کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4582886 | 1630376 | 2014 | 31 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Normal form for Ritt's Second Theorem
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
Ritt's Second Theorem deals with composition collisions g∘h=g⁎∘h⁎g∘h=g⁎∘h⁎ of univariate polynomials over a field, where degg=degh⁎. Joseph Fels Ritt (1922) presented two types of such decompositions. His main result here is that these comprise all possibilities, up to some linear transformations. We present a normal form for Ritt's Second Theorem, which is unique in many cases, and clarify the relation between the two types of examples. This yields an exact count of the number of such collisions in the “tame case”, where the characteristic of the (finite) ground field does not divide the degree of the composed polynomial.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Finite Fields and Their Applications - Volume 27, May 2014, Pages 41–71
Journal: Finite Fields and Their Applications - Volume 27, May 2014, Pages 41–71
نویسندگان
Joachim von zur Gathen,