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Computer algebra meets automated theorem proving: Integrating Maple and pvs
 Theorem Proving in Higher Order Logics (TPHOLs 2001), volume 2152 of LNCS
, 2001
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Trustable Communication Between Mathematics Systems
 IN PROC. OF CALCULEMUS 2003
, 2003
"... This paper presents a rigorous, unified framework for facilitating communication between mathematics systems. A mathematics system is given one or more interfaces which oer deductive and computational services to other mathematics systems. To achieve communication between systems, a client inter ..."
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This paper presents a rigorous, unified framework for facilitating communication between mathematics systems. A mathematics system is given one or more interfaces which oer deductive and computational services to other mathematics systems. To achieve communication between systems, a client interface is linked to a server interface by an asymmetric connection consisting of a pair of translations. Answers to requests are trustable in the sense that they are correct provided a small set of prescribed conditions are satis ed. The framework is robust with respect to interface extension and can process requests for abstract services, where the server interface is not fully specified.
Hidden Verification for Computational Mathematics
"... We present hidden verification as a means to make the power of computational logic available to users of computer algebra systems while shielding them fi'om its complexity. We have implemented in PVS a library of facts about elementary and transcendental functions, and automatic procedures ..."
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Cited by 4 (2 self)
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We present hidden verification as a means to make the power of computational logic available to users of computer algebra systems while shielding them fi'om its complexity. We have implemented in PVS a library of facts about elementary and transcendental functions, and automatic procedures to attempt proofs of continuity, convergence and differentiability for functions in this class. These are called directly from Maple by a simple pipelined interface. Hence we are able to support the analysis of differential equations in Maple by direct calls to PVS for: result refinement and verification, discharge of verification conditions, harnesses to ensure more reliable differential equation solvers, and verifiable lookup tables.
Digital Look Up Tables and Real Number Theorem Proving
, 2001
"... We consider the utility of digital look up tables, as adjuncts/helpers to computer algebra systems. The requirements for dealing with logical side conditions raised by such tables are considered and proposals for using theorem proving technology as black box aids are considered. In addition, the ..."
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We consider the utility of digital look up tables, as adjuncts/helpers to computer algebra systems. The requirements for dealing with logical side conditions raised by such tables are considered and proposals for using theorem proving technology as black box aids are considered. In addition, the use of real number theorem proving libraries to support validation of table entries is also presented.
Definite Integration of Parametric Rational Functions: Applying a DITLU
, 2000
"... In [2] we presented a Definite Integral Table Lookup (the DITLU) for parametric functions, including a minimal prototype implementation demonstrating its capabilities. In this paper we present a possible application of a DITLU, which would extend its utility for a modest investment of effort. The na ..."
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In [2] we presented a Definite Integral Table Lookup (the DITLU) for parametric functions, including a minimal prototype implementation demonstrating its capabilities. In this paper we present a possible application of a DITLU, which would extend its utility for a modest investment of effort. The naive algorithm for indefinite integration of rational functions (see e.g. [12, x2.10]) can be implemented for parametric rational functions. This involves splitting the rational function integrand using partial fractions. The resulting integrands all fall within a limited class which may be covered in a DITLU by a very small number of table entries. Extensions of this idea to less naive integration algorithms, and the number of table entries required to implement them, are also considered.
Towards an KnowledgeCentered Infrastructure for WebBased Mathematics
, 2001
"... It is plausible to assume that the way we do (conceive, develop, visualize ..."
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It is plausible to assume that the way we do (conceive, develop, visualize
Article Submitted to Journal of Symbolic Computation
"... Hidden verification for computational ..."