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-rw-r--r--macros/latex/contrib/proflycee/tex/proflycee-tools-arithm.tex390
1 files changed, 390 insertions, 0 deletions
diff --git a/macros/latex/contrib/proflycee/tex/proflycee-tools-arithm.tex b/macros/latex/contrib/proflycee/tex/proflycee-tools-arithm.tex
index db3f2bc8ac..a021fea937 100644
--- a/macros/latex/contrib/proflycee/tex/proflycee-tools-arithm.tex
+++ b/macros/latex/contrib/proflycee/tex/proflycee-tools-arithm.tex
@@ -1512,4 +1512,394 @@
{}%
}
+%====FACTORIELLE
+\defKV[calcfactorielle]{ChSignif=\def\factochfsign{#1},Sens=\def\factochfsens{#1}}
+\setKVdefault[calcfactorielle]{%
+ Complet=false,%
+ Enonce=false,%
+ Partiel=false,%
+ Grand=false,%
+ ChSignif=9,%
+ Espace=\mkern1.5mu\relax,%
+ Sens=m
+}
+
+\NewDocumentCommand\Factorielle{ s O{} m }{%
+ \restoreKV[calcfactorielle]%
+ \setKV[calcfactorielle]{#2}%
+ \ifboolKV[calcfactorielle]{Grand}%
+ {%
+ \xdef\tmpres{\xintfloateval[\factochfsign]{factorial(#3)}}%
+ }%
+ {%
+ \xdef\tmpres{\xinteval{factorial(#3)}}%
+ }%
+ \ensuremath{%
+ \ifboolKV[calcfactorielle]{Enonce}%
+ {%
+ \IfBooleanTF{#1}{#3\useKV[calcfactorielle]{Espace}!}{\num{#3}\useKV[calcfactorielle]{Espace}!}=
+ }%
+ {}%
+ \ifboolKV[calcfactorielle]{Partiel}%
+ {%
+ \IfBooleanTF{#1}%
+ {%
+ \IfStrEqCase{\factochfsens}{%
+ {m}{1 \times 2 \times \ldots \times \xinteval{#3-1} \times #3 \ifboolKV[calcfactorielle]{Grand}{\approx}{=}}%
+ {d}{#3 \times \xinteval{#3-1} \times \ldots \times 2 \times 1 \ifboolKV[calcfactorielle]{Grand}{\approx}{=}}%
+ }%
+ }%
+ {%
+ \IfStrEqCase{\factochfsens}{%
+ {m}{1 \times 2 \times \ldots \times \num{\xinteval{#3-1}} \times \num{#3} \ifboolKV[calcfactorielle]{Grand}{\approx}{=}}%
+ {d}{\num{#3} \times \num{\xinteval{#3-1}} \times \ldots \times 2 \times 1 \ifboolKV[calcfactorielle]{Grand}{\approx}{=}}%
+ }%
+ }%
+ }%
+ {}%
+ \ifboolKV[calcfactorielle]{Complet}%
+ {%
+ \IfBooleanTF{#1}%
+ {%
+ \IfStrEq{\factochfsens}{m}%
+ {%
+ 1 \xintFor* ##1 in {\xintSeq{2}{#3}}\do{\times ##1} \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ {%
+ \xintFor* ##1 in {\xintSeq{#3}{2}}\do{##1 \times} 1 \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ }%
+ {%
+ \IfStrEq{\factochfsens}{m}%
+ {%
+ 1 \xintFor* ##1 in {\xintSeq{2}{#3}}\do{\times \num{##1}} \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ {%
+ \xintFor* ##1 in {\xintSeq{#3}{2}}\do{\num{##1} \times} 1 \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ }%
+ }%
+ {}%
+ \IfBooleanTF{#1}%
+ {%
+ \tmpres%
+ }%
+ {%
+ \ifboolKV[calcfactorielle]{Grand}%
+ {%
+ \num[scientific-notation=true]{\tmpres}%
+ }%
+ {%
+ \num{\tmpres}%
+ }%
+ }%
+ }%
+}
+
+\NewDocumentCommand\Primorielle{ s O{} m }{%
+ \restoreKV[calcfactorielle]%
+ \setKV[calcfactorielle]{#2}%
+ \def\tmpres{1}%
