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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    International journal of parallel programming 8 (1979), S. 9-37 
    ISSN: 1573-7640
    Keywords: Symbolic mathematical computation ; algebraic simplification ; canonical form ; regular form ; structure theorem ; elementary transcendental functions ; exponential function ; logarithm function ; trigonometric functions ; hyperbolic functions ; algebraic independence ; differential algebra ; Liouville fields
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract This paper uses elementary algebraic methods to obtain new proofs for theorems on algebraic relationships between the logarithmic and exponential functions. The main result is a multivariate version of a special case of the structure theorem due to Risch that gives, in a very explicit fashion, the possible algebraic relationships between the exponential and logarithm functions. The structure theorem has important applications to symbolic mathematical computation in that it in essence provides a canonical form for the elementary transcendental functions, and hence solves the identity problem for this class of functions. Such applications are discussed in the last section.
    Type of Medium: Electronic Resource
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  • 2
    Publication Date: 2019-06-27
    Description: Algorithms for general partial fraction decomposition are obtained by using modular polynomial arithmetic. An algorithm is presented to compute inverses modulo a power of a polynomial in terms of inverses modulo that polynomial. This algorithm is used to make an improvement in the Kung-Tong partial fraction decomposition algorithm.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA. Langley Res. Center Proc. of the 1977 MACSYMA Users' Conf. (NASA); p 253-261
    Format: text
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