--- /dev/null
+import math
+
+# Berechnet die Summe aller vielfachen von base bis max
+def summandial(m,base=1):
+ m = int(m/base)*base
+ return m*(m+base)/(2*base)
+
+# Gibt die naechst kleine Fib zu max zurueck
+def fib(m):
+ a,b = 1,2
+ while b < m:
+ a,b = b,a+b
+ return a
+
+# Gibt die Liste aller Fib zur naechst kleineren Fib von max zurueck
+def fibV(m):
+ a = [1, 2]
+ i = 1;
+ while a[i] < m:
+ a.append(a[i] + a[i-1])
+ i = i+1
+ return a
+
+# Gibt die Summe aller d-fachen Fib zu max zurueck (d=2)
+def fibS(m,d=2):
+ a,b = 1,2
+ s = 0
+ while b < m:
+ a,b = b,a+b
+ if a%d == 0:
+ s = s +a
+ return s
+
+# Gibt alle Primzahlen bis n zurueck
+def primes(n):
+ if n < 2:
+ return 0
+ p = range(1,n+1,2)
+ q = len(p);
+ p[0] = 2;
+ for k in range(3,int(n**.5+1),2):
+ if p[(k-1)/2]:
+ for i in range(((k*k-1)/2),q,k):
+ p[i] = 0
+ return filter(lambda x:x>0,p)
+
+# Gibt alle Primfaktoren von n zurueck
+def factor(n):
+ if n<4:
+ return [n]
+ p = primes(int(n**.5+1))
+ f = []
+ while n>1:
+ p = filter(lambda x:n%x==0,p)
+ if(p==[]):
+ f.append(n)
+ break
+ f[len(f):] = p
+ n = n/prod(p)
+ f.sort()
+ return f
+
+# Gibt alle Primfaktoren von n als vektor mit Vielfachheit zurueck
+def factorD(n):
+ if n<4:
+ return {n:1}
+ p = primes(int(n**.5+1))
+ f = {}
+ while n>1:
+ p = filter(lambda x:n%x==0,p)
+ if(p==[]):
+ f[n] = 1
+ break
+ for i in range(len(p)):
+ if(p[i] in f):
+ f[p[i]]=f[p[i]]+1
+ else:
+ f[p[i]]=1
+ n = n/prod(p)
+# f.sort()
+ return f
+
+# Multipliziert alle Werte aus Liste seq auf
+def prod(seq):
+ return reduce(lambda x,y:x*y, seq, 1)
+
+# generiert Pyth tripel
+def pythtrip(u,v):
+ return [u*u-v*v, 2*u*v, u*u+v*v]
+
+#Binomial Koeffizient
+def binomial(n,k):
+ return math.factorial(n)/(math.factorial(k)*math.factorial(n-k))
+
+def ebinomial(seq):
+ vek = [1, 0]
+ for i in seq:
+ for j in range(len(vek)-1,0,-1):
+ vek[j] = vek[j]+vek[j-1]*i
+ vek[len(vek):]=[0]
+
+ return vek[:len(vek)-1]
+
+#Anzahl der Teiler
+def divisors(num):
+ test = factorD(num)
+ return sum(ebinomial(map(lambda x:test[x],test.keys()))[1:])+1
+
+
+#Euklid
+def euklid(a,b):
+ if a < b:
+ tmp = a
+ a = b
+ b = tmp
+ x = [1, 0]
+ y = [0, 1]
+ q = int(a / b)
+ while a%b:
+ [a ,b] = [b,a-q*b]
+ x = [x[1],x[0]-q*x[1]]
+ y = [y[1],y[0]-q*y[1]]
+ q = int(a/b)
+ return [b,x[1],y[1]]
+
+def euklid_tex(a,b):
+ if a < b:
+ tmp = a
+ a = b
+ b = tmp
+ x = [1, 0]
+ y = [0, 1]
+ q = int(a / b)
+ print "\\begin{array}{ccccccc}"
+ print " r_{i-2} & r_{i-1} & q_i & x_{i-2} & x_{i-1} & y_{i-2} & y_{i-1}\\\\\\hline"
+ print " ", a, "&" , b ,"&" , q,"&" ,x[0],"&",x[1] ,"&",y[0] ,"&" ,y[1],"\\\\"
+ while a%b:
+ [a ,b] = [b,a-q*b]
+ x = [x[1],x[0]-q*x[1]]
+ y = [y[1],y[0]-q*y[1]]
+ q = int(a/b)
+ if a%b:
+ print " ", a, "&" , b ,"&" , q,"&" ,x[0],"&",x[1] ,"&",y[0] ,"&" ,y[1],"\\\\"
+ else:
+ print " \\cline{2-2}\\cline{5-5}\\cline{7-7}"
+ print " \multicolumn{1}{l|}{", a, "}& \multicolumn{1}{l|}{" , b ,
+ print "}&&\multicolumn{1}{l|}{" ,x[0],"}&\multicolumn{1}{l|}{",x[1] ,
+ print "}&\multicolumn{1}{l|}{",y[0] ,"}&\multicolumn{1}{l|}{" ,y[1], "}\\\\"
+ print " \\cline{2-2}\\cline{5-5}\\cline{7-7}"
+ print "\\end{array}",
+ return [b,x[1],y[1]]
+
+def gcd(a,b):
+ return euklid(a,b)[0]
+
+#euklid_tex(2124,1764)
+
\ No newline at end of file
--- /dev/null
+%% This program is free software; you can redistribute it and/or
+%% modify it under the terms of the GNU General Public License
+%% as published by the Free Software Foundation; either version 2
+%% of the License, or (at your option) any later version.
