computing

Viklund

Fritzson

1994

Scientific Programming

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ObjectMath is a language for scientific computing that integrates object-oriented constructs with features for symbolic and numerical computation. Using ObjectMath, complex mathematical models may be implemented in a natural way. The ObjectMath programming environment provides tools for generating efficient numerical code from such models. Symbolic computation is used to rewrite and simplify equations before code is generated. One novelty of the ObjectMath approach is that it provides a comman language and an integrated environment for this kind of mixed symbolic/numerical computation. The motivation for this work is the current low-level state of the art in programming for scientific computing. Much numerical software is still being developed the traditional way in Fortran. This is especially true in application areas such as machine elements analysis, where complex nonlinear problems are the norm. We believe that tools like ObjectMath can increase productivity and quality, thus enabling users to solve problems that are too complex to handle with traditional tools.

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Section: Related Workmentioning

confidence: 99%

ObjectMath – An Object‐Oriented Language and Environment for Symbolic and Numerical Processing in Scientific Computing

Viklund

Fritzson

1994

Scientific Programming

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“…Here, a +-> b is Scratchpad II notation for the anonymous function a → b. 6 Now the recursive calls to integrate are able to access the leading terms of the series computed so far. When defined this way, the exponential function evaluates each term only once.…”

Section: Using Fixed Point Operators For Seriesmentioning

confidence: 99%

A fixed point method for power series computation

Watt

1989

Symbolic and Algebraic Computation

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This paper presents a novel technique for manipulating structures which represent infinite power series. When power series are implemented using lazy evaluation, many operations can be written as simple recursive procedures. For example, the programs to generate the series for the elementary transcendental functions are almost transliterations of the defining integral equations. However, a naive lazy algorithm provides an implementation which may be orders of magnitude slower than a method which manipulates the coefficients explicitly. The technique described here allows a power series to be defined in a very natural but computationally inefficient way and transforms it to an equivalent, efficient form. This is achieved by using a fixed point operator on the delayed part to remove redundant calculations. The paper describes this fixed point method and the class of problems to which it is applicable. It has been used in Scratchpad II to improve the performance of a number of operations on infinite series, including division, reversion, special functions and the solution of linear and non-linear ordinary differential equations. A few examples are given of the method and of the speed up obtained. To illustrate, the computation of the first n terms of exp(u) for a dense, infinite series u is reduced from O(n 4) to O(n 2) coefficient operations, the same as required by the standard on-line algorithms.

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“…Scratchpad [Jenks et al, 1988] is a computer algebra system based on the "abstract data type" view of computing, where the various data types are constructed from elementary ones, such as Integer, by means of functors (functions which return types) such as Sparse-UnivariatePolynomial or Fraction. The types consist of a data representation and operations, so that a type such as List(Integer) provides the operations length etc.…”

Section: Introductionmentioning

confidence: 99%