代数学コロキウム

過去の記録 ~02/25次回の予定今後の予定 02/26~

開催情報 水曜日 17:00~18:00 数理科学研究科棟(駒場) 056号室
担当者 今井 直毅, 三枝 洋一

2013年07月03日(水)

16:40-17:40   数理科学研究科棟(駒場) 056号室
芳木武仁 氏 (東京大学数理科学研究科)
A general formula for the discriminant of polynomials over $¥mathbb{F}_2$ determining the parity of the number of prime factors
(JAPANESE)
[ 講演概要 ]
In order to find irreducible polynomials over $\\mathbb{F}_2$ efficiently, the method using Swan's theorem is known. Swan's theorem determines the parity of the numberof irreducible factors of a polynomial $f$ over $\\mathbb{F}_2$ with no repeated root, by using the discriminant ${\\rm D}(\\tilde{f})\\pmod 8$, where $\\tilde{f}$ is a monic polynomial over $\\mathbb{Z}_2$ such that $\\tilde{f}=f\\pmod 2$. In the lecture, we will give the formula for the discriminant ${\\rm D}(\\tilde{f}) \\pmod 8$ for a polynomial $f$ over $\\mathbb{F}_2$ with no repeated root. By applying this formula to various types of polynomials, we shall get the parity of the number of irreducible factors of them.