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Консультация № 189064
02.04.2016, 03:44
0.00 руб.
02.04.2016, 06:54
0
1
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
как найти остаток от деления многочлена x^(5)+x^(3)+2*x^(2)+x+2 на x^(3)+2*x^(2)+x+1 в кольце Z/3Z?
как найти остаток от деления многочлена x^(5)+x^(3)+2*x^(2)+x+2 на x^(3)+2*x^(2)+x+1 в кольце Z/3Z?
Обсуждение
02.04.2016, 04:47
общий
это ответ
Здравствуйте, bill1091989!
Выполняем деление многочлена на многочлен обычным образом, только все действия с коэффициентами выполняем в кольце вычетов по модулю 3, например, 2*2=1 (а не 4), 0-1=2 (а не -1) и т.п.
Для проверки умножим полученное частное на делитель и прибавим остаток (так же выполняя все действия с коэффициентами в кольце вычетов по модулю 3):
Результат совпадает с исходным многочленом, следовательно, деление выполнено правильно и остаток от деления x[sup]5[/sup]+x[sup]3[/sup]+2x[sup]2[/sup]+x+2 на x[sup]3[/sup]+2x[sup]2[/sup]+x+1 в кольце Z/3Z равен x[sup]2[/sup]+2x+1.
Выполняем деление многочлена на многочлен обычным образом, только все действия с коэффициентами выполняем в кольце вычетов по модулю 3, например, 2*2=1 (а не 4), 0-1=2 (а не -1) и т.п.
Для проверки умножим полученное частное на делитель и прибавим остаток (так же выполняя все действия с коэффициентами в кольце вычетов по модулю 3):
Результат совпадает с исходным многочленом, следовательно, деление выполнено правильно и остаток от деления x[sup]5[/sup]+x[sup]3[/sup]+2x[sup]2[/sup]+x+2 на x[sup]3[/sup]+2x[sup]2[/sup]+x+1 в кольце Z/3Z равен x[sup]2[/sup]+2x+1.
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