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Консультация № 198032
24.03.2020, 20:18
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Найдите остаток от деления многочлена -> 2x^5 + 2x^3 + 2x^2 + x на -> 2x^3+x^2+2x+1 в кольце -> Z/3Z[X]
Найдите остаток от деления многочлена -> 2x^5 + 2x^3 + 2x^2 + x на -> 2x^3+x^2+2x+1 в кольце -> Z/3Z[X]
Обсуждение
29.03.2020, 04:55
общий
это ответ
Здравствуйте, stepan.gavrilov.spb!
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]5[/sup]+2x[sup]3[/sup]+2x[sup]2[/sup]+x на 2x[sup]3[/sup]+x[sup]2[/sup]+2x+1 в кольце Z/3Z равен x[sup]2[/sup]+x+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]5[/sup]+2x[sup]3[/sup]+2x[sup]2[/sup]+x на 2x[sup]3[/sup]+x[sup]2[/sup]+2x+1 в кольце Z/3Z равен x[sup]2[/sup]+x+2.
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