View source for कम्प्यूटेशनल संख्या सिद्धांत

{{short description|Study of algorithms for performing number theoretic computations}}
गणित और [[कंप्यूटर विज्ञान]] में, '''कम्प्यूटेशनल [[संख्या सिद्धांत]] हैं''', जिसे एल्गोरिथम संख्या सिद्धांत के रूप में भी जाना जाता है, संख्या सिद्धांत और [[अंकगणित ज्यामिति]] में समस्याओं की जांच और समाधान के लिए [[गणना]] का अध्ययन किया जाता है, जिसमें [[प्रारंभिक परीक्षण]] और [[पूर्णांक गुणनखंडन]] के लिए एल्गोरिदम, [[डायोफैंटाइन समीकरण]] के समाधान ढूंढना और अंकगणित ज्यामिति में स्पष्ट विधियाँ सम्मिलित होती हैं। {{r|pcm}} कम्प्यूटेशनल संख्या सिद्धांत में [[क्रिप्टोग्राफी]] के लिए अनुप्रयोग होते हैं, जिसमें [[आरएसए (क्रिप्टोसिस्टम)]], [[अण्डाकार वक्र क्रिप्टोग्राफी]] और [[पोस्ट-क्वांटम क्रिप्टोग्राफी]] सम्मिलित है, और इसका उपयोग संख्या सिद्धांत में [[अनुमान]] और विवर्त समस्याओं की जांच करने के लिए किया जाता है, जिसमें यह [[रीमैन परिकल्पना]], [[बिर्च और स्विनर्टन-डायर अनुमान]], [[एबीसी अनुमान]], [[मॉड्यूलैरिटी प्रमेय]], [[सातो-टेट अनुमान]], और [[लैंगलैंड्स कार्यक्रम|लैंगलैंड्स प्रोग्राम]] के स्पष्ट रूप से सम्मिलित होते हैं। {{r|pcm}}{{r|bachshallit}}{{r|cohen}}
==सॉफ़्टवेयर पैकेज==
* [[मैग्मा कंप्यूटर बीजगणित प्रणाली]]
* [[सेजमैथ]]
* [[संख्या सिद्धांत पुस्तकालय|संख्या सिद्धांत लाइब्रेरी]] 
* पारी/जीपी
* [[संख्या सिद्धांत के लिए फास्ट लाइब्रेरी]]

==अग्रिम पठन==
*{{cite book
| author1   = Eric Bach | author1-link = Eric Bach
| author2   = Jeffrey Shallit | author2-link = Jeffrey Shallit
| title     = Algorithmic Number Theory, Volume 1: Efficient Algorithms
| publisher = MIT Press
| year      = 1996
| isbn      = 0-262-02405-5
| url       = https://cs.uwaterloo.ca/~shallit/ant.html
}}

*{{cite book
| author     = David M. Bressoud
| authorlink = David Bressoud
| title      = Factorisation and Primality Testing
| publisher  = Springer-Verlag
| year       = 1989
| isbn       = 0-387-97040-1
| url-access = registration
| url        = https://archive.org/details/factorizationpri0000bres
}}

* {{cite book
| editor1   = Joe P. Buhler | editor1-link = Joe P. Buhler
| editor2   = Peter Stevenhagen
| title     = Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography
| series    = MSRI Publications
| volume    = 44
| publisher = [[Cambridge University Press]]
| year      = 2008
| isbn      = 978-0-521-20833-8
| zbl       = 1154.11002
| url       = https://www.cambridge.org/us/academic/subjects/mathematics/number-theory/algorithmic-number-theory-lattices-number-fields-curves-and-cryptography?format=HB&isbn=9780521808545
}}

* {{cite book
| author    = Henri Cohen | author-link = Henri Cohen (number theorist)
| title     = A Course In Computational Algebraic Number Theory 
| year      = 1993
| isbn      = 0-387-55640-0
| publisher = [[Springer-Verlag]]
| series    = [[Graduate Texts in Mathematics]]
| volume    = 138
| doi = 10.1007/978-3-662-02945-9
}}

