تعمیم الگوریتم بوخبرگر در جبرهای تفاضلی نسبت به ترتیب­های چندگانه

Abstract

p align=center dir=rtl style=margin-left: 0.6in; margin-right: 0.6in; margin-bottom: 0.14in; line-height: 0.29infont face=Arialspan lang=ar-SAfont color=#000000font size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalپایه/span/font/font/span/font/font/spanfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;shy;/span/font/font/span/font/font/fontfont face=Arialspan lang=ar-SAfont color=#000000font size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan lang=fa-IRspan style=font-weight: normalی/span/span/font/font/span/font/fontfont color=#000000font size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normal گربنر نسبت به چند ترتیب برای یک مدول تفاضلی، مهمترین ابزار برای یافتن چندجمله/span/font/font/span/font/font/span/fontfont color=#000000font face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;/span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalای بعد دستگاه/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;/span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalهای دیفرانسیلی و تفاضلی است/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normal. /span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalدر این مقاله، الگوریتمی برای محاسبه/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;/span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalی این پایه/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;/span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalی گربنر، ارایه /span/font/font/span/font/span/fontfont color=#000000font size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan lang=fa-IRspan style=font-weight: normalشده است/span/span/font/font/span/font/font/fontfont color=#000000font face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normal. /span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalبرای این منظور، ابتدا برای هر عضو از یک مدول تفاضلی نوعی نمایش، موسوم به نمایش نسبت به چند ترتیب، معرفی می کنیم/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normal. /span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalسپس با استفاده از این نمایش، اثباتی برای تعمیم قضیه/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;/span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalی بوخبرگر در مدول/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;/span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalهای تفاضلی متناهی مولد، ارایه می/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;/span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalدهیم/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normal. /span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalهمچنین شرط لازم و کافی برای وجود پایه/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;/span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalی گربنر نسبت به چند ترتیب را برای یک مدول تفاضلی بیان می/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;/span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalکنیم/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normal. /span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalدر ادامه، الگوریتمی برای محاسبه/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;/span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalی پایه/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;/span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalی/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy; /span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalگربنر یک زیر مدول تفاضلی متناهی مولد نسبت به چند ترتیب، ارایه می/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normalshy;/span/font/font/span/font/fontfont face=Arialspan lang=ar-SAfont size=3 style=font-size: 13ptspan style=font-style: normalfont face=B Nazaninfont size=3 style=font-size: 12ptspan style=font-weight: normalشود/span/font/font/span/font/span/fontfont face=Yas-Bold, seriffont size=3 style=font-size: 13ptspan style=font-style: normalfont face=Times New Roman, seriffont size=3 style=font-size: 12ptspan style=font-weight: normal./span/font/font/span/font/font/font/p

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