پديد آورنده :
رحماني، نازنين
عنوان :
نرمال سازي نوتر با استفاده از تجزيه ي مخروطي
مقطع تحصيلي :
كارشناسي ارشد
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
صفحه شمار :
هفت،112ص.: مصور،جدول،نمودار
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
امير هاشمي
استاد مشاور :
مجتبي آقايي
توصيفگر ها :
پايه گربنر , تقسيم تودرتو , متمم تجزيه ي مخروطي
تاريخ نمايه سازي :
19/1/93
استاد داور :
مسعود سبزواري، مجيد گازر
چكيده فارسي :
به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي
چكيده انگليسي :
Noether Normalization Using Cone Decompositions Nazanin Rahmani n rahmani@math iut ac ir 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Amir Hashemi amir hashemi@cc iut ac ir Advisor Dr Mojtaba Aghaei aghaei@cc iut ac ir 2010 MSC 13P10 68W30 Keywords Gr bner bases Noether normalization involutive division involutive basiscone decomposition complement cone decomposition Abstract For computing di erent invariants of an ideal its position may be very important and has highe ect on relevant computations For instance if an ideal is in an appropriate position we can computeits dimension and radical easier So one of the important subject in algebraic geometry and computeralgebra is to nd a good position for a given ideal such that we can compute its invariants simply It should be noted that when we change the position of an ideal many of its invarinant remainstable One of the most important position in the polynomial ideal theory is Noether normalizationor equivalently Noether position Noether normalization is a very important part of commutativealgebra cf e g Eisebud 1995 The Noether normalization lemma is usually proved in aconstructive manner but a computationally satisfactory solution exists For most of the computationalapproaches today it is common that the application of a random change of coordinates produces verylarge results which are di cult to handle afterwards A general algorithm for the computation ofa Noether normalization was outlined by Vasconcelos Vasconcelos 1998 The method for Noethernormalization given in Section 2 of the present thesis can be understood as a specialization of thisalgorithm In particular the problem of deciding whether an ideal contains a monic polynomial ina given variable is addressed without computing the intersection of the ideal with a subring and away to choose a sparse coordinate change is explained Along these lines a probabilistic algorithmwas presented by A Logar in Logar 1989 which comes up with a relatively sparse coordinate
استاد راهنما :
امير هاشمي
استاد مشاور :
مجتبي آقايي
استاد داور :
مسعود سبزواري، مجيد گازر
