做純數題目時，發現有好幾條題目的問法相似：
1(b) Find polynomials u(x) and v(x) such that u(x)f(x)+v(x)g(x)=d(x) for all x.
2(b) Find polynomials u(x) and v(x) such that u(x)f(x)+v(x)g(x)=1.
這個關係式 u(x)f(x)+v(x)g(x)=? 在數學上有什麼意義呢？ Represent whether f(x) and g(x) are relatively prime or not? How? Could you please answer in details?
Euclidean algorithm
2011-10-28 3:39 am
回答 (2)
2011-11-11 5:59 am
✔ 最佳答案
Given two poly. f(x), g(x), let d(x) be the HCF of f(x), g(x) ,then{ u(x)f(x)+v(x)g(x) | any poly. u(x), v(x) }={ k(x) d(x) | any poly. k(x) }
If f(x), g(x) are relatively prime then
{ u(x)f(x)+v(x)g(x) | any poly. u(x), v(x) } = { any poly. }
( since we can choice some u(x), v(x) , such that u(x)f(x)+v(x)g(x) = 1 )
2011-10-29 8:09 pm
These statements seem to mean the same thing. i.e. if f(x) and g(x) are coprime, then there exists u(x) and v(x) so that u(x)f(x) + v(x)g(x) = 1
收錄日期: 2021-04-30 15:46:27
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20111027000051KK00676