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authorNorbert Preining <norbert@preining.info>2024-03-26 03:03:59 +0000
committerNorbert Preining <norbert@preining.info>2024-03-26 03:03:59 +0000
commit904f56f2c26edc7eb11d5a27579bccbeca29c618 (patch)
tree8a4d6d2e163e93dd2c13a28db996b419aee856b4 /graphics/pgf/contrib/profsio/tex/ProfSio.sty
parent05f8146ef2eea2cd71b9c96583c6d893e6c76af5 (diff)
CTAN sync 202403260303
Diffstat (limited to 'graphics/pgf/contrib/profsio/tex/ProfSio.sty')
-rw-r--r--graphics/pgf/contrib/profsio/tex/ProfSio.sty175
1 files changed, 162 insertions, 13 deletions
diff --git a/graphics/pgf/contrib/profsio/tex/ProfSio.sty b/graphics/pgf/contrib/profsio/tex/ProfSio.sty
index 55c01c7e32..169c5b8151 100644
--- a/graphics/pgf/contrib/profsio/tex/ProfSio.sty
+++ b/graphics/pgf/contrib/profsio/tex/ProfSio.sty
@@ -3,7 +3,8 @@
% : Luatruthtable from Chetan Shirore and Dr. Ajit Kumar https://ctan.org/pkg/luatruthtable
\NeedsTeXFormat{LaTeX2e}
-\ProvidesPackage{ProfSio}[2023/03/17 0.2.2 Pour les enseignants de Maths en BTS SIO]
+\ProvidesPackage{ProfSio}[2023/03/25 0.2.3 Pour les enseignants de Maths en BTS SIO]
+%0.2.3 Ajout d'une clé [Dense] pour condenser la résolution matricielle de système + commande \KarnaughBlocRegroupAuto pour créer les blocs automatiquement
%0.2.2 Ajout d'une clé [enonce] pour la résolution matricielle de système (aff/naff la ligne d'énoncé)
%0.2.1 Opérations posées (+,-,×) avec bin/hex/dec
%0.2.0 Travail sur les systèmes 3x3 par matrices et la présentation d'un produit matriciel
@@ -556,8 +557,6 @@
}%
}
-
-
\newcommand\KarnaughBlocRegroup[3][]{%
\useKVdefault[blockarnaugh]%
\setKV[blockarnaugh]{#1}%
@@ -588,6 +587,144 @@
{}%
}
+\defKV[blocksarnaugh]{%
+ Decalages=\def\KGHdecalage{#1},%
+ Couleurs=\def\KGHcouleur{#1}
+}
+
+\setKVdefault[blocksarnaugh]{%
+ Decalages={2pt,1pt,-1pt},%
+ Couleurs={red,blue,violet}
+}
+
+\newcommand\KarnaughBlocRegroupAuto[2][]{%
+ %1 = clés blocs
+ \useKVdefault[blocksarnaugh]%
+ \setKV[blocksarnaugh]{#1}%
+ \itemtomacro\ListeVariablesKGH[1]{\VarTMPA}%
+ \itemtomacro\ListeVariablesKGH[2]{\VarTMPB}%
+ \itemtomacro\ListeVariablesKGH[3]{\VarTMPC}%
+ %substitutions pour placement auto
+ \StrSubstitute{#2}{\VarTMPA}{AA}[\knghbintransf]%
+ \StrSubstitute{\knghbintransf}{\VarTMPB}{BB}[\knghbintransf]%
+ \StrSubstitute{\knghbintransf}{\VarTMPC}{CC}[\knghbintransf]%
+ %liste des regroupements
+ \setsepchar{+}%
+ \readlist*\knghlstblocks{\knghbintransf}%
+ %liste décalages/couleurs
+ \setsepchar{,}%
+ \readlist*\knghlstblockscolors{\KGHcouleur}%
+ \readlist*\knghlstblocksdecals{\KGHdecalage}%
+ \xintFor* ##1 in {\xintSeq{1}{\knghlstblockslen}}\do{%
+ \itemtomacro\knghlstblocks[##1]\tmpblockkngh%
+ \itemtomacro\knghlstblockscolors[##1]\tmpblockknghcol%
+ \itemtomacro\knghlstblocksdecals[##1]\tmpblockknghdecal%
+ \ifboolKV[tblkgh]{StyleAlternatif}%
+ {%
+ \IfStrEqCase{\tmpblockkngh}{%
+ %calculs pour 1 lettre
+ {(AA)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{42}}%
+ {(BB)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{10}{32}}
+ {(CC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{41}}%
+ {(AA*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{22}}%
+ {(BB*)}{\KarnaughBlocRegroup[Type=Gauche,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{12}\KarnaughBlocRegroup[Type=Droite,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{40}{32}}%
+ {(CC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{01}{42}}%
+ %calculs pour 2 lettres
+ {(AABB)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{31}}%
+ {(AACC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{21}{42}}%
+ {(AABB*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{30}{42}}%
+ {(AA*BB)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{10}{22}}%
+ {(AA*CC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{01}{22}}%
+ {(AA*BB*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{12}}%
+ {(AACC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{41}}%
+ {(AA*CC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{21}}%
+ {(BBCC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{10}{31}}%
+ {(BBCC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{11}{32}}%
+ {(BB*CC*)}{\KarnaughBlocRegroup[Type=Gauche,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{01}{12}\KarnaughBlocRegroup[Type=Droite,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{41}{32}}%
