# Basis grobner dari ideal polinomial

Kusumaningtyastuti , Devi (2002) Basis grobner dari ideal polinomial. Undergraduate thesis, FMIPA UNDIP.

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## Abstract

Ideal polinomial merupakan ideal dalam ring polinomial Himpunan yang membangun suatu ideal polinomial dinamakan dengan basis, dan salah satu basis yang pasti ada dari ideal polinomial adalah basis Groebner. Suatu basis G dari ideal polinomial I disebut basis Groebner apabila (LT(g1),...,LT(gt)) = (LT(I)). Ada dua algoritma untuk mencari basis Groebner yaitu algoritma Buchberger dan algoritma Buchberger yang telah dikembangkan, keduanya pada dasarnya sama yaitu menambahkan himpunan pembangun dengan polinomial — polinomial Baru. Karena basis Groebner yang didapatkan dengan kedua algoritma diatas sexing lebih besar dari yang diinginkan, maka harts dikurangi, sehingga menjadi basis Groebner tereduksi. Polynomial ideal is an ideal in polynomials ring We say that generators set of polynomial ideal are basis, and one of basis that always exists is Groebner basis. A basis G {gi,...,g,} of a polynomial ideal is said to be a Groebner basis if (LT(g, ,(LT(0).There are two algorithms to contruct a Groebner basis, they are Buchberger's algorithm and Improvement on Buchberger's algorithm. Both of them have the same, natural idea that is to extend the original generating set by adding new polynomials. Groebner basis which are computed using the two algorithms are often bigger than the necessary, then must eliminate it to become a reduced Groebner basis.

Item Type: Thesis (Undergraduate) Q Science > QA Mathematics Faculty of Science and Mathematics > Department of Mathematics 31717 Mr UPT Perpus 1 24 Nov 2011 11:35 24 Nov 2011 11:35

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