+%%
+%% This program is distributed in the hope that it will be useful,
+%% but WITHOUT ANY WARRANTY; without even the implied warranty of
+%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+%% GNU General Public License for more details.
+%%
+%% You should have received a copy of the GNU General Public License
+%% along with this program; if not, write to the Free Software
+%% Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
+%%
+%% Author: Martin R. Ehmsen, ehmsen@imada.sdu.dk.
+%% Department of Mathematics and Computer Science,
+%% University of Southern Denmark, DK
+%%
+%% You can find an online copy of the GPL at
+%% http://www.gnu.org/copyleft/gpl.html .
+%%
+%% Note: shell-escape needs to be activated for this to work.
+%% This can either be done by passing -shell-escape as an option to
+%% latex or by adding/changing "shell_escape = t" in your texmf.cnf .
+
+% 0.2 -> 0.21: Moved \newwrite\@module from \@writemodule and out, since
+% no more than 15 \newwrites are allowed (and the previous version created a new
+% every time \@writemodule was called.
+
+\NeedsTeXFormat{LaTeX2e}[1994/12/01]
+\ProvidesPackage{python}[2007/06/07 v0.21 Python in LaTeX]
+
+\newwrite\@out
+\newwrite\@module
+
+\begingroup \catcode `|=0 \catcode `[=1
+\catcode`]=2 \catcode `\{=12 \catcode `\}=12
+\catcode`\\=12 |gdef|@xpython#1\end{python}[|immediate|write|@out[#1]|end[python]]
+|endgroup
+
+\def\python{\kernel@ifnextchar [{\@python}{\@python[]}}
+
+
+\newcounter{py@codenum}
+\def\@python[#1]{%
+\stepcounter{py@codenum}
+\gdef\@pythoninclude{#1}
+\immediate\openout\@out=\jobname.py
+\newlinechar='15
+\begingroup \catcode`\^^M=12 %
+\let\do\@makeother\dospecials\obeyspaces%
+\@xpython}
+
+\def\endpython{%
+\endgroup
+\immediate\closeout\@out
+\@writemodule
+\immediate\write18{python\space\jobname.py > \jobname.py.\thepy@codenum.out 2> \jobname.py.\thepy@codenum.err}
+\immediate\input\jobname.py.\thepy@codenum.out}
+
+
+
+% \def\@python[#1]{%
+% \gdef\@pythoninclude{#1}
+% \immediate\openout\@out=\jobname.py
+% \newlinechar='15
+% \begingroup \catcode`\^^M=12 %
+% \let\do\@makeother\dospecials\obeyspaces%
+% \@xpython}
+%
+% \def\endpython{%
+% \endgroup
+% \immediate\closeout\@out
+% \@writemodule
+% \immediate\write18{cat \@pythoninclude\space\jobname.py | python > \jobname.py.out 2> \jobname.py.err}
+% \immediate\input\jobname.py.out}
+% %\immediate\write{\begin{verbatim}}
+% %\immediate\input\jobname.py.err
+% %\immediate\write{\end{verbatim}}}
+
+\def\@writemodule{%
+\immediate\openout\@module=latex.py
+\immediate\write\@module{jobname="\jobname"}
+\immediate\closeout\@module}
+
+% BUGS:
+% 1. If anything gets send to stderr then it should be included
+% in \begin{verbatim}...\end{verbatim} to be properly displayed
+%
+% \immediate\write18{cat \@pythoninclude\space\jobname.py | python > \jobname.py.out 2>\jobname.py.err}
+%
+% 2. Watch out for indentation done by aucTeX in Emacs
+%
+% 3. Let the package accept a "final version" option, such
+% that the output of each python run is saved such that it can be
+% inserted into the document by hand
+% (conference, journals are not likely to compile with
+% shell_escape or have python).
