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Консультация № 189243
22.04.2016, 23:00
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
найти остаток от деления многочлена 6x^(5)+3x^(4)+6x^(3)+5x^(2)+6x+3 на 4x^(3)+x^(2)+3x+1 в кольце Z/7Z?
найти остаток от деления многочлена 6x^(5)+3x^(4)+6x^(3)+5x^(2)+6x+3 на 4x^(3)+x^(2)+3x+1 в кольце Z/7Z?
Обсуждение
23.04.2016, 07:36
общий
это ответ
Здравствуйте, Александр!
Выполняем деление многочлена на многочлен обычным образом, только все действия с коэффициентами выполняем в кольце вычетов по модулю 7, например, 3*3=2 (а не 9), 0-2=5 (а не -2) 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 7):
Результат совпадает с исходным многочленом, следовательно, деление выполнено правильно и остаток от деления 6x[sup]5[/sup]+3x[sup]4[/sup]+6x[sup]3[/sup]+5x[sup]2[/sup]+6x+3 на 4x[sup]3[/sup]+x[sup]2[/sup]+3x+1 в кольце Z/7Z равен x[sup]2[/sup]+5x+6.
Выполняем деление многочлена на многочлен обычным образом, только все действия с коэффициентами выполняем в кольце вычетов по модулю 7, например, 3*3=2 (а не 9), 0-2=5 (а не -2) 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 7):
Результат совпадает с исходным многочленом, следовательно, деление выполнено правильно и остаток от деления 6x[sup]5[/sup]+3x[sup]4[/sup]+6x[sup]3[/sup]+5x[sup]2[/sup]+6x+3 на 4x[sup]3[/sup]+x[sup]2[/sup]+3x+1 в кольце Z/7Z равен x[sup]2[/sup]+5x+6.
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