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Консультация № 195861
16.06.2019, 16:48
0.00 руб.
19.06.2019, 03:07
0
1
1
Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
как найти остаток от деления многочлена 2x4+x3+2x2+2x на x2+x+2 в кольце Z/3Z?
как найти остаток от деления многочлена 2x4+x3+2x2+2x на x2+x+2 в кольце Z/3Z?
Обсуждение
19.06.2019, 03:43
общий
это ответ
Здравствуйте, max.f99!
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 2x[sup]4[/sup]+x[sup]3[/sup]+2x[sup]2[/sup]+2x на x[sup]2[/sup]+x+2 в кольце Z/3Z равен 2x+2.
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 2x[sup]4[/sup]+x[sup]3[/sup]+2x[sup]2[/sup]+2x на x[sup]2[/sup]+x+2 в кольце Z/3Z равен 2x+2.
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