Dixon's method for computing multivariate resultants by simultaneously eliminating many variables is reviewed. The method is found to be quite restrictive because often the Dixon matrix is singular, and the Dixon ...
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ISBN:
(纸本)9780897916387
Dixon's method for computing multivariate resultants by simultaneously eliminating many variables is reviewed. The method is found to be quite restrictive because often the Dixon matrix is singular, and the Dixon resultant vanished identically yielding no information about solutions for many algebraic and geometry problems. We extend Dixon's method for the case when the Dixon matrix is singular, but satisfies a condition. An efficient algorithm is developed based on the proposed extension for extracting conditions for the existence of affine solutions of a finite set of polynomials. Using this algorithm, numerous geometric and algebraic identities are derived for examples which appear intractable with other techniques of triangulation such as the successive resultant method, the Gro¨bner basis method, Macaulay resultants and Characteristic set method. Experimental results suggest that the resultant of a set of polynomials which are symmetric in the variables is relatively easier to compute using the extended Dixon's method.
The concept of anti-link is defined, and useful equivalence-preserving operations on propositional formulas based on anti-links are introduced. These operations eliminate a potentially large number of subsumed paths i...
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We illustrate the difference between sequential composition in process algebra axiomatisations like ACP and action prefixing in process calculi like CCS. We define both early and late input in a general framework exte...
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For whatever reason, formal methods remain one of the more contentious techniques in industrial software engineering. Despite some improvement in the uptake of formal methods, it is still the case that the vast majori...
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We extend static filtering in [8], a query optimization strategy based on seminaive evaluation on system graphs, so that it can efficiently handle stratified programs without extra overhead. The computation of static ...
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We extend static filtering in [8], a query optimization strategy based on seminaive evaluation on system graphs, so that it can efficiently handle stratified programs without extra overhead. The computation of static filters is formalized as a transformation so that the least fixed point of the transformation can be the static filters. The static filtering on stratified programs is shown to be complete with respect to the iterated fixed point semantics.
A syntactic error repair model is proposed, and is defined as a partial function from strings to sentences. The replacement of a substring of a string with a substring of a sentence is described by a repair pattern, w...
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A syntactic error repair model is proposed, and is defined as a partial function from strings to sentences. The replacement of a substring of a string with a substring of a sentence is described by a repair pattern, which is roughly a pair of strings of grammar symbols. The model can be efficient with some restriction on repair patterns. An LR-based implementation of the model is discussed.
Mixin-based inheritance is an inheritance technique that has been shown to subsume a variety of different inheritance mechanisms. It is based directly upon an incremental modification model of inheritance. This paper ...
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ObjectMath is a high-level programming environment and modeling language for scientific computing which supports variants and graphical browsing in the environment and integrates object-oriented constructs such as cla...
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Several methods to compute the prime implicants and the prime implicates of a negation normal form (NNF) formula are developed and implemented. An algorithm PI is introduced that is an extension to negation normal for...
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A formal framework for a calculus of real-time systems is presented. Specifications and program statements are combined into a single language called TAM (the Temporal Agent Model), that allows the user to express bot...
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