پديد آورنده :
كيوان فرد، نوشين
عنوان :
الگوريتم محاسبه ي پايه ي گربنر يك ايده آل چند جمله اي روي يك حلقه با مقسوم عليه صفر
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
هشت، [120]ص.: مصور
يادداشت :
ص. ع. به فارسي و انگليسي
استاد راهنما :
امير هاشمي
استاد مشاور :
رضا رضائيان فراشاهي
توصيفگر ها :
ايده آل اصلي , پايه ي گربنر
استاد داور :
مجيد گازر، مسعود سبزواري
تاريخ ورود اطلاعات :
1395/11/19
چكيده انگليسي :
Algorithm for Computing a Gr bner Basis of a Polynomial Ideal over a Ring with Zero Divisors Nooshin Keivanfard n keivanfard@math iut ac ir 14 January 2017 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Amir Hashemi amir hashemi@cc iut ac ir Advisor Dr Reza Rezaeian Farashahi farashahi@cc iut ac ir 2010 MSC 13P10 68W30 Keywords Polynomial ring Gr bner bases Buchberger s algorithm ring with zero divisors Division algorithm AbstractThe concept of a Gr bner basis of an ideal was introduced by Bruno Buchberger in 1965 in his Ph D thesis under supervision of Wolfgang Gr bner 4 Buchberger defined a specialized basis of an ideal ina polynomial ring with the coefficients in a field with the property that any element in the underlyingring has a canonical form unique normal form with respect to the ideal with respect to a givenmonomial ordering along with the canonical form for the elements in the ideal being 0 furthermore two elements in the ring modulo a given ideal have the same canonical form For polynomial ide als over a field Buchberger not only showed that every polynomial ideal has a Gr bner basis butalso gave an algorithm for computing a Gr bner basis from any basis of a given ideal w r t a givenmonomial ordering It took some years before the concept became popular among mathematiciansand computer scientists By now numerous interesting applications of the concept have been foundand many computational problems can be solved by computing Gr bner bases of polynomial ideals Most commercially available computer algebra systems provide implementations of Gr bner basisalgorithms There are highly specialized fast stand alone software systems available for computingGr bner basis as well Kandri Rody and Kapur 5 6 generalized Buchberger s algorithm by defininga rewriting relation induced by a polynomial on a polynomial ring using a division algorithm over an
استاد راهنما :
امير هاشمي
استاد مشاور :
رضا رضائيان فراشاهي
استاد داور :
مجيد گازر، مسعود سبزواري
