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authorNorbert Preining <norbert@preining.info>2023-02-27 03:05:21 +0000
committerNorbert Preining <norbert@preining.info>2023-02-27 03:05:21 +0000
commit86d5a04282aa958addab4585c4df899ec9a92e50 (patch)
tree7736ac0fb49348cb6ae88770b4b72ed5ee9d8081 /macros/latex/contrib/resolsysteme/tex
parente7ae872926eddb0de09ecfe1c578e0680033955a (diff)
CTAN sync 202302270305
Diffstat (limited to 'macros/latex/contrib/resolsysteme/tex')
-rw-r--r--macros/latex/contrib/resolsysteme/tex/ResolSysteme.sty163
1 files changed, 162 insertions, 1 deletions
diff --git a/macros/latex/contrib/resolsysteme/tex/ResolSysteme.sty b/macros/latex/contrib/resolsysteme/tex/ResolSysteme.sty
index dce5dfb6e5..847d00ebe7 100644
--- a/macros/latex/contrib/resolsysteme/tex/ResolSysteme.sty
+++ b/macros/latex/contrib/resolsysteme/tex/ResolSysteme.sty
@@ -2,7 +2,8 @@
% licence........: Released under the LaTeX Project Public License v1.3c or later, see http://www.latex-project.org/lppl.txtf
\NeedsTeXFormat{LaTeX2e}
-\ProvidesPackage{ResolSysteme}[2023/02/12 v0.1.4 Quelques commandes pour travailler avec des matrices et des sytemes lineaires]
+\ProvidesPackage{ResolSysteme}[2023/02/25 v0.1.5 Quelques commandes pour travailler avec des matrices et des sytemes lineaires]
+% 0.1.5 Inverse d'une matrice en 4x4 (même en normal !) + Système 4x4 (en normal !)
% 0.1.4 Travail sur graphe probabiliste (2x2/3x3/4x4 en python, ou 2x2 en normal...) + Calculs 4x4 en normal
% 0.1.3 Produit matriciel + Puissance matricielle (2x2/3x3 carré en normal, 2x2/3x3/4x4 avec python) + Inversion comportement commandes étoilées
% 0.1.2 Ajout pour afficher une matrice, à l'aide d'une syntaxe similaire aux autres commandes
@@ -585,6 +586,94 @@ def etat_prob_DD(AA,BB,a,b,c,d,puiss) :
\readlist*\MAMATRICEA{#4}%
\def\MatDim{\MAMATRICEAlen}%
%les coeffs de A et le déterminant et les coeff de l'inverse
+ \ifnum \MAMATRICEAlen=4
+ \itemtomacro\MAMATRICEA[1,1]\MatA
+ \itemtomacro\MAMATRICEA[1,2]\MatB
+ \itemtomacro\MAMATRICEA[1,3]\MatC
+ \itemtomacro\MAMATRICEA[1,4]\MatD
+ \itemtomacro\MAMATRICEA[2,1]\MatE
+ \itemtomacro\MAMATRICEA[2,2]\MatF
+ \itemtomacro\MAMATRICEA[2,3]\MatG
+ \itemtomacro\MAMATRICEA[2,4]\MatH
+ \itemtomacro\MAMATRICEA[3,1]\MatI
+ \itemtomacro\MAMATRICEA[3,2]\MatJ
+ \itemtomacro\MAMATRICEA[3,3]\MatK
+ \itemtomacro\MAMATRICEA[3,4]\MatL
+ \itemtomacro\MAMATRICEA[4,1]\MatM
+ \itemtomacro\MAMATRICEA[4,2]\MatN
+ \itemtomacro\MAMATRICEA[4,3]\MatO
+ \itemtomacro\MAMATRICEA[4,4]\MatP
+ %le déterminant
+ \def\DETMATRICE{\xinteval{\MatA*\MatF*\MatK*\MatP-\MatA*\MatF*\MatL*\MatO-\MatA*\MatG*\MatJ*\MatP+\MatA*\MatG*\MatL*\MatN+\MatA*\MatH*\MatJ*\MatO-\MatA*\MatH*\MatK*\MatN-\MatB*\MatE*\MatK*\MatP+\MatB*\MatE*\MatL*\MatO+\MatB*\MatG*\MatI*\MatP-\MatB*\MatG*\MatL*\MatM-\MatB*\MatH*\MatI*\MatO+\MatB*\MatH*\MatK*\MatM+\MatC*\MatE*\MatJ*\MatP-\MatC*\MatE*\MatL*\MatN-\MatC*\MatF*\MatI*\MatP+\MatC*\MatF*\MatL*\MatM+\MatC*\MatH*\MatI*\MatN-\MatC*\MatH*\MatJ*\MatM-\MatD*\MatE*\MatJ*\MatO+\MatD*\MatE*\MatK*\MatN+\MatD*\MatF*\MatI*\MatO-\MatD*\MatF*\MatK*\MatM-\MatD*\MatG*\MatI*\MatN+\MatD*\MatG*\MatJ*\MatM}}%
+ %matrice inverse, si elle existe...
