Divisionsalgorithmus.tex

%!TeX spellcheck = de_DE
%!TeX encoding = utf8
%!TEX root = ./test_div.tex
\hbadness=10000
\sProofOn
\descriptionwidth=40pt
\begin{struktogramm}(150,90)
	\assign{ 
		\begin{declaration}[]
				\description{ \( F \) }{freier 
				\( S \)-Modul mit Basis }
				\description{ \( > \) }{ Monomordnung }
				\description{ \( f \) }{ \( \in F \) }
				\description{ 	\(G= g_{1} , \dots ,g_{t}   \)}{\(  \in F \)}
		\end{declaration} %
	}
	\assign{ \( s= \left[  \right] \)}
	\assign{ \( m=\left[  \right] \)}
	\assign{ \( j= 1 \)}
	\assign{ \(f':= f\) }
	\assign{ \( \bar{m}:= ini \left( f' \right) \)}
	\while{ \( \exists  g_{q} \in G \ :\bar{m} | ini \left( g_{q} \right) \)}
		\assign{ \( i = \arg \max \left\{ g_{q} \in G \ :
			m | ini \left( g_{q} \right) \right\} \)}
		\assign{ \( s_{j} := i \)}
		\assign{ \( m_{j} := \bar{m} / ini\left( g_{s_{j}} \right) \)}
		\assign{ \( f':= f-\sum_{l=1}^{j} g_{s_{l}} * m_{l} \)}
		\assign{ \( m:= ini \left( f' \right) \)}

		\assign{ \( j:=j+1 \)}
	\whileend
	
\end{struktogramm}