پديد آورنده :
ميرزاوند، فرزاد
عنوان :
حل دستگاه هاي چند جمله اي با استفاده از روش زير منتج
مقطع تحصيلي :
كارشناسي ارشد
گرايش تحصيلي :
هندسه ﴿جبر محاسباتي﴾
محل تحصيل :
اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي
يادداشت :
ص.ع.به فارسي و انگليسي
استاد راهنما :
امير هاشمي
استاد مشاور :
قهرمان طاهريان
تاريخ نمايه سازي :
11/12/93
استاد داور :
مسعود سبزواري، رضا رضائيان فراشاهي
چكيده انگليسي :
Solving Polynomial Systems by the Subresultant Method Farzad Mirzavand f mirzavand@math iut ac ir 2014 Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Amir Hashemi amir hashemi@cc iut ac ir Advisor Dr Sayed Ghahreman Taherian taherian@cc iut ac ir 2010 MSC 13P10 68W30 Keywords Multivariate subresultant Polynomial system Solution of polynomial system Abstract This thesis is an extension and generalization of the works done by Agnes Szanto 30 31 onsolving polynomial systems using subresultants Solving systems of polynomial equations is one ofthe fundamental challenges of computational algebraic geometry On the other hand it has manyapplications in sciences and engineering In this thesis we use some methods for solving zero dimen sional polynomial equations systems having a nite number of common roots Further multivariateresultant is a fundamental tool for solving polynomial systems in computer algebra The resultant ofa polynomial system has many important properties for the geometry of the variety that the systemde nes Indeed the resultant is an algebraic condition in terms of the coe cients of the given systemof polynomials which is satis ed if and only if the system has a nontrivial common solution A number of methods exist for constructing resultant matrices i e matrices whose determinant isthe resultant or more generally a nontrivial multiple of it These matrices represent the most e cientway for computing the resultant polynomial and for solving systems of polynomial equations by meansof the resultant method An example of a matrix that gives precisely the resultant is the determinantof the coe cient matrix of n 1 linear polynomials or the Sylvester matrix of a pair of polynomials A generalization of this result can be used to decide whether a system of n 1 homogeneous equationsin n 1 variables has a solution or not This multipolynomial resultant can be used to eliminatevariables from three or more equations and it is a surprisingly powerful tool for nding solutions ofequations
استاد راهنما :
امير هاشمي
استاد مشاور :
قهرمان طاهريان
استاد داور :
مسعود سبزواري، رضا رضائيان فراشاهي
