پديد آورنده :
آرميده، نسيبه
عنوان :
تحليل ساختاري مدول هاي چندجمله اي با استفاده از پايه ي پماره
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
استاد راهنما :
امير هاشمي
استاد مشاور :
اعظم اعتماد
واژه نامه :
به فارسي و انگليسي
تاريخ نمايه سازي :
1394/09/15
استاد داور :
مجيد گازر، مليحه يوسف زاده
تاريخ ورود اطلاعات :
1396/10/05
چكيده انگليسي :
Structure analysis of polynomial modules with Pommaret basis Nasibeh Aramideh n aramideh@math iut ac ir 2015 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Amir Hashemi Amir Hashemi@cc iut ac ir Advisor Dr Azam Etemad Dehkordy ae110mat@cc iut ac ir 2010 MSC 13p10 68w30 Keywords Gr bner bases involutive division involutive bases Pommaret bases regular coor dinates Abstract Involutive bases are a special form of non reduced Gr bner bases with additional combinatorialproperties It is based on a new concept of involutive monomial division which is de ned for a mono mial set Such a division provides for each monomial the self consistent separation of the whole setof variables into two disjoint subsets They are called multiplicative and non multiplicative Givenan admissible monomial ordering this separation is applied to polynomials in terms of their lead ing monomials As special cases of the separation we consider those introduced by Janet Thomasand Pommaret for the purpose of algebraic analysis of partial di erential equations Given involutivedivision we de ne an involutive reduction and an involutive normal form Then we introduce theconcept of involutivity for polynomial systems An algorithm for construction of involutive bases isproposed It is shown that involutive divisions satisfying certain conditions for example Janet pro vide an algorithmic construction of an involutive basis for any polynomial ideal Much of the existingliterature on involutive bases concentrates on their e cient algorithmic construction By contrast we are here more concerned with their structural properties Pommaret bases are not only impor tant for di erential equations but also de ne a special type of decomposition a Rees decomposition The main topic of the fourth chapter is to show that this fact makes them a very powerful tool forcomputation algebraic geometry Most of these applications exploit that Pommaret bases possess ahighly interesting syzygy theory For example they allow for directly reading o the depth the Krull
استاد راهنما :
امير هاشمي
استاد مشاور :
اعظم اعتماد
استاد داور :
مجيد گازر، مليحه يوسف زاده
