翻訳と辞書 Words near each other ・ Primitive Man (album) ・ Primitive mantle ・ Primitive markings ・ Primitive Methodism ・ Primitive Methodist Chapel, Nantwich ・ Primitive Methodist Magazine ・ Primitive Modern ・ Primitive neuroectodermal tumor ・ Primitive notion ・ Primitive Origins ・ Primitive Peoples ・ Primitive permutation group ・ Primitive pit ・ Primitive Plus ・ Primitive polynomial ・ Primitive polynomial (field theory) ・ Primitive Quendian ・ Primitive Race ・ Primitive Race (album) ・ Primitive Radio Gods ・ Primitive Reason ・ Primitive recursive arithmetic ・ Primitive recursive function ・ Primitive recursive functional ・ Primitive recursive set function ・ Primitive reflexes ・ Primitive Rhythm Machine ・ Primitive ring ・ Primitive road ・ Primitive root Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Primitive polynomial (field theory) ： ウィキペディア英語版 Primitive polynomial (field theory) In field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite extension field GF(''p''''m''). In other words, a polynomial $F(X)$ with coefficients in is a primitive polynomial if its degree is ''m'' and it has a root $\backslash alpha$ in GF(''p''''m'') such that $\backslash \backslash \}$ is the entire field GF(''p''''m''). This means also that $\backslash alpha$ is a in GF(''p''''m''). ==Properties== Because all minimal polynomials are irreducible, all primitive polynomials are also irreducible. A primitive polynomial must have a non-zero constant term, for otherwise it will be divisible by ''x''. Over GF(2), is a primitive polynomial and all other primitive polynomials have an odd number of terms, since any polynomial mod 2 with an even number of terms is divisible by (it has ''1'' as a root). An irreducible polynomial ''F''(''x'') of degree ''m'' over GF(''p''), where ''p'' is prime, is a primitive polynomial if the smallest positive integer ''n'' such that ''F''(''x'') divides is . Over GF(''p''''m'') there are exactly primitive polynomials of degree ''m'', where ''φ'' is Euler's totient function. A primitive polynomial of degree ''m'' has ''m'' different roots in GF(''p''''m''), which all have order . This means that, if $\backslash alpha$ is such a root, then $\backslash alpha^=1$ and $\backslash alpha^i\backslash ne\; 1$ for . 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Primitive polynomial (field theory)」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.