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Computational number theory
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<h2 id="software-packages">Software packages</h2> <ul><li><a href="/facts/Magma_computer_algebra_system/0kJ0CyPo">Magma computer algebra system</a></li> <li><a href="/facts/SageMath/5mzh5TlB">SageMath</a></li> <li><a href="/facts/Number_Theory_Library/DdzyoUnt">Number Theory Library</a></li> <li><a href="/facts/PARI%2fGP/JhTL8ysP">PARI/GP</a></li> <li><a href="/facts/Fast_Library_for_Number_Theory/7NLCTfBd">Fast Library for Number Theory</a></li></ul> <h2 id="further-reading">Further reading</h2> <ul><li>Michael E. Pohst (1993): <i>Computational Algebraic Number Theory</i>, Springer, ISBN 978-3-0348-8589-8</li></ul> <ul><li><a href="/facts/Eric_Bach/QG7XPRWo">Eric Bach</a>; <a href="/facts/Jeffrey_Shallit/4bmJgyIH">Jeffrey Shallit</a> (1996). <a href="https://cs.uwaterloo.ca/~shallit/ant.html"><i>Algorithmic Number Theory, Volume 1: Efficient Algorithms</i></a>. MIT Press. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-262-02405-5.</li></ul> <ul><li><a href="/facts/David_Bressoud/tecaQkIV">David M. Bressoud</a> (1989). <a href="https://archive.org/details/factorizationpri0000bres"><i>Factorisation and Primality Testing</i></a>. Springer-Verlag. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-387-97040-1.</li></ul> <ul><li><a href="/facts/Joe_P._Buhler/KoRK3vcB">Joe P. Buhler</a>; Peter Stevenhagen, eds. (2008). <a href="https://www.cambridge.org/us/academic/subjects/mathematics/number-theory/algorithmic-number-theory-lattices-number-fields-curves-and-cryptography?format=HB&isbn=9780521808545"><i>Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography</i></a>. MSRI Publications. Vol. 44. <a href="/facts/Cambridge_University_Press/fgEBSSRq">Cambridge University Press</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-521-20833-8. <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:1154.11002">1154.11002</a>.</li></ul> <ul><li><a href="/facts/Henri_Cohen_(number_theorist)/ITral7Cr">Henri Cohen</a> (1993). <i>A Course In Computational Algebraic Number Theory</i>. <a href="/facts/Graduate_Texts_in_Mathematics/VTIfY29j">Graduate Texts in Mathematics</a>. Vol. 138. <a href="/facts/Springer-Verlag/nAesf6nT">Springer-Verlag</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-3-662-02945-9">10.1007/978-3-662-02945-9</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-387-55640-0.</li></ul> <ul><li><a href="/facts/Henri_Cohen_(number_theorist)/ITral7Cr">Henri Cohen</a> (2000). <i>Advanced Topics in Computational Number Theory</i>. <a href="/facts/Graduate_Texts_in_Mathematics/VTIfY29j">Graduate Texts in Mathematics</a>. Vol. 193. <a href="/facts/Springer-Verlag/nAesf6nT">Springer-Verlag</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-1-4419-8489-0">10.1007/978-1-4419-8489-0</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-387-98727-4.</li></ul> <ul><li><a href="/facts/Henri_Cohen_(number_theorist)/ITral7Cr">Henri Cohen</a> (2007). <i>Number Theory – Volume I: Tools and Diophantine Equations</i>. <a href="/facts/Graduate_Texts_in_Mathematics/VTIfY29j">Graduate Texts in Mathematics</a>. Vol. 239. <a href="/facts/Springer-Verlag/nAesf6nT">Springer-Verlag</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-0-387-49923-9">10.1007/978-0-387-49923-9</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-387-49922-2.</li></ul> <ul><li><a href="/facts/Henri_Cohen_(number_theorist)/ITral7Cr">Henri Cohen</a> (2007). <i>Number Theory – Volume II: Analytic and Modern Tools</i>. <a href="/facts/Graduate_Texts_in_Mathematics/VTIfY29j">Graduate Texts in Mathematics</a>. Vol. 240. <a href="/facts/Springer-Verlag/nAesf6nT">Springer-Verlag</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-0-387-49894-2">10.1007/978-0-387-49894-2</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-0-387-49893-5.