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-rw-r--r--mat/domace_naloge/30/dokument.aux37
-rw-r--r--mat/domace_naloge/30/dokument.log1463
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-rw-r--r--mat/domace_naloge/30/dokument.tex233
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-rw-r--r--mat/domace_naloge/30/kompleksnost.c27
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+\BOOKMARK [1][-]{section.1}{\376\377\000Z\000a\000k\000l\000j\000u\001\015\000e\000k}{}% 1
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@@ -0,0 +1,233 @@
+% !TeX encoding = UTF-8
+% !TeX spellcheck = sl_SI
+% do-vimlatex-onwrite
+\documentclass[]{article}
+\usepackage[utf8]{inputenc}
+\usepackage{etoolbox}
+\usepackage[hidelinks]{hyperref}
+\usepackage{xurl} % da breaka url
+\usepackage[a4paper, total={7in, 10in}]{geometry}
+\usepackage{graphicx}
+\usepackage{hologo}
+\usepackage{amssymb}
+\usepackage{calculator}
+\usepackage{pgfplots}
+\usepackage[inline]{enumitem}
+\usepackage{siunitx}
+\usepackage{multicol}
+\usepackage{tabularcalc}
+\usepackage{amsmath}
+\usepackage{float}
+\usepackage{tasks}
+\usepackage{filecontents}
+\usepackage{textcomp}
+\usepackage{tkz-euclide}
+\usepackage{dirtytalk}
+\usepackage{csquotes}
+\usepackage{listings}
+\usepackage{datetime} % [ddMMyyyy]
+\usepackage{ccicons}
+\usepackage{chemformula}
+\usepackage{gensymb}
+\usepackage[normalem]{ulem}
+\usepackage[slovene]{babel}
+\usepackage{cancel}
+\usepackage{tabularx}
+\usepackage{xcolor}
+\usepackage{colortbl}
+\usepackage{exsheets}
+\usepackage{harpoon}
+\usepackage{readarray}
+\usepackage{forloop}
+\usepackage[nomessages]{fp}
+\usepackage{multirow}
+\newcolumntype{Y}{>{\centering\arraybackslash}X}
+% \usepackage{multienum} % weird with labels
+\usetikzlibrary{calc} %% not really needed............. idk.
+%\usetikzlibrary{external}
+% \usetkzobj{all} % tkz-euclide > 3.02 tega ne potrebuje več (:
+%\tikzexternalize
+\sisetup{output-decimal-marker = {,}, quotient-mode=fraction,per-mode=fraction} % per-mode=symbol
+\newcommand\ddfrac[2]{\frac{\displaystyle #1}{\displaystyle #2}}
+\newcommand{\functionSamples}{100} % fix to fancier value upon release, keep low during development
+\newcommand{\razhroscevanje}{1}
+\definecolor{codegreen}{rgb}{0,0.6,0}
+\definecolor{codered}{rgb}{1,0,0}
+\definecolor{codegray}{rgb}{0.5,0.5,0.5}
+\definecolor{codepurple}{rgb}{0.58,0,0.82}
+\definecolor{backcolour}{rgb}{0.95,0.95,0.92}
+\renewcommand{\dateseparator}{. }
+\settimeformat{hhmmsstime}
+\lstdefinestyle{mystyle}{
+ backgroundcolor=\color{backcolour},
+ commentstyle=\color{codegreen},
+ keywordstyle=\color{magenta},
+ numberstyle=\tiny\color{codegray},
+ stringstyle=\color{codepurple},
+ basicstyle=\ttfamily\footnotesize,
+ breakatwhitespace=false,
+ breaklines=true,
+ captionpos=b,
+ keepspaces=true,
+ numbers=left,
+ numbersep=5pt,
+ showspaces=false,
+ showstringspaces=false,
+ showtabs=false,
+ tabsize=2
+}
+\lstset{style=mystyle}
+\def\@maketitle{%
+ \newpage
+ \null
+ \vskip 2em%
+ \begin{center}%
+ \let \footnote \thanks
+ {\LARGE \@title \par}%
+ \vskip 1.5em%
+ {\large
+ \lineskip .5em%
+ \begin{tabular}[t]{c}% <------
+ \@author% <------ Authors
+ \end{tabular}\par}% <------
+ \vskip 1em%
+ {\large \@date}%
+ \end{center}%
+ \par
+ \vskip 1.5em}
+%opening
+\newcommand{\snovdn}{Potence z racionalnimi eksponenti }
+\newcommand{\predmdn}{mat}
+\newcommand{\predmkaj}{domace\_naloge}
+\newcommand{\stevilkadn}{30}
+\newcommand{\cm}[1]{\SI{#1}{\centi\meter}}
