VSDITLU: A Verifiable Symbolic Definite Integral Table Look-Up

Adams, Andrew A.; Gottliebsen, Hanne; Linton, Steve; Martin, Ursula

doi:10.1007/3-540-48660-7_8

Cited by 8 publications

(2 citation statements)

References 14 publications

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“…Particular interest is in the combination of computer algebra systems (CAS) and deduction systems (DS), either for the purpose of enhancing the computational power of the DS (Ballarin et al, 1995;Harrison and Théry, 1998;Kerber et al, 1998) or in order to strengthen the reasoning capabilities of a CAS (Bauer et al, 1998;Adams et al, 1999).…”

Section: Introductionmentioning

confidence: 99%

MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems

Kohlhase

Franke

2001

Journal of Symbolic Computation

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In this article we describe the data model of the MBase system, a web-based, distributed mathematical knowledge base. This system is a mathematical service in MathWeb that offers a universal repository of formalized mathematics where the formal representation allows semantics-based retrieval of distributed mathematical facts.We classify the data necessary to represent mathematical knowledge and analyze its structure. For the logical formulation of mathematical concepts, we propose a methodology for developing representation formalisms for mathematical knowledge bases. We propose to concretely equip knowledge bases with a hierarchy of logical systems that are linked by logic morphisms. These mappings relativize formulae and proofs and thus support translation of the knowledge to the various formats currently in use in deduction systems. On the other hand they define higher language features from simpler ones and ultimately serve as a means to found the whole knowledge base in axiomatic set theory.The viability of this approach is proven by developing a sorted record-λ-calculus with dependent sorts and labeled abstraction that is well-suited both for formalizing mathematical practice and supporting efficient inference services. This "mathematical vernacular" is an extension of a sorted λ-calculus by records, dependent record sorts and selection sorts.

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Section: Introductionmentioning

confidence: 99%

MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems

Kohlhase

Franke

2001

Journal of Symbolic Computation

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“…We can obtain the infinite series forms of these six types of integrals by using integration term by term theorem; these are the major results of this paper (i.e., Theorems1-6). The study of related integral problems can refer to [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. On the other hand, we provide some integrals to do calculation practically.…”

Section: Introductionmentioning

confidence: 99%

Solving Some Types of Integrals Using Maple

Yu¹,

Chen²

2014

ujcmj

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This paper uses the mathematical software Maple for the auxiliary tool to study six types of integrals.We can obtain the infinite series forms of these six types of integrals by using integration term by term theorem. In addition, we propose some examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions by using Maple. This type of research method not only allows the discovery of calculation errors, but also helps modify the original directions of thinking from manual and Maple calculations. Therefore, Maple provides insights and guidance regarding problem-solving methods.

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Non-trivial Symbolic Computations in Proof Planning

Sorge

2000

Frontiers of Combining Systems

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VSDITLU: A Verifiable Symbolic Definite Integral Table Look-Up

Cited by 8 publications

References 14 publications

MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems

MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems

Solving Some Types of Integrals Using Maple

Non-trivial Symbolic Computations in Proof Planning

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