+ \xintFor* ##1 in {\xintSeq{1}{#3}}\do{%
+ \pgfmathisprime{##1}\ifnum\pgfmathresult=1\xdef\tmpres{\xinteval{\tmpres*##1}}\fi%
+ }%
+ \ifboolKV[calcfactorielle]{Grand}%
+ {%
+ \xdef\tmpres{\xintfloateval[\factochfsign]{\tmpres}}%
+ }%
+ {}%
+ \ensuremath{%
+ \ifboolKV[calcfactorielle]{Enonce}%
+ {%
+ \IfBooleanTF{#1}{#3\#}{\num{#3}\#}=
+ }%
+ {}%
+ \ifboolKV[calcfactorielle]{Complet}%
+ {%
+ \IfBooleanTF{#1}%
+ {%
+ \IfStrEq{\factochfsens}{m}%
+ {%
+ 2 \xintFor* ##1 in {\xintSeq{3}{#3}}\do{\pgfmathisprime{##1}\ifnum\pgfmathresult=1\times##1\fi} \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ {%
+ \xintFor* ##1 in {\xintSeq{#3}{3}}\do{\pgfmathisprime{##1}\ifnum\pgfmathresult=1##1\times\fi} 2 \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ }%
+ {%
+ \IfStrEq{\factochfsens}{m}%
+ {%
+ 2 \xintFor* ##1 in {\xintSeq{3}{#3}}\do{\pgfmathisprime{##1}\ifnum\pgfmathresult=1\times\num{##1}\fi} \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ {%
+ \xintFor* ##1 in {\xintSeq{#3}{3}}\do{\pgfmathisprime{##1}\ifnum\pgfmathresult=1\num{##1}\times\fi} 2 \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ }%
+ }%
+ {}%
+ \IfBooleanTF{#1}%
+ {%
+ \tmpres%
+ }%
+ {%
+ \ifboolKV[calcfactorielle]{Grand}%
+ {%
+ \num[scientific-notation=true]{\tmpres}%
+ }%
+ {%
+ \num{\tmpres}%
+ }%
+ }%
+ }%
+}
+
+\NewDocumentCommand\DoubleFactorielle{ s O{} m }{%
+ \restoreKV[calcfactorielle]%
+ \setKV[calcfactorielle]{#2}%
+ \def\tmpres{1}%
+ \xintFor* ##1 in {\xintSeq{1}{#3}}\do{%
+ \xintifboolexpr{\xintiiOdd{#3} == \xintiiOdd{##1} 'or' \xintiiEven{#3} == \xintiiEven{##1}}%
+ {%
+ \xdef\tmpres{\xinteval{\tmpres*##1}}%
+ }%
+ {}%
+ }%
+ \ifboolKV[calcfactorielle]{Grand}%
+ {%
+ \xdef\tmpres{\xintfloateval[\factochfsign]{\tmpres}}%
+ }%
+ {}%
+ \ensuremath{%
+ \ifboolKV[calcfactorielle]{Enonce}%
+ {%
+ \IfBooleanTF{#1}{#3\useKV[calcfactorielle]{Espace}!!}{\num{#3}\useKV[calcfactorielle]{Espace}!!}=
+ }%
+ {}%
+ \ifboolKV[calcfactorielle]{Complet}%
+ {%
+ \IfBooleanTF{#1}%
+ {%
+ \IfStrEq{\factochfsens}{m}%
+ {%
+ \xintifboolexpr{\xintiiOdd{#3} == 1}%
+ {%
+ 1 \xintFor* ##1 in {\xintSeq{3}{#3}}\do{%
+ \xintifboolexpr{\xintiiOdd{##1} == 1}{\times##1}{}%
+ }%
+ }%
+ {%
+ 2 \xintFor* ##1 in {\xintSeq{3}{#3}}\do{%
+ \xintifboolexpr{\xintiiOdd{##1} != 1}{\times##1}{}%
+ }%
+ }%
+ \ifboolKV[calcfactorielle]{Grand}{\approx}{=}%
+ }%
+ {%
+ \xintifboolexpr{\xintiiOdd{#3} == 1}%
+ {%
+ \xintFor* ##1 in {\xintSeq{#3}{3}}\do{%
+ \xintifboolexpr{\xintiiOdd{##1} == 1}{##1\times}{}%
+ }1%
+ }%
+ {%
+ \xintFor* ##1 in {\xintSeq{#3}{3}}\do{%
+ \xintifboolexpr{\xintiiOdd{##1} != 1}{##1\times}{}%
+ }2%
+ }%
+ \ifboolKV[calcfactorielle]{Grand}{\approx}{=}%
+ }%
+ }%
+ {%
+ \IfStrEq{\factochfsens}{m}%
+ {%
+ \xintifboolexpr{\xintiiOdd{#3} == 1}%
+ {%
