Computable number (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Computable number" in English language version.

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10doi.org

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2eudml.org

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abelard.org

Turing (1936). Turing, A. M. (1936). "On Computable Numbers, with an Application to the Entscheidungsproblem". Proceedings of the London Mathematical Society. Series 2. 42 (1) (published 1937): 230–65. doi:10.1112/plms/s2-42.1.230. S2CID 73712.
Turing, A. M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. Series 2. 43 (6) (published 1937): 544–6. doi:10.1112/plms/s2-43.6.544. Computable numbers (and Turing's a-machines) were introduced in this paper; the definition of computable numbers uses infinite decimal sequences.

ams.org

mathscinet.ams.org

Pour-El, Marian Boykan; Richards, Ian (1983). "Noncomputability in analysis and physics: a complete determination of the class of noncomputable linear operators". Advances in Mathematics. 48 (1): 44–74. doi:10.1016/0001-8708(83)90004-X. MR 0697614.
Rogers, Hartley, Jr. (1959). "The present theory of Turing machine computability". Journal of the Society for Industrial and Applied Mathematics. 7: 114–130. MR 0099923.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Kushner, Boris A. (2006). "The constructive mathematics of A. A. Markov". The American Mathematical Monthly. 113 (6): 559–566. doi:10.2307/27641983. MR 2231143.

archive.org

Minsky (1967). Minsky, Marvin (1967). "9. The Computable Real Numbers". Computation: Finite and Infinite Machines. Prentice-Hall. ISBN 0-13-165563-9. OCLC 0131655639.

arxiv.org

O’Connor, Russell (2008). "Certified Exact Transcendental Real Number Computation in Coq". Theorem Proving in Higher Order Logics. Lecture Notes in Computer Science. Vol. 5170. pp. 246–261. arXiv:0805.2438. doi:10.1007/978-3-540-71067-7_21. ISBN 978-3-540-71065-3. S2CID 17959745.

books.google.com

Bridges & Richman (1987), p. 58. Bridges, Douglas; Richman, Fred (1987). Varieties of Constructive Mathematics. Cambridge University Press. ISBN 978-0-521-31802-0.

doi.org

van der Hoeven (2006). van der Hoeven, Joris (2006). "Computations with effective real numbers". Theoretical Computer Science. 351 (1): 52–60. doi:10.1016/j.tcs.2005.09.060.
Pour-El, Marian Boykan; Richards, Ian (1983). "Noncomputability in analysis and physics: a complete determination of the class of noncomputable linear operators". Advances in Mathematics. 48 (1): 44–74. doi:10.1016/0001-8708(83)90004-X. MR 0697614.
Turing (1936). Turing, A. M. (1936). "On Computable Numbers, with an Application to the Entscheidungsproblem". Proceedings of the London Mathematical Society. Series 2. 42 (1) (published 1937): 230–65. doi:10.1112/plms/s2-42.1.230. S2CID 73712.
Turing, A. M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. Series 2. 43 (6) (published 1937): 544–6. doi:10.1112/plms/s2-43.6.544. Computable numbers (and Turing's a-machines) were introduced in this paper; the definition of computable numbers uses infinite decimal sequences.
Rice (1954). Rice, Henry Gordon (1954). "Recursive real numbers". Proceedings of the American Mathematical Society. 5 (5): 784–791. doi:10.1090/S0002-9939-1954-0063328-5. JSTOR 2031867.
Specker (1949). Specker, E. (1949). "Nicht konstruktiv beweisbare Sätze der Analysis" (PDF). Journal of Symbolic Logic. 14 (3): 145–158. doi:10.2307/2267043. JSTOR 2267043. S2CID 11382421. Archived (PDF) from the original on 2018-07-21.
Hirst (2007). Hirst, Jeffry L. (2007). "Representations of reals in reverse mathematics". Bulletin of the Polish Academy of Sciences, Mathematics. 55 (4): 303–316. doi:10.4064/ba55-4-2.
Kushner, Boris A. (2006). "The constructive mathematics of A. A. Markov". The American Mathematical Monthly. 113 (6): 559–566. doi:10.2307/27641983. MR 2231143.
Boehm, Hans-J.; Cartwright, Robert; Riggle, Mark; O'Donnell, Michael J. (8 August 1986). "Exact real arithmetic: A case study in higher order programming" (PDF). Proceedings of the 1986 ACM conference on LISP and functional programming - LFP '86. pp. 162–173. doi:10.1145/319838.319860. ISBN 0897912004. S2CID 12934546. Archived (PDF) from the original on 2020-09-24.
O’Connor, Russell (2008). "Certified Exact Transcendental Real Number Computation in Coq". Theorem Proving in Higher Order Logics. Lecture Notes in Computer Science. Vol. 5170. pp. 246–261. arXiv:0805.2438. doi:10.1007/978-3-540-71067-7_21. ISBN 978-3-540-71065-3. S2CID 17959745.
Gowland, Paul; Lester, David (2001). "A Survey of Exact Arithmetic Implementations" (PDF). Computability and Complexity in Analysis. Lecture Notes in Computer Science. Vol. 2064. Springer. pp. 30–47. doi:10.1007/3-540-45335-0_3. ISBN 978-3-540-42197-9. Archived (PDF) from the original on 2022-03-24.

