پایه گروبنر

در جبر محاسباتی، و هندسه جبری محاسباتی، یک پایه‌گروبنر عبارت است از نوعی خاص از زیرمجموعه مولد برای یک ایدئال I در حلقه چندجمله‌ای‌های R.

در واقع، یک پایه‌گروبنر عبارت است از مجموعه چندجمله‌ایهای چندمتغیره که دارای ویژگی‌های مفیدی است که یک راه‌حل الگوریتمی برای بسیاری از مسائل بنیادی در ریاضیات و علوم ارائه نموده است. از منظر دیگر روش پایه‌گروبنر تعمیم چندمتغیره غیرخطی از:

  1. الگوریتم اقلیدس برای محاسبه بزرگترین مقسوم علیه مشترک (ب.م.م) در چندجمله‌ای‌های تک‌متغیره،
  2. روش حذفی گاوس برای سیستم‌های خطی، و
  3. مسائل برنامه‌ریزی خطی می‌باشد.

منابع

  • Thomas Becker, Volker Weispfenning, and H. Kredel (1993). Gröbner Bases: A Computational Approach to Commutative Algebra. Springer. ISBN 0387979719.{{cite book}}: نگهداری یادکرد:نام‌های متعدد:فهرست نویسندگان (link)
  • David Cox, John Little, and Donal O'Shea (1997). "Chapter 2: Gröbner Bases". Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer. ISBN 0-387-94680-2.{{cite book}}: نگهداری یادکرد:نام‌های متعدد:فهرست نویسندگان (link)
  • Gert-Martin Greuel, Gerhard Pfister (2002). A Singular Introduction to Commutative Algebra. Springer. ISBN 3540428976.

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