+%
+% \gdef\@prepython{}
+% \def\prepython#1{%
+% \gdef\@prepython{#1}
+% }
+% sed -e 's/^ //g' cluster.py
+% \immediate\write18{\@prepython\space\jobname.py > \
\ No newline at end of file
-
+import lib
def f(x,m=120):
return (2*x**3-3*x**2+5*x+6)%m
+++ /dev/null
-import math
-
-# Berechnet die Summe aller vielfachen von base bis max
-def summandial(m,base=1):
- m = int(m/base)*base
- return m*(m+base)/(2*base)
-
-# Gibt die naechst kleine Fib zu max zurueck
-def fib(m):
- a,b = 1,2
- while b < m:
- a,b = b,a+b
- return a
-
-# Gibt die Liste aller Fib zur naechst kleineren Fib von max zurueck
-def fibV(m):
- a = [1, 2]
- i = 1;
- while a[i] < m:
- a.append(a[i] + a[i-1])
- i = i+1
- return a
-
-# Gibt die Summe aller d-fachen Fib zu max zurueck (d=2)
-def fibS(m,d=2):
- a,b = 1,2
- s = 0
- while b < m:
- a,b = b,a+b
- if a%d == 0:
- s = s +a
- return s
-
-# Gibt alle Primzahlen bis n zurueck
-def primes(n):
- if n < 2:
- return 0
- p = range(1,n+1,2)
- q = len(p);
- p[0] = 2;
- for k in range(3,int(n**.5+1),2):
- if p[(k-1)/2]:
- for i in range(((k*k-1)/2),q,k):
- p[i] = 0
- return filter(lambda x:x>0,p)
-
-# Gibt alle Primfaktoren von n zurueck
-def factor(n):
- if n<4:
- return [n]
- p = primes(int(n**.5+1))
- f = []
- while n>1:
- p = filter(lambda x:n%x==0,p)
- if(p==[]):
- f.append(n)
- break
- f[len(f):] = p
- n = n/prod(p)
- f.sort()
- return f
-
-# Gibt alle Primfaktoren von n als vektor mit Vielfachheit zurueck
-def factorD(n):
- if n<4:
- return {n:1}
- p = primes(int(n**.5+1))
- f = {}
- while n>1:
- p = filter(lambda x:n%x==0,p)
- if(p==[]):
- f[n] = 1
- break
- for i in range(len(p)):
- if(p[i] in f):
- f[p[i]]=f[p[i]]+1
- else:
- f[p[i]]=1
- n = n/prod(p)
-# f.sort()
- return f
-
-# Multipliziert alle Werte aus Liste seq auf
-def prod(seq):
- return reduce(lambda x,y:x*y, seq, 1)
-
-# generiert Pyth tripel
-def pythtrip(u,v):
- return [u*u-v*v, 2*u*v, u*u+v*v]
-
-#Binomial Koeffizient
-def binomial(n,k):
- return math.factorial(n)/(math.factorial(k)*math.factorial(n-k))
-
-def ebinomial(seq):
- vek = [1, 0]
- for i in seq:
- for j in range(len(vek)-1,0,-1):
- vek[j] = vek[j]+vek[j-1]*i
- vek[len(vek):]=[0]
-
- return vek[:len(vek)-1]
-
-#Anzahl der Teiler
-def divisors(num):
- test = factorD(num)
- return sum(ebinomial(map(lambda x:test[x],test.keys()))[1:])+1
\ No newline at end of file
+++ /dev/null
-%% This program is free software; you can redistribute it and/or
-%% modify it under the terms of the GNU General Public License
-%% as published by the Free Software Foundation; either version 2
-%% of the License, or (at your option) any later version.
-%%
-%% This program is distributed in the hope that it will be useful,
-%% but WITHOUT ANY WARRANTY; without even the implied warranty of
-%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
-%% GNU General Public License for more details.
-%%
-%% You should have received a copy of the GNU General Public License
-%% along with this program; if not, write to the Free Software
-%% Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
-%%
-%% Author: Martin R. Ehmsen, ehmsen@imada.sdu.dk.
-%% Department of Mathematics and Computer Science,
-%% University of Southern Denmark, DK
-%%
-%% You can find an online copy of the GPL at
-%% http://www.gnu.org/copyleft/gpl.html .
-%%
-%% Note: shell-escape needs to be activated for this to work.
-%% This can either be done by passing -shell-escape as an option to
-%% latex or by adding/changing "shell_escape = t" in your texmf.cnf .
-
-% 0.2 -> 0.21: Moved \newwrite\@module from \@writemodule and out, since
-% no more than 15 \newwrites are allowed (and the previous version created a new
-% every time \@writemodule was called.
