algorithms which compute modulo triangular sets must respect zero divisors. We present Hensel lifting as a tool for resolving them. We give an application: a modular algorithm for computing gcds of univariate polynomi...
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ISBN:
(纸本)9781538626276
algorithms which compute modulo triangular sets must respect zero divisors. We present Hensel lifting as a tool for resolving them. We give an application: a modular algorithm for computing gcds of univariate polynomials with coefficients modulo a radical triangular set over the rational numbers. We have implemented our algorithm using Maple's RECDEN package. We compare our implementation withthe procedure RegularGcd in the RegularChains package.
Hybrid sets are generalizations of sets and multisets, in which the multiplicities of elements can take any integers. this construction was proposed by Whitney in 1933 in terms of characteristic functions. Hybrid sets...
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ISBN:
(纸本)9781509057085
Hybrid sets are generalizations of sets and multisets, in which the multiplicities of elements can take any integers. this construction was proposed by Whitney in 1933 in terms of characteristic functions. Hybrid sets have been used by combinatorists to give combinatorial interpretations for several generalizations of binomial coefficients and Stirling numbers and by computer scientists to design fast algorithms for symbolic domain decompositions. We present in this paper some combinatorial results on subsets and partitions of hybrid sets.
One of the most useful computer algebra used today is calgebra and its versions, e.g. stream calculus. In the paper I show that p-adic arithmetic can be regarded as one of the natural interpretation of stream calculus...
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One of the most useful computer algebra used today is calgebra and its versions, e.g. stream calculus. In the paper I show that p-adic arithmetic can be regarded as one of the natural interpretation of stream calculus on a finite set of positive integers. Further, I define probabilities on streams using bisimulation and construct probability logic with non-well-founded syntax and non-well-founded semantics.
In this paper we represent a class of queries that contain sub-formulas with universally quantified variables using views. the queries and views considered can contain input parameters. Both views and queries are expr...
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In this paper we represent a class of queries that contain sub-formulas with universally quantified variables using views. the queries and views considered can contain input parameters. Both views and queries are expressed as unions of conjunctive formulas, where the predicates of literals are views or database relations. the negation is allowed in body views or body queries. We study the equivalence of a query and one of its expansions.
Common Logic (CL) is a recent ISO standard for exchanging logic-based information between disparate computer systems. Sharing and reasoning upon knowledge represented in CL require equation solving over terms of this ...
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Common Logic (CL) is a recent ISO standard for exchanging logic-based information between disparate computer systems. Sharing and reasoning upon knowledge represented in CL require equation solving over terms of this language. We study computationally well-behaved fragments of such solving problems and show how they can influence reasoning in CL and transformations of CL expressions.
In the design of symbolic mathematical computation systems, it is a popular choice to use the same syntax for both mathematical indeterminates and programming variables. While mathematical indeterminates are to be use...
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In the design of symbolic mathematical computation systems, it is a popular choice to use the same syntax for both mathematical indeterminates and programming variables. While mathematical indeterminates are to be used without specific values, programming variables must be initialized before being used in expressions. A problem occurs when mistakenly uninitialized programming variables are silently taken to be mathematical indeterminates. this article explores how this problem can arise and its consequences. An algorithm to analyze programs for this defect is shown along with a Maple implementation.
We show that Lagrange inversion can be used to obtain closed-form expressions for a number of series expansions of the Lambert W function. Equivalently, we obtain expressions for the nth derivative. Various integer se...
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We show that Lagrange inversion can be used to obtain closed-form expressions for a number of series expansions of the Lambert W function. Equivalently, we obtain expressions for the nth derivative. Various integer sequences related to the series expansions now can be expressed in closed form.
Modern program analysis and model-based tools are increasingly complex and multi-faceted software systems. However, at their core is invariably a component using logic for describing states and transformations between...
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Modern program analysis and model-based tools are increasingly complex and multi-faceted software systems. However, at their core is invariably a component using logic for describing states and transformations between system states. the system Z3, developed at Microsoft Research, is a Satisfiability Modulo theories (SMT) solver. It provides logic inference capabilities that are critical for the functionality of these systems. the tutorial exemplifies a number of applications of Z3 at Microsoft.
We provide an effective algorithmic method for computation of Gross-Keel-Hacking-Kontsevich potential, Fpolynomials and Bernstein-Kazhdan decoration function and it’s complexity bounds. For simply laced Lie algebras ...
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We provide an effective algorithmic method for computation of Gross-Keel-Hacking-Kontsevich potential, Fpolynomials and Bernstein-Kazhdan decoration function and it’s complexity bounds. For simply laced Lie algebras we make conjecture and provide experimental evidence that Newton polytopes for Gross-Keel-Hacking-Kontsevich potential do not contain any interior lattice points.
In this paper we investigate some Importance Sampling strategies and we apply them for the first time to the pricing of the spread options. We compare the Least Squares method to the f-divergence method in order to ch...
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In this paper we investigate some Importance Sampling strategies and we apply them for the first time to the pricing of the spread options. We compare the Least Squares method to the f-divergence method in order to choose the importance sampling functions. Our numerical results reveals that the use of the divergences is frequently less computationally and time costly.
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