Ana sayfa Bilimsel Modüller SymPy ile Calculus hesaplamaları – Bölüm 7.1 (Denklem & Denklem sistemleri çözümleri...

SymPy ile Calculus hesaplamaları – Bölüm 7.1 (Denklem & Denklem sistemleri çözümleri )

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Bu yazımızda, çok değişkenli cebirsel denklemlerin SymPy kütüphanesi ile nasıl çözümleneceğini göstereceğiz.

İlk olarak iki bilinmeyenli denklemlerden söz edecek olursak, denklem sistemindeki değişkenlerin değerlerini bulmak için bir çok yöntem kullanabiliriz. Bunlardan biri Cramer yöntemi

Daha önce duymamış olanlar için, basit bir problem Cramer yöntemi ile aşağıda çözülmüştür. Arzu edenler inceleyebilirler.

Bu zahmetli yöntemle boğuşmak yerine iki üç satır kodla bu işlemi SymPy kütüphanesi yardımı ile çözümleyebiliriz.

Denklem sistemini çözümlemek için gerekli fonksiyonun genel hatları şu şekildedir.                                  solve([denklem1,denklem2,…],[değişken1,değişken2,..])

Hadi bunu şimdi koda dökelim !

Gördüğünüz gibi matrisler ile boğuşmak yerine bu yöntem çok daha efektif.

Şimdi denklem sistemimizdeki denklem sayısını attıralım.

Burada dikkat edilmesi gereken tek nokta, denklem sistemindeki A matrisinin determinantının “0” olması durumunda anlamlı bir çözüm veremeyeceğinden dolayı, program [] şeklinde çıktı verecektir. Fakat sadece bu yöntem için…

İstisna olarak, aşağıdaki kodu inceleyecek olursak şayet:

Burada determinant yine “0” dır. Ancak bir değişkenin, başka bir değişken cinsinden yararlanılarak bir çözüm yapılabilir. Buna benzer olarak,

x ve y’nin çözümü, üçüncü bir z değişkeni cinsinden çözümlemelerde yapılabilir.

Sonraki yazılarımızda, daha farklı denklem ve denklem sistemlerinin çözümleri ile ilgileneceğiz. 🙂

Bilimle kalın !

Kaynaklar:

http://docs.sympy.org/0.7.1/tutorial.html

http://docs.sympy.org/latest/modules/solvers/solvers.html

 

 

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