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% Copyright 2011 by Alain Matthes
%
% This file may be distributed and/or modified
%
% 1. under the LaTeX Project Public License and/or
% 2. under the GNU Public License.
\def\fileversion{1.161 c}
\def\filedate{2011/06/12}
% 1.161 test if "isfactor" is already defined
%<--------------------------------------------------------------------------–>
% Objet : tools for arithmetic
%<--------------------------------------------------------------------------–>
% [About integers numbers]
%<--------------------------------------------------------------------------–>
\ProvidesFile{tkz-tool-arith.tex}[tkz-tool-arith 1.161 c]
\edef\tkzAtCode{\the\catcode`\@}
\catcode`\@=11\relax
%<--------------------------------------------------------------------------–>
% arithmetic tools
%<--------------------------------------------------------------------------–>
\tkzutil@ifundefined{pgfmath@function@gcd}{%
\pgfmathdeclarefunction{gcd}{2}{%
\begingroup%
\pgfmathcontinuelooptrue
\pgfmath@xa=#1pt\relax%
\pgfmath@xb=#2pt\relax%
\ifdim\pgfmath@xa=0pt \pgfmathcontinueloopfalse
\pgfmath@xa=\pgfmath@xb
\fi
\ifdim\pgfmath@xb=0pt \pgfmathcontinueloopfalse
\pgfmath@xb=\pgfmath@xa
\fi
\loop
\ifpgfmathcontinueloop
\ifdim \pgfmath@xa=\pgfmath@xb\pgfmathcontinueloopfalse
\else
\ifdim \pgfmath@xa>\pgfmath@xb
\advance \pgfmath@xa by-\pgfmath@xb
\else
\advance \pgfmath@xb by-\pgfmath@xa
\fi
\fi
\repeat
\edef\pgfmathresult{\pgfmath@tonumber{\pgfmath@xa}}%
\pgfmath@smuggleone\pgfmathresult
\endgroup
}
}{}
%<--------------------------------------------------------------------------->
\tkzutil@ifundefined{pgfmath@function@isprime}{%
\newif\ifpgf@unknown
\newif\ifpgf@isaprime
\pgfmathdeclarefunction{isprime}{1}{%
\begingroup%
\pgf@unknowntrue
\c@pgfmath@counta#1\relax%
\ifcase#1\relax
% |#1| = 0
\pgf@isaprimefalse\pgf@unknownfalse
\or
% |#1| = 1
\pgf@isaprimefalse\pgf@unknownfalse
\or
% |#1| = 2
\pgf@isaprimetrue\pgf@unknownfalse
\or
% |#1| = 3
\pgf@isaprimetrue\pgf@unknownfalse
\else
% |#1| > 3
\ifodd#1\relax
\else
\pgf@isaprimefalse\pgf@unknownfalse
\fi
\fi
\ifpgf@unknown
\c@pgfmath@countd=\thr@@ \pgf@isaprimetrue
\loop
\c@pgfmath@countb=\c@pgfmath@counta
\divide\c@pgfmath@countb by\c@pgfmath@countd
\ifnum\c@pgfmath@countb>\c@pgfmath@countd \pgf@unknowntrue
\else\pgf@unknownfalse\fi
\multiply\c@pgfmath@countb by\c@pgfmath@countd
\ifnum\c@pgfmath@countb=\c@pgfmath@counta
\global\pgf@isaprimefalse\pgf@unknownfalse\fi
\ifpgf@unknown\advance\c@pgfmath@countd by 2\relax%
\repeat
\fi
\ifpgf@isaprime
\def\pgfmathresult{1}%
\else
\def\pgfmathresult{0}%
\fi
\pgfmath@smuggleone\pgfmathresult%
\endgroup
}}{}
%<--------------------------------------------------------------------------->
\tkzutil@ifundefined{pgfmath@function@isodd}{%
\pgfmathdeclarefunction{isodd}{1}{%
\begingroup
\ifodd #1 \def\pgfmathresult{1}%
\else\def\pgfmathresult{0}%
\fi
\pgfmath@smuggleone\pgfmathresult%
\endgroup}
}{}