+\newcommand{\kmh}[1]{\SI{#1}{\kilo\meter\per\hour}}
+\makeatletter
+\newcommand{\xslalph}[1]{\expandafter\@xslalph\csname c@#1\endcsname}
+\newcommand{\@xslalph}[1]{%
+ \ifcase#1\or a\or b\or c\or \v{c}\or d\or e\or f\or g\or h\or i%
+ \or j\or k\or l\or m\or n\or o\or p\or r\or s\or \v{s}%
+ \or t\or u\or v\or z\or \v{z}
+ \else\@ctrerr\fi%
+}
+\AddEnumerateCounter{\xslalph}{\@xslalph}{m}
+\makeatother
+\newcommand\gauss[2]{1/(#2*sqrt(2*pi))*exp(-((x-#1)^2)/(2*#2^2))} % Gauss function, parameters mu and sigma
+\newcommand*\textfrac[2]{
+ \frac{\text{#1}}{\text{#2}}
+}
+\NewTasks[counter-format=\xslalph*),label-format=\bfseries]{primerTasks}(3)
+\newcommand\vektor{\overrightarrow}
+\newcommand{\iic}{I\textsuperscript{2}C }
+\title{%
+ \snovdn --- \stevilkadn. domača naloga
+ \\
+ \large Matematika, Gimnazija Bežigrad}
+\author{\begin{tabular}{rl}
+ \textbf{Profesor:} & prof. Vilko Domajnko \\
+ \textbf{Avtor:} & Anton Luka Šijanec, 2. a
+% \textbf{Avtor:} & Anton Luka Šijanec \\ & Member 2 \\ & Member 3
+\end{tabular}}
+\newcommand\hcancel[2][black]{\setbox0=\hbox{$0#2$}%
+\rlap{\raisebox{.45\ht0}{\textcolor{#1}{\rule{\wd0}{1pt}}}}#2}
+\everymath{\displaystyle} % https://tex.stackexchange.com/a/32847/212260
+\begin{document}
+\maketitle
+\begin{abstract}
+Ta dokument vsebuje navodila in rešitve domače naloge snovi \textit{\snovdn}pri matematiki, ki sem jih spisal sam.
+Kjer je bilo potrebno izbrati neke poljubne naloge, sem jih vedno izbiral naključno.
+\end{abstract}
+\paragraph{Navodilo naloge} \textbf{listi}: \textit{Potence z racionalnimi eksponenti} / 1, ... 6 (povsod po en primer)
+%\tableofcontents
+\begin{enumerate}[label=\textbf{\arabic*.}]
+ \item Zapiši v obliki potence z racionalnim eksponentom:
+ \begin{enumerate}[label=\textbf{\xslalph*)}]
+ \setcounter{enumii}{3}
+ \item $\sqrt{a^3}\cdot\sqrt{a^5}=a^4$
+ \end{enumerate}
+ \item Zapiši v obliki potence z racionalnim eksponentom:
+ \begin{enumerate}[label=\textbf{\xslalph*)}]
+ \item $\sqrt{a\sqrt{a}}=\sqrt{a\cdot a^\frac{1}{2}}=\sqrt{a^\frac{3}{2}}=\left(a^\frac{3}{2}\right)^\frac{1}{2}=a^\frac{3}{4}$
+ \end{enumerate}
+ \item Izračunaj:
+ \begin{enumerate}[label=\textbf{\xslalph*)}]
+ \setcounter{enumii}{5}
+ \item
+ $$
+ \left(\sqrt[6]{9-4\sqrt{5}+\sqrt[3]{2-\sqrt{5}}}\right)\sqrt[3]{2+\sqrt{5}}
+ =\left(\sqrt[6]{\left(2-\sqrt{5}\right)^2}+\sqrt[3]{2+\sqrt{5}}\right)\sqrt[3]{2+\sqrt{5}}=
+ $$
+ $$
+ =\left(\sqrt[3]{\sqrt{5}-2}+\sqrt[3]{2-\sqrt{5}}\right)\sqrt[3]{2+\sqrt{5}}
+ =\sqrt[3]{\left(\sqrt{5}-2\right)\cdot\left(2+\sqrt{5}\right)}+\sqrt[3]{\left(2-\sqrt{5}\right)\cdot\left(2+\sqrt{5}\right)}=
+ $$
+ $$
+ =\sqrt[3]{\left(\sqrt{5}-2\right)\cdot\left(\sqrt{5}+2\right)}+\sqrt[3]{4-5}=
+ \sqrt[3]{5-4}+\sqrt[3]{-1}=1-1=0
+ $$
+ \end{enumerate}
+ \item Poenostavi in zapiši v obliki ulomka (brez negativnih eksponentov):
+ \begin{enumerate}[label=\textbf{\xslalph*)}]
+ \setcounter{enumii}{1}
+ \item $\left(2x^\frac{1}{5}y^\frac{4}{5}\right)^{-5}=\frac{1}{\left(2x^\frac{1}{5}y^\frac{4}{5}\right)^5}=\frac{1}{32xy^4}$
+ \end{enumerate}
+ \item Poenostavi:
+ \begin{enumerate}[label=\textbf{\xslalph*)}]
+ \setcounter{enumii}{1}
+ \item $\sqrt{a^3\cdot\sqrt[3]{\frac{1}{a^2}\cdot\sqrt{a}}}=\sqrt{a^3\cdot a^\frac{-1}{2}}=\sqrt{a^\frac{5}{2}}
+ =\left(a^\frac{5}{2}\right)^\frac{1}{2}=a^\frac{5}{4}=\sqrt[4]{a^5}=a\sqrt[4]{a}$
+ \end{enumerate}
+ \item Poenostavi:
+ \begin{enumerate}[label=\textbf{\xslalph*)}]
+ \setcounter{enumii}{1}
+ \item Vau, štiri korene smo spremenili v enega! Spodaj je praktična zanimivost.
