Rule-based integration: An extensive system of symbolic integration rules

Rich, Albert D.; Scheibe, Patrick; Abbasi, Nasser M

doi:10.21105/joss.01073

Cited by 25 publications

(15 citation statements)

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“…Later research focused more on methods that are complete for certain types of integrands, such as Risch's algorithm [19]. More recently, Rubi (rule-based integration) has been demonstrated to be a powerful technique [39]. However, none of these work focuses on formal verification.…”

Section: Related Workmentioning

confidence: 99%

Verified Interactive Computation of Definite Integrals

Zhan

2021

Automated Deduction – CADE 28

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Symbolic computation is involved in many areas of mathematics, as well as in analysis of physical systems in science and engineering. Computer algebra systems present an easy-to-use interface for performing these calculations, but do not provide strong guarantees of correctness. In contrast, interactive theorem proving provides much stronger guarantees of correctness, but requires more time and expertise. In this paper, we propose a general framework for combining these two methods, and demonstrate it using computation of definite integrals. It allows the user to carry out step-by-step computations in a familiar user interface, while also verifying the computation by translating it to proofs in higher-order logic. The system consists of an intermediate language for recording computations, proof automation for simplification and inequality checking, and heuristic integration methods. A prototype is implemented in Python based on HolPy, and tested on a large collection of examples at the undergraduate level.

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Section: Related Workmentioning

confidence: 99%

Verified Interactive Computation of Definite Integrals

Zhan

2021

Automated Deduction – CADE 28

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“…Rewriting using a database is perhaps most likely to be successful for specific tasks and in combination with advanced hand-written search heuristics (or heuristics generated via machine learning). A prominent example of the hand-written approach is Rubi [9] which uses a decision tree of thousands of rewrite rules to simplify indefinite integrals.…”

Section: Formulas As Rewrite Rulesmentioning

confidence: 99%

FunGrim: A Symbolic Library for Special Functions

Johansson¹

2020

Lecture Notes in Computer Science

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“…Some of these integrals were evaluated using the Rule-based integrator [14]. In order to get the contribution from an entire triangle, which can always be decomposed into two right triangles, as shown in Fig.…”

Section: Modelmentioning

confidence: 99%

The Stray and Demagnetizing Field of a Homogeneously Magnetized Tetrahedron

2019

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Rule-based integration: An extensive system of symbolic integration rules

Abstract: LicenseAuthors of papers retain copyright and release the work under a Creative Commons Attribution 4.0 International License (CC-BY).

Cited by 25 publications

References 3 publications

Verified Interactive Computation of Definite Integrals

Verified Interactive Computation of Definite Integrals

FunGrim: A Symbolic Library for Special Functions

The Stray and Demagnetizing Field of a Homogeneously Magnetized Tetrahedron

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