+ 1 \xintFor* ##1 in {\xintSeq{3}{#3}}\do{%
+ \xintifboolexpr{\xintiiOdd{##1} == 1}{\times\num{##1}}{}%
+ }%
+ }%
+ {%
+ 2 \xintFor* ##1 in {\xintSeq{3}{#3}}\do{%
+ \xintifboolexpr{\xintiiOdd{##1} != 1}{\times\num{##1}}{}%
+ }%
+ }%
+ \ifboolKV[calcfactorielle]{Grand}{\approx}{=}%
+ }%
+ {%
+ \xintifboolexpr{\xintiiOdd{#3} == 1}%
+ {%
+ \xintFor* ##1 in {\xintSeq{#3}{3}}\do{%
+ \xintifboolexpr{\xintiiOdd{##1} == 1}{\num{##1}\times}{}%
+ }1%
+ }%
+ {%
+ \xintFor* ##1 in {\xintSeq{#3}{3}}\do{%
+ \xintifboolexpr{\xintiiOdd{##1} != 1}{\num{##1}\times}{}%
+ }2%
+ }%
+ \ifboolKV[calcfactorielle]{Grand}{\approx}{=}%
+ }%
+ }%
+ }%
+ {}%
+ \IfBooleanTF{#1}%
+ {%
+ \tmpres%
+ }%
+ {%
+ \ifboolKV[calcfactorielle]{Grand}%
+ {%
+ \num[scientific-notation=true]{\tmpres}%
+ }%
+ {%
+ \num{\tmpres}%
+ }%
+ }%
+ }%
+}
+
+\NewDocumentCommand\HyperFactorielle{ s O{} m }{%
+ \restoreKV[calcfactorielle]%
+ \setKV[calcfactorielle]{#2}%
+ \def\tmpres{1}%
+ \xintFor* ##1 in {\xintSeq{2}{#3}}\do{\xdef\tmpres{\xinteval{\tmpres*(##1)^(##1)}}}%
+ \ifboolKV[calcfactorielle]{Grand}%
+ {%
+ \xdef\tmpres{\xintfloateval[\factochfsign]{\tmpres}}%
+ }%
+ {}%
+ \ensuremath{%
+ \ifboolKV[calcfactorielle]{Enonce}%
+ {%
+ \IfBooleanTF{#1}{\text{H}(#3)}{\text{H}(\rm{#3})}=
+ }%
+ {}%
+ \ifboolKV[calcfactorielle]{Partiel}%
+ {%
+ \IfBooleanTF{#1}%
+ {%
+ \IfStrEqCase{\factochfsens}{%
+ {m}{1^1 \times 2^2 \times \ldots \times \xinteval{#3-1}^{\xinteval{#3-1}} \times #3^{#3} \ifboolKV[calcfactorielle]{Grand}{\approx}{=}}%
+ {d}{#3^{#3} \times \xinteval{#3-1}^{\xinteval{#3-1}} \times \ldots \times 2^2 \times 1^1 \ifboolKV[calcfactorielle]{Grand}{\approx}{=}}%
+ }%
+ }%
+ {%
+ \IfStrEqCase{\factochfsens}{%
+ {m}{1 \times 2 \times \ldots \times \num{\xinteval{#3-1}}^{\num{\xinteval{#3-1}}} \times \num{#3}^{\num{#3}} \ifboolKV[calcfactorielle]{Grand}{\approx}{=}}%
+ {d}{\num{#3}^{\num{#3}} \times \num{\xinteval{#3-1}}^{\num{\xinteval{#3-1}}} \times \ldots \times 2^2 \times 1^1 \ifboolKV[calcfactorielle]{Grand}{\approx}{=}}%
+ }%
+ }%
+ }%
+ {}%
+ \ifboolKV[calcfactorielle]{Complet}%
+ {%
+ \IfBooleanTF{#1}%
+ {%
+ \IfStrEq{\factochfsens}{m}%
+ {%
+ 1^1 \xintFor* ##1 in {\xintSeq{2}{#3}}\do{\times ##1^{##1}} \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ {%
+ \xintFor* ##1 in {\xintSeq{#3}{2}}\do{##1^{##1} \times} 1^1 \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ }%
+ {%
+ \IfStrEq{\factochfsens}{m}%
+ {%
+ 1^1 \xintFor* ##1 in {\xintSeq{2}{#3}}\do{\times \num{##1}^{\num{##1}}} \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ {%
+ \xintFor* ##1 in {\xintSeq{#3}{2}}\do{\num{##1}^{\num{##1}} \times} 1^1 \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ }%
+ }%
+ {}%
+ \IfBooleanTF{#1}%
+ {%
+ \tmpres%
+ }%
+ {%
+ \ifboolKV[calcfactorielle]{Grand}%
+ {%