+ \xintifboolexpr{\DETMATRICE == 0}%
+ {\text{Matrice non inversible}}%
+ {%
+ \IfBooleanTF{#1}%
+ {%
+ \def\MatInvA{\ConvVersFrac*[#2]{(\MatF*\MatK*\MatP+\MatG*\MatL*\MatN+\MatH*\MatJ*\MatO-\MatF*\MatL*\MatO-\MatG*\MatJ*\MatP-\MatH*\MatK*\MatN)/\DETMATRICE}}%
+ \def\MatInvB{\ConvVersFrac*[#2]{(\MatB*\MatL*\MatO+\MatC*\MatJ*\MatP+\MatD*\MatK*\MatN-\MatB*\MatK*\MatP-\MatC*\MatL*\MatN-\MatD*\MatJ*\MatO)/\DETMATRICE}}%
+ \def\MatInvC{\ConvVersFrac*[#2]{(\MatB*\MatG*\MatP+\MatC*\MatH*\MatN+\MatD*\MatF*\MatO-\MatB*\MatH*\MatO-\MatC*\MatF*\MatP-\MatD*\MatG*\MatN)/\DETMATRICE}}%
+ \def\MatInvD{\ConvVersFrac*[#2]{(\MatB*\MatH*\MatK+\MatC*\MatF*\MatL+\MatD*\MatG*\MatJ-\MatB*\MatG*\MatL-\MatC*\MatH*\MatJ-\MatD*\MatF*\MatK)/\DETMATRICE}}%
+ \def\MatInvE{\ConvVersFrac*[#2]{(\MatE*\MatL*\MatO+\MatG*\MatI*\MatP+\MatH*\MatK*\MatM-\MatE*\MatK*\MatP-\MatG*\MatL*\MatM-\MatH*\MatI*\MatO)/\DETMATRICE}}%
+ \def\MatInvF{\ConvVersFrac*[#2]{(\MatA*\MatK*\MatP+\MatC*\MatL*\MatM+\MatD*\MatI*\MatO-\MatA*\MatL*\MatO-\MatC*\MatI*\MatP-\MatD*\MatK*\MatM)/\DETMATRICE}}%
+ \def\MatInvG{\ConvVersFrac*[#2]{(\MatA*\MatH*\MatO+\MatC*\MatE*\MatP+\MatD*\MatG*\MatM-\MatA*\MatG*\MatP-\MatC*\MatH*\MatM-\MatD*\MatE*\MatO)/\DETMATRICE}}%
+ \def\MatInvH{\ConvVersFrac*[#2]{(\MatA*\MatG*\MatL+\MatC*\MatH*\MatI+\MatD*\MatE*\MatK-\MatA*\MatH*\MatK-\MatC*\MatE*\MatL-\MatD*\MatG*\MatI)/\DETMATRICE}}%
+ \def\MatInvI{\ConvVersFrac*[#2]{(\MatE*\MatJ*\MatP+\MatF*\MatL*\MatM+\MatH*\MatI*\MatN-\MatE*\MatL*\MatN-\MatF*\MatI*\MatP-\MatH*\MatJ*\MatM)/\DETMATRICE}}%
+ \def\MatInvJ{\ConvVersFrac*[#2]{(\MatA*\MatL*\MatN+\MatB*\MatI*\MatP+\MatD*\MatJ*\MatM-\MatA*\MatJ*\MatP-\MatB*\MatL*\MatM-\MatD*\MatI*\MatN)/\DETMATRICE}}%
+ \def\MatInvK{\ConvVersFrac*[#2]{(\MatA*\MatF*\MatP+\MatB*\MatH*\MatM+\MatD*\MatE*\MatN-\MatA*\MatH*\MatN-\MatB*\MatE*\MatP-\MatD*\MatF*\MatM)/\DETMATRICE}}%
+ \def\MatInvL{\ConvVersFrac*[#2]{(\MatA*\MatH*\MatJ+\MatB*\MatE*\MatL+\MatD*\MatF*\MatI-\MatA*\MatF*\MatL-\MatB*\MatH*\MatI-\MatD*\MatE*\MatJ)/\DETMATRICE}}%
+ \def\MatInvM{\ConvVersFrac*[#2]{(\MatE*\MatK*\MatN+\MatF*\MatI*\MatO+\MatG*\MatJ*\MatM-\MatE*\MatJ*\MatO-\MatF*\MatK*\MatM-\MatG*\MatI*\MatN)/\DETMATRICE}}%
+ \def\MatInvN{\ConvVersFrac*[#2]{(\MatA*\MatJ*\MatO+\MatB*\MatK*\MatM+\MatC*\MatI*\MatN-\MatA*\MatK*\MatN-\MatB*\MatI*\MatO-\MatC*\MatJ*\MatM)/\DETMATRICE}}%
