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Pell Equation. IV. Fastest algorithm for solving the Pell equation
http://hdl.handle.net/10083/35235
http://hdl.handle.net/10083/35235d30639e7-6e93-4966-b467-08c097244e8b
名前 / ファイル | ライセンス | アクション |
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58-1p.29-37.pdf (402.8 kB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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公開日 | 2009-10-22 | |||||
タイトル | ||||||
タイトル | Pell Equation. IV. Fastest algorithm for solving the Pell equation | |||||
言語 | ||||||
言語 | eng | |||||
資源タイプ | ||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||
タイプ | departmental bulletin paper | |||||
著者 |
Hosoya, haruo
× Hosoya, haruo |
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著者(ヨミ) | ||||||
識別子 | 70941 | |||||
識別子Scheme | WEKO | |||||
姓名 | ホソヤ, ハルオ | |||||
内容記述 | ||||||
内容記述タイプ | Other | |||||
内容記述 | The fastest algorithm for solving the Pell equations, x^2-Dy^2=1 (called Pell-1) and x^2-Dy^2=-1 (Llep-1) , are demonstrated with two typical examples. The essence of the algorithm is i) to obtain the periodic continued fraction expression for the square root of D, ii) to prepare four caterpillar graphs by using the terms derived above, and iii) to set a 3×3(for Pell) or 2×2(for Llep) determinant whose elements are the topological indices (Z’s) of those graphs, and iv) to calculate the determinant. The dramatic shortening of the procedure comes from the finding that the continuant is equivalent to the topological index of the caterpillar graph directly derived from the continued fraction expansion of the square root of D. | |||||
書誌情報 |
お茶の水女子大學自然科學報告 巻 58, 号 1, p. 29-37, 発行日 2007-09 |
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ISSN | ||||||
収録物識別子タイプ | ISSN | |||||
収録物識別子 | 00298190 | |||||
書誌レコードID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AN00033958 | |||||
フォーマット | ||||||
内容記述タイプ | Other | |||||
内容記述 | application/pdf | |||||
形態 | ||||||
402759 bytes | ||||||
著者版フラグ | ||||||
値 | publisher | |||||
日本十進分類法 | ||||||
主題Scheme | NDC | |||||
主題 | 400 | |||||
出版者 | ||||||
出版者 | お茶の水女子大学 | |||||
資源タイプ | ||||||
内容記述タイプ | Other | |||||
内容記述 | 紀要論文 | |||||
資源タイプ・ローカル | ||||||
紀要論文 | ||||||
資源タイプ・NII | ||||||
Departmental Bulletin Paper | ||||||
資源タイプ・DCMI | ||||||
text | ||||||
資源タイプ・ローカル表示コード | ||||||
03 |