+ $$
+ \sqrt[3]{\frac{x^2}{x-1}}\cdot\sqrt{\frac{\left(x-1\right)^2}{x^5}}\cdot\sqrt[6]{\frac{x^{20}}{\left(x+ 1\right)^3}}\cdot\sqrt{\frac{x+1}{x^3}}=
+ \sqrt[6]{\left(\frac{x^2}{x-1}\right)^2\cdot\left(\frac{\left(x-1\right)^2}{x^5}\right)^3\cdot\frac{x^{20}}{\left(x+1}\right)^3\cdot\left(\frac{x+1}{x^3}\right)^3}=
+ $$
+ $$
+ =\sqrt[6]{\left(\frac{x^2}{x-1}\right)^2\cdot\left(\frac{\left(x-1\right)^2}{x^5}\right)^3
+ \cdot\frac{x^{20}}{\left(x+1\right)^3}\cdot\left(\frac{x+1}{x^3}\right)^3}=
+ \sqrt[6]{\frac{x^4}{\left(x-1\right)^2}\cdot\frac{\left(x-1\right)^6}{x^{15}}
+ \cdot\frac{x^{20}}{\left(x+1\right)^3}\cdot\frac{\left(x+1\right)^3}{x^9}}=
+ $$
+ $$
+ =\sqrt[6]{\left(x-1\right)^4\cdot x^5\cdot\frac{1}{x^5}}=
+ \sqrt[6]{\left(x-1\right)^4}=\sqrt[3]{\left(x-1\right)^2}
+ $$
+ \paragraph{Zanimivost} Želim preveriti, kako taka optimizacija vpliva v resničnem življenju. Recimo, da se ta račun v računalniku izvede desetmilijonkrat v sklopu nekega procesa. Koliko procesorskega časa smo pridobili s tem, da smo štiri korene spremenili v enega? Kljub vsemu smo na koncu optimizacije dobili šesti koren, kar nikakor ni mačji kašelj za X86 arhitekturo. Najlažje je računalniku računati korene kvadratnih eksponentov (2, 4, 16, ...).
+ \lstinputlisting[language=Octave]{kompleksnost.c}
+
+\texttt{a@upor:[0]\$ ./kompleksnost \\
+neoptimizirana enacba je za 10e6 iteracij porabila 15.330899 sekund, optimizirana pa 4.157521 \\
+rezultat = 278495353224.555294, rezultat2 = 278495353224.555814 \\
+a@upor:[0]\$ \\}
+
+ Ojej! Mislim, da je razlika očitna. Neoptimizirana enačba je porabila 10 sekund več. Optimizacija je torej zelo pomembna. Ampak zakaj tega namesto nas ne delajo računalniki? V GNU prevajalniku C jezika sem avtomatilno optimizacijo nastavil na nivo \texttt{0}, kar pomeni, da prevajalnik ne dela optimizacij, v navodilih za uporabo pa sem, poleg drugih, zasledil še eno opcijo, \texttt{fast}. Opcija \texttt{fast} je sicer eksperimentalna in nepriporočena, vendar dela čudeže! Če program prevedem z optimizacijskim nivojem \texttt{fast}, bo računanje neoptimizirane enačbe in optimizirane trajalo približno enako dolgo.