+ \num[scientific-notation=true]{\tmpres}%
+ }%
+ {%
+ \num{\tmpres}%
+ }%
+ }%
+ }%
+}
+
+\NewDocumentCommand\SuperFactorielle{ s O{} m }{%
+ \restoreKV[calcfactorielle]%
+ \setKV[calcfactorielle]{#2}%
+ \def\tmpres{1}%
+ \xintFor* ##1 in {\xintSeq{2}{#3}}\do{\xdef\tmpres{\xinteval{\tmpres*factorial(##1)}}}%
+ \ifboolKV[calcfactorielle]{Grand}%
+ {%
+ \xdef\tmpres{\xintfloateval[\factochfsign]{\tmpres}}%
+ }%
+ {}%
+ \ensuremath{%
+ \ifboolKV[calcfactorielle]{Enonce}%
+ {%
+ \IfBooleanTF{#1}{\text{sf}(#3)}{\text{sf}(\num{#3})}=
+ }%
+ {}%
+ \ifboolKV[calcfactorielle]{Partiel}%
+ {%
+ \IfBooleanTF{#1}%
+ {%
+ \IfStrEqCase{\factochfsens}{%
+ {m}{1\useKV[calcfactorielle]{Espace}! \times 2\useKV[calcfactorielle]{Espace}! \times \ldots \times \xinteval{#3-1}\useKV[calcfactorielle]{Espace}! \times #3\useKV[calcfactorielle]{Espace}! \ifboolKV[calcfactorielle]{Grand}{\approx}{=}}%
+ {d}{#3\useKV[calcfactorielle]{Espace}! \times \xinteval{#3-1}\useKV[calcfactorielle]{Espace}! \times \ldots \times 2\useKV[calcfactorielle]{Espace}! \times 1\useKV[calcfactorielle]{Espace}! \ifboolKV[calcfactorielle]{Grand}{\approx}{=}}%
+ }%
+ }%
+ {%
+ \IfStrEqCase{\factochfsens}{%
+ {m}{1\useKV[calcfactorielle]{Espace}! \times 2\useKV[calcfactorielle]{Espace}! \times \ldots \times \num{\xinteval{#3-1}}\useKV[calcfactorielle]{Espace}! \times \num{#3}\useKV[calcfactorielle]{Espace}! \ifboolKV[calcfactorielle]{Grand}{\approx}{=}}%
+ {d}{\num{#3}\useKV[calcfactorielle]{Espace}! \times \num{\xinteval{#3-1}}\useKV[calcfactorielle]{Espace}! \times \ldots \times 2\useKV[calcfactorielle]{Espace}! \times 1\useKV[calcfactorielle]{Espace}! \ifboolKV[calcfactorielle]{Grand}{\approx}{=}}%
+ }%
+ }%
+ }%
+ {}%
+ \ifboolKV[calcfactorielle]{Complet}%
+ {%
+ \IfBooleanTF{#1}%
+ {%
+ \IfStrEq{\factochfsens}{m}%
+ {%
+ 1\useKV[calcfactorielle]{Espace}! \xintFor* ##1 in {\xintSeq{2}{#3}}\do{\times ##1\useKV[calcfactorielle]{Espace}!} \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ {%
+ \xintFor* ##1 in {\xintSeq{#3}{2}}\do{##1\useKV[calcfactorielle]{Espace}! \times} 1\useKV[calcfactorielle]{Espace}! \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ }%
+ {%
+ \IfStrEq{\factochfsens}{m}%
+ {%
+ 1\useKV[calcfactorielle]{Espace}! \xintFor* ##1 in {\xintSeq{2}{#3}}\do{\times \num{##1}\useKV[calcfactorielle]{Espace}!} \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ {%
+ \xintFor* ##1 in {\xintSeq{#3}{2}}\do{\num{##1}\useKV[calcfactorielle]{Espace}! \times} 1\useKV[calcfactorielle]{Espace}! \ifboolKV[calcfactorielle]{Grand}{\approx}{=}
+ }%
+ }%
+ }%
+ {}%
+ \IfBooleanTF{#1}%
+ {%
+ \tmpres%
+ }%
+ {%
+ \ifboolKV[calcfactorielle]{Grand}%
+ {%
+ \num[scientific-notation=true]{\tmpres}%
+ }%
+ {%
+ \num{\tmpres}%
+ }%
+ }%
+ }%
+}
+
\endinput \ No newline at end of file