</li></ul> <ul><li><a href="/facts/Richard_Crandall/asxnT8bD">Richard Crandall</a>; <a href="/facts/Carl_Pomerance/mmKNsTUr">Carl Pomerance</a> (2001). <i>Prime Numbers: A Computational Perspective</i>. Springer-Verlag. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1007%2F978-1-4684-9316-0">10.1007/978-1-4684-9316-0</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-387-94777-9.</li></ul> <ul><li><a href="/facts/Hans_Riesel/0DqQFoM9">Hans Riesel</a> (1994). <i>Prime Numbers and Computer Methods for Factorization</i>. Progress in Mathematics. Vol. 126 (second ed.). Birkhäuser. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 0-8176-3743-5. <a href="/facts/Zbl_(identifier)/P6rFxKKx">Zbl</a> <a href="https://zbmath.org/?format=complete&q=an:0821.11001">0821.11001</a>.</li></ul> <ul><li><a href="/facts/Victor_Shoup/QVWxQhUG">Victor Shoup</a> (2012). <a href="http://www.shoup.net/ntb/"><i>A Computational Introduction to Number Theory and Algebra</i></a>. <a href="/facts/Cambridge_University_Press/fgEBSSRq">Cambridge University Press</a>. <a href="/facts/Doi_(identifier)/muM9Etpq">doi</a>:<a href="https://doi.org/10.1017%2FCBO9781139165464">10.1017/CBO9781139165464</a>. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 9781139165464.</li></ul> <ul><li><a href="/facts/Samuel_S._Wagstaff%2c_Jr./23qeUItG">Samuel S. Wagstaff, Jr.</a> (2013). <a href="https://www.ams.org/bookpages/stml-68"><i>The Joy of Factoring</i></a>. American Mathematical Society. <a href="/facts/ISBN_(identifier)/15AdSPa9">ISBN</a> 978-1-4704-1048-3.</li></ul> <ul><li>Peter Giblin (1993): <i>Primes and Programming: An Introduction to Number Theory with Computing</i>, Cambridge University Press, ISBN 0-521-40988-8</li> <li>Nigel P. Smart (1998): <i>The Algorithmic Resolution of Diophantine Equations</i>, Cambridge University Press, ISBN 0-521-64633-2</li> <li>Ramanujachary Kumanduri and Cristina Romero (1998): <i>Number Theory with Computer Applications</i>, Prentice Hall, ISBN 0-13-801812-X</li> <li>Fernando Rodriguez Villegas (2007): <i>Experimental Number Theory</i>, Oxford University Press, ISBN 978-0-19-922730-3</li> <li>Harold M. Edwards (2008): <i>Higher Arithmetic: An Algorithmic Introduction to Number Theory</i>, American Mathematical Society, ISBN 978-1-4704-2153-3</li> <li>Lasse Rempe-Gillen and Rebecca Waldecker (2014). <i>Primality Testing for Beginners</i>. American Mathematical Society. ISBN 978-0-8218-9883-3</li></ul> <h2 id="external-links">External links</h2> <ul><li> Media related to Computational number theory at Wikimedia Commons</li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>Carl Pomerance (2009), Timothy Gowers (ed.), "Computational Number Theory" (PDF), The Princeton Companion to Mathematics, Princeton University Press <a href="/wiki/Carl_Pomerance" target="_blank">/wiki/Carl_Pomerance</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Carl Pomerance (2009), Timothy Gowers (ed.), "Computational Number Theory" (PDF), The Princeton Companion to Mathematics, Princeton University Press <a href="/wiki/Carl_Pomerance" target="_blank">/wiki/Carl_Pomerance</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Eric Bach; Jeffrey Shallit (1996). Algorithmic Number Theory, Volume 1: Efficient Algorithms. MIT Press. ISBN 0-262-02405-5. <a href="0-262-02405-5" target="_blank">0-262-02405-5</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>Henri Cohen (1993). A Course In Computational Algebraic Number Theory. Graduate Texts in Mathematics. Vol. 138. Springer-Verlag. doi:10.1007/978-3-662-02945-9. ISBN 0-387-55640-0. <a href="0-387-55640-0" target="_blank">0-387-55640-0</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> </ol>