کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4601097 | 1336876 | 2012 | 5 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Roots multiplicity and square-free factorization of polynomials using companion matrices
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let F be a field of characteristic 0 and let f be a monic polynomial of positive degree in F[X]. Let K be a splitting field for f over F and let α1,…,αs be the distinct roots of f in K with respective multiplicities m(α1),…,m(αs). By Lagrange Interpolation Formula there is a unique polynomial Mf∈K[X] of degree less than s satisfying Mf(αj)=m(αj) for 1⩽j⩽s. The polynomial Mf actually lies in F[X] and we present an explicit rational procedure to obtain Mf from f by means of companion matrices. As an application of Mf, we furnish a new method to compute each component of the square-free factorization , where m=max1⩽j⩽sm(αj) and Pk is the product of all X-αj such that m(αj)=k
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 436, Issue 9, 1 May 2012, Pages 3160-3164
Journal: Linear Algebra and its Applications - Volume 436, Issue 9, 1 May 2012, Pages 3160-3164