+ \def\MatInvO{\ConvVersFrac*[#2]{(\MatA*\MatG*\MatN+\MatB*\MatE*\MatO+\MatC*\MatF*\MatM-\MatA*\MatF*\MatO-\MatB*\MatG*\MatM-\MatC*\MatE*\MatN)/\DETMATRICE}}%
+ \def\MatInvP{\ConvVersFrac*[#2]{(\MatA*\MatF*\MatK+\MatB*\MatG*\MatI+\MatC*\MatE*\MatJ-\MatA*\MatG*\MatJ-\MatB*\MatE*\MatK-\MatC*\MatF*\MatI)/\DETMATRICE}}%
+ }%
+ {%
+ \def\MatInvA{\ConvVersFrac[#2]{(\MatF*\MatK*\MatP+\MatG*\MatL*\MatN+\MatH*\MatJ*\MatO-\MatF*\MatL*\MatO-\MatG*\MatJ*\MatP-\MatH*\MatK*\MatN)/\DETMATRICE}}%
+ \def\MatInvB{\ConvVersFrac[#2]{(\MatB*\MatL*\MatO+\MatC*\MatJ*\MatP+\MatD*\MatK*\MatN-\MatB*\MatK*\MatP-\MatC*\MatL*\MatN-\MatD*\MatJ*\MatO)/\DETMATRICE}}%
+ \def\MatInvC{\ConvVersFrac[#2]{(\MatB*\MatG*\MatP+\MatC*\MatH*\MatN+\MatD*\MatF*\MatO-\MatB*\MatH*\MatO-\MatC*\MatF*\MatP-\MatD*\MatG*\MatN)/\DETMATRICE}}%
+ \def\MatInvD{\ConvVersFrac[#2]{(\MatB*\MatH*\MatK+\MatC*\MatF*\MatL+\MatD*\MatG*\MatJ-\MatB*\MatG*\MatL-\MatC*\MatH*\MatJ-\MatD*\MatF*\MatK)/\DETMATRICE}}%
+ \def\MatInvE{\ConvVersFrac[#2]{(\MatE*\MatL*\MatO+\MatG*\MatI*\MatP+\MatH*\MatK*\MatM-\MatE*\MatK*\MatP-\MatG*\MatL*\MatM-\MatH*\MatI*\MatO)/\DETMATRICE}}%
+ \def\MatInvF{\ConvVersFrac[#2]{(\MatA*\MatK*\MatP+\MatC*\MatL*\MatM+\MatD*\MatI*\MatO-\MatA*\MatL*\MatO-\MatC*\MatI*\MatP-\MatD*\MatK*\MatM)/\DETMATRICE}}%
+ \def\MatInvG{\ConvVersFrac[#2]{(\MatA*\MatH*\MatO+\MatC*\MatE*\MatP+\MatD*\MatG*\MatM-\MatA*\MatG*\MatP-\MatC*\MatH*\MatM-\MatD*\MatE*\MatO)/\DETMATRICE}}%
+ \def\MatInvH{\ConvVersFrac[#2]{(\MatA*\MatG*\MatL+\MatC*\MatH*\MatI+\MatD*\MatE*\MatK-\MatA*\MatH*\MatK-\MatC*\MatE*\MatL-\MatD*\MatG*\MatI)/\DETMATRICE}}%
+ \def\MatInvI{\ConvVersFrac[#2]{(\MatE*\MatJ*\MatP+\MatF*\MatL*\MatM+\MatH*\MatI*\MatN-\MatE*\MatL*\MatN-\MatF*\MatI*\MatP-\MatH*\MatJ*\MatM)/\DETMATRICE}}%
+ \def\MatInvJ{\ConvVersFrac[#2]{(\MatA*\MatL*\MatN+\MatB*\MatI*\MatP+\MatD*\MatJ*\MatM-\MatA*\MatJ*\MatP-\MatB*\MatL*\MatM-\MatD*\MatI*\MatN)/\DETMATRICE}}%
+ \def\MatInvK{\ConvVersFrac[#2]{(\MatA*\MatF*\MatP+\MatB*\MatH*\MatM+\MatD*\MatE*\MatN-\MatA*\MatH*\MatN-\MatB*\MatE*\MatP-\MatD*\MatF*\MatM)/\DETMATRICE}}%
+ \def\MatInvL{\ConvVersFrac[#2]{(\MatA*\MatH*\MatJ+\MatB*\MatE*\MatL+\MatD*\MatF*\MatI-\MatA*\MatF*\MatL-\MatB*\MatH*\MatI-\MatD*\MatE*\MatJ)/\DETMATRICE}}%
+ \def\MatInvM{\ConvVersFrac[#2]{(\MatE*\MatK*\MatN+\MatF*\MatI*\MatO+\MatG*\MatJ*\MatM-\MatE*\MatJ*\MatO-\MatF*\MatK*\MatM-\MatG*\MatI*\MatN)/\DETMATRICE}}%
