From 2a6fb8abc92fedb62c69339b395334609bc7870d Mon Sep 17 00:00:00 2001 From: Martin Thoma Date: Sun, 1 Sep 2013 17:40:24 +0200 Subject: [PATCH] misc --- documents/eaz/eaz.pdf | Bin 193059 -> 197051 bytes documents/eaz/eaz.tex | 30 ++++++++++- .../SolveLinearCongruences/Makefile | 36 +++++++++++++ .../SolveLinearCongruences/Readme.md | 3 ++ .../SolveLinearCongruences.png | Bin 0 -> 25306 bytes .../SolveLinearCongruences.tex | 46 ++++++++++++++++ .../solveLinearCongruences.py | 49 ++++++++++++++++++ 7 files changed, 163 insertions(+), 1 deletion(-) create mode 100644 source-code/Pseudocode/SolveLinearCongruences/Makefile create mode 100644 source-code/Pseudocode/SolveLinearCongruences/Readme.md create mode 100644 source-code/Pseudocode/SolveLinearCongruences/SolveLinearCongruences.png create mode 100644 source-code/Pseudocode/SolveLinearCongruences/SolveLinearCongruences.tex create mode 100644 source-code/Pseudocode/SolveLinearCongruences/solveLinearCongruences.py diff --git 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In diesem Zusammenhang begegnet uns die Normabbildung. (Ein Beispiel, das in der Vorlesung gesehen wurde, waren die gauß'schen Zahlen.) diff --git a/source-code/Pseudocode/SolveLinearCongruences/Makefile b/source-code/Pseudocode/SolveLinearCongruences/Makefile new file mode 100644 index 0000000..00bfb75 --- /dev/null +++ b/source-code/Pseudocode/SolveLinearCongruences/Makefile @@ -0,0 +1,36 @@ +SOURCE = SolveLinearCongruences +DELAY = 80 +DENSITY = 300 +WIDTH = 500 + +make: + pdflatex $(SOURCE).tex -output-format=pdf + pdflatex $(SOURCE).tex -output-format=pdf + make clean + +clean: + rm -rf $(TARGET) *.class *.html *.log *.aux *.data *.gnuplot + +gif: + pdfcrop $(SOURCE).pdf + convert -verbose -delay $(DELAY) -loop 0 -density $(DENSITY) $(SOURCE)-crop.pdf $(SOURCE).gif + make clean + +png: + make + make svg + inkscape $(SOURCE).svg -w $(WIDTH) --export-png=$(SOURCE).png + +transparentGif: + convert $(SOURCE).pdf -transparent white result.gif + make clean + +svg: + make + #inkscape $(SOURCE).pdf --export-plain-svg=$(SOURCE).svg + pdf2svg $(SOURCE).pdf $(SOURCE).svg + # Necessary, as pdf2svg does not always create valid svgs: + inkscape $(SOURCE).svg --export-plain-svg=$(SOURCE).svg + rsvg-convert -a -w $(WIDTH) -f svg $(SOURCE).svg -o $(SOURCE)2.svg + inkscape $(SOURCE)2.svg --export-plain-svg=$(SOURCE).svg + rm $(SOURCE)2.svg diff --git a/source-code/Pseudocode/SolveLinearCongruences/Readme.md b/source-code/Pseudocode/SolveLinearCongruences/Readme.md new file mode 100644 index 0000000..360fff8 --- /dev/null +++ b/source-code/Pseudocode/SolveLinearCongruences/Readme.md @@ -0,0 +1,3 @@ +Compiled example +---------------- +![Example](SolveLinearCongruences.png) diff --git a/source-code/Pseudocode/SolveLinearCongruences/SolveLinearCongruences.png b/source-code/Pseudocode/SolveLinearCongruences/SolveLinearCongruences.png new file mode 100644 index 0000000000000000000000000000000000000000..7cb9a95d3a35c7f6d6d2b3a63e2a43f17cd45504 GIT binary patch literal 25306 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zkizp*FLExofF;$IXEr#or-v=32+dzD}3) z`p~uxLvLnRWyph?F;KPXR5*=r56oQ9s7hbzntjqSK5b8p{>f9eQjw zlme&v)(|CQJ*e|;HoLZw?+u%%{)}^t&)eX$s@cP3ma`sB8&?XC&fXjoo`3ml*dOTs zd3Sm9RshiMU`Y$b6$HWy%{Qf(w%YD8s@?8n&$Ys(=|GQy5(7n-WLaKFm_XQjv%$<( z?6Z%(lqj-h&UKyjL#KfRbmz{6Y%UXa&X9kyxvIVmtW}8~s2GWT^3 z8oQW1{8K+t0rsHMN$h#QHa?`~Zcp9&$~M4l-YG(H4M(_Fm!H4QJZjfGfHc@XJ^<7l zHoi%@0mHU2|BbMaj%fhJWIq8={r4LS|2sVUI)8QrGa0dV_%G^#SL`PM+FMUlzv4Xz zXZu3_la{pO-K{J+{tN+>> solveLinearCongruenceEquations([4, 12, 14], [19, 37, 43]) + {'congruence class': 22804, 'modulo': 30229} + """ + assert len(rests) == len(modulos) + x = 0 + M = reduce(lambda x, y: x*y, modulos) + + for mi, resti in zip(modulos, rests): + Mi = M / mi + s = ExtendedEuclideanAlgorithm(Mi, mi)["x"] + e = s * Mi + x += resti * e + return {"congruence class": ((x % M) + M) % M, "modulo": M} + +if __name__ == "__main__": + import doctest + doctest.testmod()