8682

8063

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1392

نه،154ص.جدول

ص.ع.به فارسي و انگليسي

امير هاشمي

منصور آقاسي

19/1/93

مليحه يوسف زاده، رضا رضاييان فراشاهي

رياضي

ID8063

به فارسي و انگليسي: قابل رويت در نسخه ديجيتالي

Algorithms for Computing Triangular Decomposition of Polynomial Systems Safoura Gholami s gholami@math iut ac ir 2013 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisor Dr Amir Hashemi amir hashemi@cc iut ac ir Advisor Dr Mansour Aghasi m aghasi@cc iut ac ir 2010 MSC 13P10 68W30 Keywords Gr bner basis Characteristic set Triangular decomposition Regular chain Resultant GCD AbstractSolving polynomial system is a basic problem in the eld of computational sciences andengineering Gr bner bases is a powerful tool in solving non linear polynomial systems overdi erent kind of elds However the complexity of Gr bner bases computation lies in theworst complexity class and this may avoid us from using this technique in practice Onthe other hand triangular decomposition provides an algorithmic and e cient method toanalyze a given system of non linear polynomials This method has its origin in the valuableworks of the chinese mathematician Wu The characteristic set method of Wu has freedRitt s decomposition from polynomial factorization opening the door to a variety of discov eries in polynomial and di erential algebra During the past 25 years the work of Wu hasbeen extended to allow for more powerful decompositon algorithms and applied to di erenttypes of polynomial systems Today triangular decompositon algorithms are available inseveral software package system solvers such as MAPLE S solve command

امير هاشمي

منصور آقاسي

مليحه يوسف زاده، رضا رضاييان فراشاهي