+ {(BB*CC)}{\KarnaughBlocRegroup[Type=Gauche,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{11}\KarnaughBlocRegroup[Type=Droite,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{40}{31}}%
+ %calculs pour 3 lettres
+ {(AABBCC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{31}}%
+ {(AABBCC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{21}{32}}%
+ {(AABB*CC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{31}{42}}%
+ {(AABB*CC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{30}{41}}%
+ {(AA*BBCC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{10}{21}}%
+ {(AA*BBCC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{11}{22}}%
+ {(AA*BB*CC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{01}{12}}%
+ {(AA*BB*CC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{11}}%
+ }%
+ }%
+ {%styles classiques, normal ou swap
+ \ifboolKV[tblkgh]{Swap}%
+ {%
+ \IfStrEqCase{\tmpblockkngh}{%
+ %calculs pour 1 lettre
+ {(AA)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{01}{42}}%
+ {(BB)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{22}}%
+ {(CC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{10}{32}}
+ {(AA*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{41}}%
+ {(BB*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{44}}%
+ {(CC*)}{\KarnaughBlocRegroup[Type=Gauche,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{12}\KarnaughBlocRegroup[Type=Droite,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{40}{32}}%%
+ %calculs pour 2 lettres
+ {(AABB)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{01}{22}}%
+ {(AACC*)}{\KarnaughBlocRegroup[Type=Gauche,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{01}{12}\KarnaughBlocRegroup[Type=Droite,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{41}{32}}%
+ {(AABB*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{21}{42}}%
+ {(AA*BB)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{21}}%
+ {(AA*CC*)}{\KarnaughBlocRegroup[Type=Gauche,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{11}\KarnaughBlocRegroup[Type=Droite,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{40}{31}}%
+ {(AA*BB*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{41}}%
+ {(AACC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{11}{32}}%
+ {(AA*CC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{10}{31}}%
+ {(BBCC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{10}{22}}%
+ {(BBCC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{12}}%
+ {(BB*CC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{30}{42}}%
+ {(BB*CC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{32}}%
+ %calculs pour 3 lettres
+ {(AABBCC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{11}{22}}%
+ {(AABBCC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{01}{12}}%
+ {(AABB*CC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{31}{42}}%
+ {(AABB*CC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{31}}%
+ {(AA*BBCC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{10}{21}}%
+ {(AA*BBCC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{11}}%
+ {(AA*BB*CC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{30}{41}}%
+ {(AA*BB*CC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{31}}%
+ }%
+ }%
+ {%
+ \IfStrEqCase{\tmpblockkngh}{%
+ %calculs pour 1 lettre
+ {(AA)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{01}{42}}%
+ {(BB)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{22}}%
+ {(CC)}{\KarnaughBlocRegroup[Type=Gauche,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{12}\KarnaughBlocRegroup[Type=Droite,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{40}{32}}%
+ {(AA*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{41}}%
+ {(BB*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{44}}%
+ {(CC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{10}{32}}%
+ %calculs pour 2 lettres
+ {(AABB)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{01}{22}}%
+ {(AACC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{11}{32}}%
+ {(AABB*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{21}{42}}%
+ {(AA*BB)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{21}}%
+ {(AA*CC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{10}{31}}%
+ {(AA*BB*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{41}}%
+ {(AACC)}{\KarnaughBlocRegroup[Type=Gauche,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{01}{12}\KarnaughBlocRegroup[Type=Droite,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{41}{32}}%
