A survey of certain characterizations of complexity classes in an algebraic, machine-independent manner is presented, together with some applications to weak theories of arithmetic and higher-order functionals. Functi...
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A survey of certain characterizations of complexity classes in an algebraic, machine-independent manner is presented, together with some applications to weak theories of arithmetic and higher-order functionals. Function algebras are examined, and hierarchies are defined. Bounded arithmetic theories are presented.< >
A demonstration of how to use the mathematical properties of available algebraic theory for developing optimized computations on efficient architectures is presented. A systematic description of the theoretical concep...
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A demonstration of how to use the mathematical properties of available algebraic theory for developing optimized computations on efficient architectures is presented. A systematic description of the theoretical concepts of the algebra of surrogate fields that constitute the foundations of quadratic residue arithmetic is presented. Using the properties of the quadratic residue number system for developing complex digital signal-processing architectures is explained through the design of a fast Fourier transform processor.< >
Poly topes of (characteristic) polynomials arise when systems experience realparameter variations. The paper presents a sufficient condition, requiring only a finite number of computations, for determining if all the ...
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Poly topes of (characteristic) polynomials arise when systems experience realparameter variations. The paper presents a sufficient condition, requiring only a finite number of computations, for determining if all the roots of a polytope of polynomials have prescribed damping ratios of discrete-time systems. It also gives a measure of robustness for a given polytope of polynomials.
The proceedings contain 79 papers. The special focus in this conference is on computeralgebra. The topics include: Expression optimization using high-level knowledge;catfact: computeralgebraic tools for applications...
ISBN:
(纸本)9783540515173
The proceedings contain 79 papers. The special focus in this conference is on computeralgebra. The topics include: Expression optimization using high-level knowledge;catfact: computeralgebraic tools for applications of catastrophe theory;computeralgebra application for investigating integrability of nonlinear evolution systems;computer classification of integrable seventh order MKdV — Like equations;symbolic computation and the finite element method;application of lie group and computeralgebra to nonliner mechanics;hierarchical symbolic computations in the analysis of large-scale dynamical systems;schoonschip for computing of gravitino interaction cross sections in N=2 supergravity;creation of efficient symbolic-numeric interface;complexity of quantifier elimination in the theory of ordinary differential equations;Automatic generation of FORTRAN-Coded Jacobians and Hessians;laplace transformations in reduce 3;Reduce 3. 2 on iAPX86/286 — based personal computers;some extensions and applications of reduce system;Infinite structures in scratchpad II;Application of a structured LISP system to computeralgebra;number-theoretic transforms of prescribed length;A hybrid algebraic-numeric system ANS and its preliminary implementation;The calculation of QCD triangular Feynman graphs in the external gluonic field using reduce-2 system;computeralgebra application for determining local symmetries of differential equations;groups and polynomials;trace calculations for gauge theories on a personal computer;evaluation of plasma fluid equations collision integrals using reduce;computerized system of analytic transformations for analysing of differential equations;integral equation with hidden eigenparameter solver: Reduce + fortran in tandem;combinatorial aspects of simplification of algebraic expressions;dynamic program improvement;computeralgebra and numerical convergence;symbolic computation in relativity theory.
Determinantal representations of algebraic curves are interesting in themselves, and their classification is equivalent to the simultaneous classification of triples of matrices. We present a complete description of d...
Determinantal representations of algebraic curves are interesting in themselves, and their classification is equivalent to the simultaneous classification of triples of matrices. We present a complete description of determinantal representations of smooth irreducible curves over any algebraically closed field. We used the notion of the class of divisors of the vector bundle corresponding to a determinantal representation; we prove that two determinantal representations of a smooth curve F are equivalent if and only if the classes of divisors of the corresponding vector bundles coincide. We give a precise characterization of those classes of divisors that arise from vector bundles corresponding to determinantal representations of F . Then we obtain a parametrization of determinantal representations of F , up to equivalence, by the points of the Jacobian variety of F not on some exceptional subvariety. In particular it follows that any smooth curve of order 3 or greater possesses an infinite number of nonequivalent determinantal representations. We also specialize our results to symmetrical and self-adjoint representations.
The number of publications about burst-correcting codes during the last few years suggest a certain revival of this topic. Clearly in all kinds of applications one observes that stored or transmitted data can be corru...
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In recent years a wide variety of process algebras has been proposed in the literature. Often these process algebras are closely related: they can be viewed as homomorphic images, submodels or restrictions of each oth...
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The characteristic polynomial assignment for discrete 2-dimensional systems described by the Fornasini-Marchesini model is considered. The similarities and differences of the solutions to this problem, using Roesser&#...
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The characteristic polynomial assignment for discrete 2-dimensional systems described by the Fornasini-Marchesini model is considered. The similarities and differences of the solutions to this problem, using Roesser's and Fornasini and Marchesini's models, are discussed. Furthermore, the assignment of a part of the characteristic polynomial and the simultaneous calculation of the residual polynomial for the Fornasini-Marchesini model is considered.
The proceedings contain 13 papers. The special focus in this conference is on Trends in computeralgebra. The topics include: Application of scratchpad to problems in special functions and combinatorics;Programming wi...
ISBN:
(纸本)9783540189282
The proceedings contain 13 papers. The special focus in this conference is on Trends in computeralgebra. The topics include: Application of scratchpad to problems in special functions and combinatorics;Programming with abstract data types: The symmetry package SPDE in scratchpad;algebraic computation, numerical computation and verified inclusions;intelligent computeralgebra system: Myth, fancy or reality?;Scratchpad II: An abstract datatype system for mathematical computation;current trends in rewriting techniques and related problems;applications of Gröbner bases in non-linear computational geometry;factorisation of polynomials: Old ideas and recent results;generalized fourier transforms;representations of groups over finite fields;computational methods in constructive Galois theory.
Gröbner bases are certain finite sets of multivariate polynomials. Many problems in polynomial ideal theory (algebraic geometry, non-linear computational geometry) can be solved by easy algorithms after transform...
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