eudml.org

Mazur, Stanisław (1963). Grzegorczyk, Andrzej; Rasiowa, Helena (eds.). Computable analysis. Rozprawy Matematyczne. Vol. 33. Institute of Mathematics of the Polish Academy of Sciences. p. 4.
Hirst (2007). Hirst, Jeffry L. (2007). "Representations of reals in reverse mathematics". Bulletin of the Polish Academy of Sciences, Mathematics. 55 (4): 303–316. doi:10.4064/ba55-4-2.

github.com

Lambov (2015). Lambov, Branimir (5 April 2015). "RealLib". GitHub.

jstor.org

Rice (1954). Rice, Henry Gordon (1954). "Recursive real numbers". Proceedings of the American Mathematical Society. 5 (5): 784–791. doi:10.1090/S0002-9939-1954-0063328-5. JSTOR 2031867.
Specker (1949). Specker, E. (1949). "Nicht konstruktiv beweisbare Sätze der Analysis" (PDF). Journal of Symbolic Logic. 14 (3): 145–158. doi:10.2307/2267043. JSTOR 2267043. S2CID 11382421. Archived (PDF) from the original on 2018-07-21.

rero.ch

doc.rero.ch

Specker (1949). Specker, E. (1949). "Nicht konstruktiv beweisbare Sätze der Analysis" (PDF). Journal of Symbolic Logic. 14 (3): 145–158. doi:10.2307/2267043. JSTOR 2267043. S2CID 11382421. Archived (PDF) from the original on 2018-07-21.

semanticscholar.org

api.semanticscholar.org

Turing (1936). Turing, A. M. (1936). "On Computable Numbers, with an Application to the Entscheidungsproblem". Proceedings of the London Mathematical Society. Series 2. 42 (1) (published 1937): 230–65. doi:10.1112/plms/s2-42.1.230. S2CID 73712.
Turing, A. M. (1938). "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction". Proceedings of the London Mathematical Society. Series 2. 43 (6) (published 1937): 544–6. doi:10.1112/plms/s2-43.6.544. Computable numbers (and Turing's a-machines) were introduced in this paper; the definition of computable numbers uses infinite decimal sequences.
Specker (1949). Specker, E. (1949). "Nicht konstruktiv beweisbare Sätze der Analysis" (PDF). Journal of Symbolic Logic. 14 (3): 145–158. doi:10.2307/2267043. JSTOR 2267043. S2CID 11382421. Archived (PDF) from the original on 2018-07-21.
Boehm, Hans-J.; Cartwright, Robert; Riggle, Mark; O'Donnell, Michael J. (8 August 1986). "Exact real arithmetic: A case study in higher order programming" (PDF). Proceedings of the 1986 ACM conference on LISP and functional programming - LFP '86. pp. 162–173. doi:10.1145/319838.319860. ISBN 0897912004. S2CID 12934546. Archived (PDF) from the original on 2020-09-24.
O’Connor, Russell (2008). "Certified Exact Transcendental Real Number Computation in Coq". Theorem Proving in Higher Order Logics. Lecture Notes in Computer Science. Vol. 5170. pp. 246–261. arXiv:0805.2438. doi:10.1007/978-3-540-71067-7_21. ISBN 978-3-540-71065-3. S2CID 17959745.

springer.com

link.springer.com

Gowland, Paul; Lester, David (2001). "A Survey of Exact Arithmetic Implementations" (PDF). Computability and Complexity in Analysis. Lecture Notes in Computer Science. Vol. 2064. Springer. pp. 30–47. doi:10.1007/3-540-45335-0_3. ISBN 978-3-540-42197-9. Archived (PDF) from the original on 2022-03-24.

uni.wroc.pl

fricas-wiki.math.uni.wroc.pl

Boehm, Hans-J.; Cartwright, Robert; Riggle, Mark; O'Donnell, Michael J. (8 August 1986). "Exact real arithmetic: A case study in higher order programming" (PDF). Proceedings of the 1986 ACM conference on LISP and functional programming - LFP '86. pp. 162–173. doi:10.1145/319838.319860. ISBN 0897912004. S2CID 12934546. Archived (PDF) from the original on 2020-09-24.

web.archive.org

Specker (1949). Specker, E. (1949). "Nicht konstruktiv beweisbare Sätze der Analysis" (PDF). Journal of Symbolic Logic. 14 (3): 145–158. doi:10.2307/2267043. JSTOR 2267043. S2CID 11382421. Archived (PDF) from the original on 2018-07-21.
Boehm, Hans-J.; Cartwright, Robert; Riggle, Mark; O'Donnell, Michael J. (8 August 1986). "Exact real arithmetic: A case study in higher order programming" (PDF). Proceedings of the 1986 ACM conference on LISP and functional programming - LFP '86. pp. 162–173. doi:10.1145/319838.319860. ISBN 0897912004. S2CID 12934546. Archived (PDF) from the original on 2020-09-24.
Gowland, Paul; Lester, David (2001). "A Survey of Exact Arithmetic Implementations" (PDF). Computability and Complexity in Analysis. Lecture Notes in Computer Science. Vol. 2064. Springer. pp. 30–47. doi:10.1007/3-540-45335-0_3. ISBN 978-3-540-42197-9. Archived (PDF) from the original on 2022-03-24.

worldcat.org

Minsky (1967). Minsky, Marvin (1967). "9. The Computable Real Numbers". Computation: Finite and Infinite Machines. Prentice-Hall. ISBN 0-13-165563-9. OCLC 0131655639.