%<--------------------------------------------------------------------------->
\tkzutil@ifundefined{pgfmath@function@isfactor}{%
\pgfmathdeclarefunction{isfactor}{2}{%
\begingroup
\c@pgfmath@counta#1\relax%
\c@pgfmath@countb#2\relax%
\c@pgfmath@countc#1\relax%
\divide\c@pgfmath@counta by\c@pgfmath@countb%
\multiply\c@pgfmath@counta by\c@pgfmath@countb%
\advance\c@pgfmath@countc by-\c@pgfmath@counta%
\ifnum\c@pgfmath@countc=0 \def\pgfmathresult{1}%
\else
\def\pgfmathresult{0}%
\fi
\pgfmath@smuggleone\pgfmathresult%
\endgroup}
}{}
%<--------------------------------------------------------------------------->
\def\tkzfactors#1{%
\begingroup
\c@pgfmath@countb#1
\pgfmathisprime{\c@pgfmath@countb}%
\ifnum\pgfmathresult=1
\number\c@pgfmath@countb\ % prime number
\else% we can found factors
\tkz@factors{#1}
\fi
\endgroup}%
%<--------------------------------------------------------------------------–>
\def\tkz@factors#1{%
\begingroup
\c@pgfmath@countb#1
\c@pgfmath@countd2\relax
\loop
\ifodd\c@pgfmath@countb\relax%
\else
\divide\c@pgfmath@countb by2 %
\number\c@pgfmath@countd\ %
\repeat%
%%%%%%%%%%%%%%
\def\tkzprim@last{1}%
\loop% first loop
\ifnum\c@pgfmath@countb>1\relax
\c@pgfmath@countd\tkzprim@last\relax
\c@pgfmath@countc1\relax
%%%%%%%%%%%%%%
\tkz@find@last
%%%%%%%%%%%%%%
\divide\c@pgfmath@countb by\c@pgfmath@countd\relax
\number\c@pgfmath@countd\ % affiche le facteur
\repeat% end first loop
%%%%%%%%%%%%%%
\endgroup%
}%
%<--------------------------------------------------------------------------->
\def\tkz@find@last{%
\ifnum\c@pgfmath@countc>\z@
\edef\tkzprim@last{\the\c@pgfmath@countd}%
\advance\c@pgfmath@countd by2\relax% begins with 3
\c@pgfmath@counta\c@pgfmath@countb% macro mod !!
\c@pgfmath@countc\c@pgfmath@counta%
\divide\c@pgfmath@counta by\c@pgfmath@countd
\multiply\c@pgfmath@counta by\c@pgfmath@countd
\advance\c@pgfmath@countc by-\c@pgfmath@counta
\let\tkz@find@next=\tkz@find@last
\else
\let\tkz@find@next=\relax%
\fi
\tkz@find@next
}%
%<--------------------------------------------------------------------------->
%<--------------------------------------------------------------------------->
\def\tkzReducFrac#1#2{%
\begingroup
\ifnum#1<0\relax%
\c@pgfmath@counta=0\relax
\advance\c@pgfmath@counta by-#1
\else
\c@pgfmath@counta#1
\fi
\c@pgfmath@countb#2
\pgfmathgcd{\c@pgfmath@counta}{\c@pgfmath@countb}%
\pgfmathsetcount\c@pgfmath@countc{\pgfmathresult}
\ifnum\c@pgfmath@counta=0\relax
\c@pgfmath@counta#1
\c@pgfmath@countb#2
\else
\c@pgfmath@counta#1
\c@pgfmath@countb#2
\divide\c@pgfmath@counta by\c@pgfmath@countc%
\divide\c@pgfmath@countb by\c@pgfmath@countc%
\fi
\global\edef\tkzMathFirstResult{\the\c@pgfmath@counta}
\global\edef\tkzMathSecondResult{\the\c@pgfmath@countb}
\endgroup}
%<--------------------------------------------------------------------------->
%<--------------------------------------------------------------------------->
%<--------------------------------------------------------------------------->
\catcode`\@=\tkzAtCode\relax
\endinput
|
