Computational number theory




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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