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Conway polynomial (finite fields)
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<p>In mathematics, the Conway polynomial <i>C</i><i>p</i>,<i>n</i> for the <a href="/facts/Finite_field/UkMGJo3m">finite field</a> F<i>p</i><i>n</i> is a particular <a href="/facts/Irreducible_polynomial/PTeuKm4W">irreducible polynomial</a> of degree n over F<i>p</i> that can be used to define a standard representation of F<i>p</i><i>n</i> as a <a href="/facts/Splitting_field/m38eWUH1">splitting field</a> of <i>C</i><i>p</i>,<i>n</i>. Conway polynomials were named after <a href="/facts/John_H._Conway/g3PA1zoK">John H. Conway</a> by <a href="/facts/Richard_A._Parker/TB9hrlEp">Richard A. Parker</a>, who was the first to define them and compute examples. Conway polynomials satisfy a certain compatibility condition that had been proposed by Conway between the representation of a field and the representations of its subfields. They are important in <a href="/facts/Computer_algebra/hjun1KAX">computer algebra</a> where they provide portability among different mathematical databases and computer algebra systems. Since Conway polynomials are expensive to compute, they must be stored to be used in practice. Databases of Conway polynomials are available in the computer algebra systems <a href="/facts/GAP_computer_algebra_system/1yL7xaNk">GAP</a>, <a href="/facts/Macaulay2/lv4FmNP7">Macaulay2</a>, <a href="/facts/Magma_computer_algebra_system/0kJ0CyPo">Magma</a>, <a href="/facts/SageMath/5mzh5TlB">SageMath</a>, at the web site of Frank Lübeck, and at the <a href="/facts/Online_Encyclopedia_of_Integer_Sequences/yow6cVsU">Online Encyclopedia of Integer Sequences</a>. </p>