+ {(AA*CC)}{\KarnaughBlocRegroup[Type=Gauche,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{11}\KarnaughBlocRegroup[Type=Droite,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{40}{31}}%
+ {(BBCC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{12}}%
+ {(BBCC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{10}{22}}%
+ {(BB*CC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{32}}%
+ {(BB*CC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{30}{42}}%
+ %calculs pour 3 lettres
+ {(AABBCC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{01}{12}}%
+ {(AABBCC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{11}{22}}%
+ {(AABB*CC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{21}{32}}%
+ {(AABB*CC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{30}{41}}%
+ {(AA*BBCC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{00}{11}}%
+ {(AA*BBCC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{10}{21}}%
+ {(AA*BB*CC*)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{20}{31}}%
+ {(AA*BB*CC)}{\KarnaughBlocRegroup[Type=Centre,Couleur=\tmpblockknghcol,Decalage=\tmpblockknghdecal]{30}{41}}%
+ }%
+ }%
+ }%
+ }%
+}
+
%------Graphes
\defKV[GraphSIO]{%
Police=\def\GrphPoliceSommets{#1},%
@@ -2068,7 +2205,8 @@ end
Inconnues=xyz,%
Brut=false,%
OptionNiceMatrix={1pt},%
- Enonce=true
+ Enonce=true,%
+ Dense=false
}
\NewDocumentCommand\ResolSystemeMatrices{ O{} D<>{} m O{#3} O{xyz} }{%
@@ -2199,21 +2337,32 @@ end
}%
{}%
Matriciellement, le système s'écrit sous la forme $\tmpnamematA\times \tmpnamematX = \tmpnamematB$ avec :%
- \[%
- \tmpnamematA = \begin{pNiceMatrix}[cell-space-limits=\ResolSysMatOpt] {\MatAffA}&{\MatAffB}&{\MatAffC} \\ {\MatAffD}&{\MatAffE}&{\MatAffF} \\ {\MatAffG}&{\MatAffH}&{\MatAffI} \end{pNiceMatrix}
- \text{ ; }
- \tmpnamematX = \begin{pNiceMatrix}[cell-space-limits=\ResolSysMatOpt] \tmpinconnuex \\ \tmpinconnuey \\ \tmpinconnuez \end{pNiceMatrix}
- \text{ et }
- \tmpnamematB = \begin{pNiceMatrix}[cell-space-limits=\ResolSysMatOpt] {\MatAffBA} \\ {\MatAffBB} \\ {\MatAffBC} \end{pNiceMatrix}
- \]%
+ \ifboolKV[resolsysmatrix]{Dense}%
+ {%
+ ~$\tmpnamematA = \begin{pNiceMatrix}[cell-space-limits=\ResolSysMatOpt] {\MatAffA}&{\MatAffB}&{\MatAffC} \\ {\MatAffD}&{\MatAffE}&{\MatAffF} \\ {\MatAffG}&{\MatAffH}&{\MatAffI} \end{pNiceMatrix}$ ; $\tmpnamematX = \begin{pNiceMatrix}[cell-space-limits=\ResolSysMatOpt] \tmpinconnuex \\ \tmpinconnuey \\ \tmpinconnuez \end{pNiceMatrix}$ et $\tmpnamematB = \begin{pNiceMatrix}[cell-space-limits=\ResolSysMatOpt] {\MatAffBA} \\ {\MatAffBB} \\ {\MatAffBC} \end{pNiceMatrix}$.\\
+ }%
+ {%
+ \[%
+ \tmpnamematA = \begin{pNiceMatrix}[cell-space-limits=\ResolSysMatOpt] {\MatAffA}&{\MatAffB}&{\MatAffC} \\ {\MatAffD}&{\MatAffE}&{\MatAffF} \\ {\MatAffG}&{\MatAffH}&{\MatAffI} \end{pNiceMatrix}
+ \text{ ; }
+ \tmpnamematX = \begin{pNiceMatrix}[cell-space-limits=\ResolSysMatOpt] \tmpinconnuex \\ \tmpinconnuey \\ \tmpinconnuez \end{pNiceMatrix}
+ \text{ et }
+ \tmpnamematB = \begin{pNiceMatrix}[cell-space-limits=\ResolSysMatOpt] {\MatAffBA} \\ {\MatAffBB} \\ {\MatAffBC} \end{pNiceMatrix}
+ \]%
+ }%
\xintifboolexpr{\DETMATRICE == 0}%
{%
La matrice $\tmpnamematA$ n'est pas inversible, donc le système n'admet pas de solution (ou admet une unifinité de solutions).%
}%
{%
La matrice $\tmpnamematA$ est inversible, et :%
- \[\tmpnamematA\times \tmpnamematX = \tmpnamematB \implies \underbrace{\ResolSysMatInv \times \tmpnamematA}_{{=}I_3} \times \tmpnamematX = \ResolSysMatInv \times \tmpnamematB \implies I_3 \times \tmpnamematX = \ResolSysMatInv\times \tmpnamematB \implies \tmpnamematX=\ResolSysMatInv\times \tmpnamematB.\]
- %
+ \ifboolKV[resolsysmatrix]{Dense}%
+ {%
+ ~$\tmpnamematA\times \tmpnamematX = \tmpnamematB \implies \underbrace{\ResolSysMatInv \times \tmpnamematA}_{{=}I_3} \times \tmpnamematX = \ResolSysMatInv \times \tmpnamematB \implies \tmpnamematX=\ResolSysMatInv\times \tmpnamematB$.\\%
+ }%
+ {%
+ \[\tmpnamematA\times \tmpnamematX = \tmpnamematB \implies \underbrace{\ResolSysMatInv \times \tmpnamematA}_{{=}I_3} \times \tmpnamematX = \ResolSysMatInv \times \tmpnamematB \implies I_3 \times \tmpnamematX = \ResolSysMatInv\times \tmpnamematB \implies \tmpnamematX=\ResolSysMatInv\times \tmpnamematB.\]%
+ }%
La calculatrice nous donne $\tmpnamematX = \begin{pNiceMatrix}[cell-space-limits=\ResolSysMatOpt] {\MatResA} \\ {\MatResB} \\ {\MatResC} \end{pNiceMatrix}$. Ainsi on obtient $\tmpinconnuex=\MatResA$ et $\tmpinconnuey=\MatResB$ et $\tmpinconnuez=\MatResC$.%
}%
}%