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Консультация № 189193
14.04.2016, 22:13
0.00 руб.
14.04.2016, 22:29
0
1
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
при нахождении НОД многочленов какую роль играет степень?
то есть, скажем, мы находим НОД(F(x), G(x)). НОД будет последний остаток не равный нулю.
если мы запишем процесс деления и выписывания остатков в цикл, то он будет длится пока степень делимого не будет равно нулю, я правильно понимаю?
при нахождении НОД многочленов какую роль играет степень?
то есть, скажем, мы находим НОД(F(x), G(x)). НОД будет последний остаток не равный нулю.
если мы запишем процесс деления и выписывания остатков в цикл, то он будет длится пока степень делимого не будет равно нулю, я правильно понимаю?
Обсуждение
14.04.2016, 22:44
общий
это ответ
Здравствуйте, Александр!
В теории, связанной с делением многочленов, степень многочлена играет ту же роль, которую модуль целого числа играет в соответствующей теории целых чисел. Вообще, теорию, связанную с понятиями НОД и НОК многочленов, можно построить, повторяя соответствующие определения и доказательства утверждений из теории, связанной с понятиями НОД и НОК целых чисел (с заменой целых чисел на многочлены и слов "модуль числа" на слова "степень многочлена").
Про НОД многочленов Вы понимаете правильно. Можно рассмотреть пример здесь.
С уважением.
В теории, связанной с делением многочленов, степень многочлена играет ту же роль, которую модуль целого числа играет в соответствующей теории целых чисел. Вообще, теорию, связанную с понятиями НОД и НОК многочленов, можно построить, повторяя соответствующие определения и доказательства утверждений из теории, связанной с понятиями НОД и НОК целых чисел (с заменой целых чисел на многочлены и слов "модуль числа" на слова "степень многочлена").
Про НОД многочленов Вы понимаете правильно. Можно рассмотреть пример здесь.
С уважением.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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