إنشاء مخطط هاس لشبكات القواسم برمجيا
Abstract
إن شبكات قواسم عدد صحيح هي من أبرز الأمثلة على الشبكات، لأنها تتنوع تنوعا كبيراً فبعضها يحقق شرط الشبكة التامة، و منها ما يحقق شرط الشبكة التوزيعية، و منها ما يحقق الشرطين و بالتالي يشكل جبر بول.
إن الهدف من هذا البحث هو تقديم خوارزمية برمجية لإنشاء مخطط هاس تفاعلي لبعض شبكات قواسم عدد صحيح، هذه الخوارزمية تولد تلقائيا مخطط شبكة قواسم العدد المطلوب بمجرد إعطائها تحليل هذا العدد إلى عوامله الأولية. حيث إننا لن نخوض في خوارزميات تحليل الأعداد الصحيحة إلى عواملها الأولية وسنأخذ هذه العوامل مباشرة كمعطيات دخل. تُعدّ هذه الخوارزمية خطوة هامة نحو إيجاد تطبيقات برمجية على البنى الجبرية بشكل عام، وعلى دراسة الشبكات بشكل خاص. لأن مخطط هاس له فائدة كبيرة في تبيان طبيعة وخواص الشبكة التي يمثلها.
The lattices of divisors of an integer are one of the most important examples on lattices, there are many kinds of it, some are completed, some are distributed, and some other form Boolean algebra. In this paper we will give a program algorithm to create an interactive Hass Diagram of some of divisors lattices. This algorithm will generate automatically the diagram of the lattice of divisors of a given integer. The integer number must be given as product of its prime factors, because we will not talk about factoring algorithms, and we will input those factors manually.
This algorithm is an important step to develop software applications on algebraic structures, especially on lattices, because of the great importance of Hass diagram in the study of lattices theory.
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