* {{cite book
| author    = Henri Cohen | author-link = Henri Cohen (number theorist)
| title     = Advanced Topics in Computational Number Theory
| year      = 2000
| isbn      = 0-387-98727-4
| publisher = [[Springer-Verlag]]
| series    = [[Graduate Texts in Mathematics]]
| volume    = 193
| doi = 10.1007/978-1-4419-8489-0
}}

* {{cite book
| author    = Henri Cohen | author-link = Henri Cohen (number theorist)
| title     = Number Theory – Volume I: Tools and Diophantine Equations
| year      = 2007 
| isbn      = 978-0-387-49922-2
| publisher = [[Springer-Verlag]]
| series    = [[Graduate Texts in Mathematics]]
| volume    = 239
| doi = 10.1007/978-0-387-49923-9
}}

* {{cite book
| author    = Henri Cohen | author-link = Henri Cohen (number theorist)
| title     = Number Theory – Volume II: Analytic and Modern Tools
| year      = 2007 
| isbn      = 978-0-387-49893-5
| publisher = [[Springer-Verlag]]
| series    = [[Graduate Texts in Mathematics]]
| volume    = 240
| doi = 10.1007/978-0-387-49894-2
}}

* {{cite book
| author1   = Richard Crandall | author1-link = Richard Crandall
| author2   = Carl Pomerance | author2-link = Carl Pomerance
| title     = Prime Numbers: A Computational Perspective
| publisher = Springer-Verlag
| year      = 2001
| isbn      = 0-387-94777-9
| doi = 10.1007/978-1-4684-9316-0
}}

* {{cite book
| author     = Hans Riesel
| authorlink = Hans Riesel
| title      = Prime Numbers and Computer Methods for Factorization
| edition    = second
| publisher  = Birkhäuser
| year       = 1994
| isbn       = 0-8176-3743-5
| zbl        = 0821.11001
| series     = Progress in Mathematics
| volume     = 126
}}

* {{cite book
| author      = Victor Shoup
| author-link = Victor Shoup
| title       = A Computational Introduction to Number Theory and Algebra
| publisher   = [[Cambridge University Press]]
| year        = 2012
| isbn        = 9781139165464
| doi         = 10.1017/CBO9781139165464
}}

* {{cite book 
| author     = Samuel S. Wagstaff, Jr.
| authorlink = Samuel S. Wagstaff, Jr.
| title      = The Joy of Factoring 
| publisher  = American Mathematical Society 
| year       = 2013 
| isbn       = 978-1-4704-1048-3 
| url        = https://www.ams.org/bookpages/stml-68 
}}
==संदर्भ==
{{reflist|refs=

<ref name=pcm>{{citation 
| author1    = Carl Pomerance | author1-link = Carl Pomerance
| editor1    = Timothy Gowers | editor1-link = Timothy Gowers
| title      = Computational Number Theory
| work       = The Princeton Companion to Mathematics
| publisher  = [[Princeton University Press]]
| year       = 2009
| url        = https://math.dartmouth.edu/~carlp/PDF/pcm0049.pdf
}}</ref>

<ref name=bachshallit>{{cite book
| author1   = Eric Bach | author1-link = Eric Bach
| author2   = Jeffrey Shallit | author2-link = Jeffrey Shallit
| title     = Algorithmic Number Theory, Volume 1: Efficient Algorithms
| publisher = MIT Press
| year      = 1996
| isbn      = 0-262-02405-5
}}</ref>

<ref name=cohen>{{cite book
| author    = Henri Cohen | author-link = Henri Cohen (number theorist)
| title     = A Course In Computational Algebraic Number Theory 
| year      = 1993
| isbn      = 0-387-55640-0
| publisher = [[Springer-Verlag]]
| series    = [[Graduate Texts in Mathematics]]
| volume    = 138
| doi = 10.1007/978-3-662-02945-9
}}</ref>
}}
==बाहरी संबंध==
*{{Commonscatinline}}

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