Computational number theory

Multi tool use
Multi tool use




In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of algorithms for performing number theoretic computations.



See also



  • Computational complexity of mathematical operations

  • SageMath

  • Number Theory Library

  • PARI/GP

  • Fast Library for Number Theory



Further reading




  • Eric Bach and Jeffrey Shallit, Algorithmic Number Theory, volume 1: Efficient Algorithms. MIT Press, 1996, .mw-parser-output cite.citation{font-style:inherit}.mw-parser-output q{quotes:"""""""'""'"}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:inherit;padding:inherit}.mw-parser-output .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/6/65/Lock-green.svg/9px-Lock-green.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-limited a,.mw-parser-output .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/d/d6/Lock-gray-alt-2.svg/9px-Lock-gray-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Lock-red-alt-2.svg/9px-Lock-red-alt-2.svg.png")no-repeat;background-position:right .1em center}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration,.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}
    ISBN 0-262-02405-5


  • D. M. Bressoud (1989). Factorisation and Primality Testing. Springer-Verlag. ISBN 0-387-97040-1.




  • Buhler, J.P.; P., Stevenhagen, eds. (2008). Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography. MSRI Publications. 44. Cambridge University Press. ISBN 978-0-521-20833-8. Zbl 1154.11002.


  • Henri Cohen, A Course in Computational Algebraic Number Theory, Graduate Texts in Mathematics 138, Springer-Verlag, 1993.


  • Richard Crandall and Carl Pomerance, Prime Numbers: A Computational Perspective, Springer-Verlag, 2001,
    ISBN 0-387-94777-9


  • Riesel, Hans (1994). Prime Numbers and Computer Methods for Factorization. Progress in Mathematics. 126 (second ed.). Boston, MA: Birkhäuser. ISBN 0-8176-3743-5. Zbl 0821.11001.


  • Victor Shoup, A Computational Introduction to Number Theory and Algebra. Cambridge, 2005,
    ISBN 0-521-85154-8



  • Samuel S. Wagstaff, Jr. (2013). The Joy of Factoring. Providence, RI: American Mathematical Society. ISBN 978-1-4704-1048-3.











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