12237

11210

كارشناسي ارشد

رياضي محض

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1395

پنج، [101]ص.: مصور.

ص. ع. به فارسي و انگليسي

امير هاشمي

مجيد گازر

واژه نامه

رضا رضائيان، مسعود سبزواري

1395/12/04

كتابنامه

علوم رياضي

رياضي

ID11210

Computing Comprehensive Grobner Systems and Comprehensive Grobner Bases Nasime Hosseini Joozdani Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 Iran Supervisor Dr Amir Hashemi Advisor Dr Majid Gazor mgazor@cc iut ac ir 2010 MSC 13P10 68W30 Keywords Polynomial Ideals Grobner Bases Comprehensive Grobner Systems ComprehensiveGrobner Bases AbstractA new efficient algorithm for computing a comprehensive Gr bner system CGS of a parametricpolynomial ideal over K A X is presented where A is a sequence of parameter X is a sequence ofvariables and K is a field This algorithm generates fewer branches compared to previously proposedalgorithms as Suzuki and Sato s algorithm As a result the algorithm is able to compute CGS ofa parametric polynomial ideals arising from applications which have been beyond the reach of otherwell known algorithms The starting point of the new algorithm is Weispfenning s algorithm witha key insight by Suzuki and Sato who proposed computing first a Gr bner basis of an ideal overK A X before performing any branches based on parametric constraints The proposed algorithmexploits the result that along any branch in a tree corresponding to a CGS it is only necessary toconsider one polynomial for each nondivisible leading monomial in K A X with the condition thatthe product of their leading coefficients is not 0 other branches correspond to the cases where thisproduct is 0 In addition for dealing with a disequality parametric constraint a probabilistic checkis employed for radical membership test of an ideal of parametric constraints This is in contrast toa general expensive check based on Rabinovitch s trick using a new variable The proposed algorithmhas been implemented in Maple and exprimented with a number of examples In the other sectionof the master thesis we introduce a new approach for computing a comprehensive Gr bner basis ofa parameterized polynomial system The key new idea is not to simplify a polynomial under various

امير هاشمي

مجيد گازر

رضا رضائيان، مسعود سبزواري