-
-\NeedsTeXFormat{LaTeX2e}[1994/12/01]
-\ProvidesPackage{python}[2007/06/07 v0.21 Python in LaTeX]
-
-\newwrite\@out
-\newwrite\@module
-
-\begingroup \catcode `|=0 \catcode `[=1
-\catcode`]=2 \catcode `\{=12 \catcode `\}=12
-\catcode`\\=12 |gdef|@xpython#1\end{python}[|immediate|write|@out[#1]|end[python]]
-|endgroup
-
-\def\python{\kernel@ifnextchar [{\@python}{\@python[]}}
-
-
-\newcounter{py@codenum}
-\def\@python[#1]{%
-\stepcounter{py@codenum}
-\gdef\@pythoninclude{#1}
-\immediate\openout\@out=\jobname.py
-\newlinechar='15
-\begingroup \catcode`\^^M=12 %
-\let\do\@makeother\dospecials\obeyspaces%
-\@xpython}
-
-\def\endpython{%
-\endgroup
-\immediate\closeout\@out
-\@writemodule
-\immediate\write18{python\space\jobname.py > \jobname.py.\thepy@codenum.out 2> \jobname.py.\thepy@codenum.err}
-\immediate\input\jobname.py.\thepy@codenum.out}
-
-
-
-% \def\@python[#1]{%
-% \gdef\@pythoninclude{#1}
-% \immediate\openout\@out=\jobname.py
-% \newlinechar='15
-% \begingroup \catcode`\^^M=12 %
-% \let\do\@makeother\dospecials\obeyspaces%
-% \@xpython}
-%
-% \def\endpython{%
-% \endgroup
-% \immediate\closeout\@out
-% \@writemodule
-% \immediate\write18{cat \@pythoninclude\space\jobname.py | python > \jobname.py.out 2> \jobname.py.err}
-% \immediate\input\jobname.py.out}
-% %\immediate\write{\begin{verbatim}}
-% %\immediate\input\jobname.py.err
-% %\immediate\write{\end{verbatim}}}
-
-\def\@writemodule{%
-\immediate\openout\@module=latex.py
-\immediate\write\@module{jobname="\jobname"}
-\immediate\closeout\@module}
-
-% BUGS:
-% 1. If anything gets send to stderr then it should be included
-% in \begin{verbatim}...\end{verbatim} to be properly displayed
-%
-% \immediate\write18{cat \@pythoninclude\space\jobname.py | python > \jobname.py.out 2>\jobname.py.err}
-%
-% 2. Watch out for indentation done by aucTeX in Emacs
-%
-% 3. Let the package accept a "final version" option, such
-% that the output of each python run is saved such that it can be
-% inserted into the document by hand
-% (conference, journals are not likely to compile with
-% shell_escape or have python).
-%
-% \gdef\@prepython{}
-% \def\prepython#1{%
-% \gdef\@prepython{#1}
-% }
-% sed -e 's/^ //g' cluster.py
-% \immediate\write18{\@prepython\space\jobname.py > \
\ No newline at end of file
%& -shell-escape
\documentclass[a4paper,10pt,fleqn]{article}
-\usepackage{template}
+\usepackage{../template}
\usepackage{python}
\begin{document}
- \begin{python}
- print "hello"
- \end{python}
-
- \begin{python}
- print "hello2"
- \end{python}
+
+
+
+\begin{python}
+import lib
+euklid_tex(
+\end{python}
+
\end{document}
\usepackage{fancyhdr}
% \usepackage{emaxima}
+\usepackage{python}
+
\def\P{\mathbb{P}}
\def\N{\mathbb{N}}
\def\R{\mathbb{R}}
\end{align}
\aufgabe{3}{}
+\begin{center}$
+\begin{python}
+import lib
+lib.euklid_tex(312,269)
+\end{python}$
+\end{center}
+
\begin{align}
-&\begin{array}{ccccccc}
- r_{i-2} & r_{i-1}& q_i & x_{i-2} & x_{i-1} & y_{i-2} & y_{i-1}\\
- 312 & 269 & 1 & 1 & 0 & 0 & 1\\
- 269 & 43 & 6 & 0 & 1 & 1 & -1\\
- 43 & 11 & 3 & 1 & -6 & -1 & 7\\
- 11 & 10 & 1 & -6 & 19 & 7 & - 22\\
- 10 & 1 & & 19 & -25 & -22 & 29\\
-\end{array}\\
\ggT(312,269) & = 1\\
1 & = -25*312+29*269\\
5 & = -125*312+145*269\\
projects / zahlenTA.git / commitdiff