+
+\texttt{a@upor:[0]\$ gcc kompleksnost.c -pedantic -Wall -Wextra -g -okompleksnost -lm -Ofast \\
+a@upor:[0]\$ ./kompleksnost \\
+neoptimizirana enacba je za 10e6 iteracij porabila 5.326709 sekund, optimizirana pa 4.017244 \\
+rezultat = 278495353224.555294, rezultat2 = 278495353224.555814 \\
+a@upor:[0]\$ \\}
+ \end{enumerate}
+\end{enumerate}
+\section{Zaključek}
+Ta dokument je informativne narave in se lahko še spreminja. Najnovejša različica, torej PDFji in
+\hologo{LaTeX}\footnote{Za izdelavo dokumenta potrebujete \texttt{TeXLive 2020}.}
+izvorna koda, zgodovina sprememb in prejšnje različice, je na voljo v mojem šolskem Git repozitoriju na
+\url{https://git.sijanec.eu/sijanec/sola-gimb-2} v mapi
+\href{https://git.sijanec/sola-gimb-2/src/branch/master/\predmdn/\predmkaj/\stevilkadn/}{/\predmdn/\predmkaj/\stevilkadn/}. Povezava za ogled zadnje različice tega dokumenta v PDF obliki je \url{http://razor.arnes.si/~asija3/files/sola/gimb/2/\predmdn/\predmkaj/\stevilkadn/dokument.pdf} in/ali \url{https://git.sijanec.eu/sijanec/sola-gimb-2/raw/branch/master/\predmdn/\predmkaj/\stevilkadn/dokument.pdf}.
+\if\razhroscevanje1
+\vfill
+\section*{Razhroščevalne informacije}
+Te informacije so generirane, ker je omogočeno razhroščevanje. Pred objavo dokumenta izklopite razhroščevanje. To naredite tako, da nastavite ukaz \texttt{razhroscevanje} na 0 v začetku dokumenta.
+
+Grafi imajo natančnost \functionSamples\space točk na graf.
+
+Konec generiranja dokumenta: \today\ ob \currenttime\footnote{To ne nakazuje dejanskega časa, ko je bil dokument napisan, temveč čas, ko je bi dokument generiran v PDF/DVI obliko. Isto velja za datum v glavi dokumenta. Če berete direktno iz LaTeX datoteke, bo to vedno današnji datum.}%\input|"date -Ins"
+
+Dokument se je generiral R0qK1KR2 \SI{}{\second}.
+\fi
+% \item $$$$ aaasecgeninsaaa R0qK1KR2
+\end{document}
diff --git a/mat/domace_naloge/30/kompleksnost b/mat/domace_naloge/30/kompleksnost
new file mode 100755
index 0000000..31f2eff
--- /dev/null
+++ b/mat/domace_naloge/30/kompleksnost
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diff --git a/mat/domace_naloge/30/kompleksnost.c b/mat/domace_naloge/30/kompleksnost.c
new file mode 100644
index 0000000..ae36c99
--- /dev/null
+++ b/mat/domace_naloge/30/kompleksnost.c
@@ -0,0 +1,27 @@
+/* gcc kompleksnost.c -pedantic -E -Wall -Wextra -g -okompleksnost -lm -O0 */
+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <time.h>
+#define KOLIKOKRAT 10000001
+#define nrx(x, y) powl((x), 1.0 / (y)) /* nti koren izpeljemo iz potence na 1/eks */
+int main (void) { /* za kvadratne in kubicne korene uporabimo sqrt in cbrt */
+ long double rezultat = 0; /* da prevajalnik ne bi optimiziral */
+ long double rezultat2 = 0;
+ clock_t cas_zacetek, cas_konec, cas2_konec;
+ cas_zacetek = clock();
+ for (unsigned long long int x = 2; x <= KOLIKOKRAT; x++)
+ rezultat += cbrtl(powl(x, 2)/(x-1))*sqrtl(powl(x-1, 2)/powl(x, 5))*nrx(powl(x, 20)/powl(x+1, 3), 6)*sqrtl((x+1)/powl(x, 3));
+ cas_konec = clock();
+ for (unsigned long long int x = 2; x <= KOLIKOKRAT; x++)
+ rezultat2 += nrx(pow(x-1, 2), 3);
+ cas2_konec = clock();
+ fprintf(stdout, "neoptimizirana enacba je za 10e6 iteracij porabila %lf sekund, optimizirana pa %lf\n"
+ "rezultat = %Lf, rezultat2 = %Lf\n",
+ ((double) (cas_konec-cas_zacetek))/CLOCKS_PER_SEC,
+ ((double) (cas2_konec-cas_konec))/CLOCKS_PER_SEC,
+ rezultat,
+ rezultat2
+ );
+ return 0;
+}
diff --git a/mat/domace_naloge/30/stderr.log b/mat/domace_naloge/30/stderr.log
new file mode 100644
index 0000000..e69de29
--- /dev/null
+++ b/mat/domace_naloge/30/stderr.log
diff --git a/mat/domace_naloge/30/stdout.log b/mat/domace_naloge/30/stdout.log
new file mode 100644
index 0000000..4b3f4f9
--- /dev/null
+++ b/mat/domace_naloge/30/stdout.log
@@ -0,0 +1,475 @@
+This is pdfTeX, Version 3.14159265-2.6-1.40.21 (TeX Live 2020) (preloaded format=pdflatex)
+ \write18 enabled.
+entering extended mode
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