+ \def\MatInvN{\ConvVersFrac[#2]{(\MatA*\MatJ*\MatO+\MatB*\MatK*\MatM+\MatC*\MatI*\MatN-\MatA*\MatK*\MatN-\MatB*\MatI*\MatO-\MatC*\MatJ*\MatM)/\DETMATRICE}}%
+ \def\MatInvO{\ConvVersFrac[#2]{(\MatA*\MatG*\MatN+\MatB*\MatE*\MatO+\MatC*\MatF*\MatM-\MatA*\MatF*\MatO-\MatB*\MatG*\MatM-\MatC*\MatE*\MatN)/\DETMATRICE}}%
+ \def\MatInvP{\ConvVersFrac[#2]{(\MatA*\MatF*\MatK+\MatB*\MatG*\MatI+\MatC*\MatE*\MatJ-\MatA*\MatG*\MatJ-\MatB*\MatE*\MatK-\MatC*\MatF*\MatI)/\DETMATRICE}}%
+ }%
+ \IfStrEq{#5}{Aff}%si matrice
+ {%
+ \IfBooleanTF{#1}%
+ {%
+ {\begin{pNiceMatrix}[#3]
+ \ConvVersFrac*[#2]{\MatA} & \ConvVersFrac*[#2]{\MatB} & \ConvVersFrac*[#2]{\MatC} & \ConvVersFrac*[#2]{\MatD} \\
+ \ConvVersFrac*[#2]{\MatE} & \ConvVersFrac*[#2]{\MatF} & \ConvVersFrac*[#2]{\MatG} & \ConvVersFrac*[#2]{\MatH} \\
+ \ConvVersFrac*[#2]{\MatI} & \ConvVersFrac*[#2]{\MatJ} & \ConvVersFrac*[#2]{\MatK} & \ConvVersFrac*[#2]{\MatL} \\
+ \ConvVersFrac*[#2]{\MatM} & \ConvVersFrac*[#2]{\MatN} & \ConvVersFrac*[#2]{\MatO} & \ConvVersFrac*[#2]{\MatP}
+ \end{pNiceMatrix}}^{-1}=
+ }%
+ {%
+ {\begin{pNiceMatrix}[#3]
+ \ConvVersFrac[#2]{\MatA} & \ConvVersFrac[#2]{\MatB} & \ConvVersFrac[#2]{\MatC} & \ConvVersFrac[#2]{\MatD} \\
+ \ConvVersFrac[#2]{\MatE} & \ConvVersFrac[#2]{\MatF} & \ConvVersFrac[#2]{\MatG} & \ConvVersFrac[#2]{\MatH} \\
+ \ConvVersFrac[#2]{\MatI} & \ConvVersFrac[#2]{\MatJ} & \ConvVersFrac[#2]{\MatK} & \ConvVersFrac[#2]{\MatL} \\
+ \ConvVersFrac[#2]{\MatM} & \ConvVersFrac[#2]{\MatN} & \ConvVersFrac[#2]{\MatO} & \ConvVersFrac[#2]{\MatP}
+ \end{pNiceMatrix}}^{-1}=
+ }%
+ }{}%
+ \begin{pNiceMatrix}[#3]
+ {\MatInvA}&{\MatInvB}&{\MatInvC}&{\MatInvD}\\
+ {\MatInvE}&{\MatInvF}&{\MatInvG}&{\MatInvH}\\
+ {\MatInvI}&{\MatInvJ}&{\MatInvK}&{\MatInvL}\\
+ {\MatInvM}&{\MatInvN}&{\MatInvO}&{\MatInvP}
+ \end{pNiceMatrix}%
+ }%
+ \fi
\ifnum \MAMATRICEAlen=3
\itemtomacro\MAMATRICEA[1,1]\MatA
\itemtomacro\MAMATRICEA[1,2]\MatB
@@ -771,6 +860,78 @@ def etat_prob_DD(AA,BB,a,b,c,d,puiss) :
\readlist*\MAMATRICEB{#5}%
\def\MatDim{\MAMATRICEAlen}%
%les coeffs de A et le déterminant et les coeff de l'inverse
+ \ifnum \MAMATRICEAlen=4
+ \itemtomacro\MAMATRICEA[1,1]\MatA
+ \itemtomacro\MAMATRICEA[1,2]\MatB
+ \itemtomacro\MAMATRICEA[1,3]\MatC
+ \itemtomacro\MAMATRICEA[1,4]\MatD
+ \itemtomacro\MAMATRICEA[2,1]\MatE
+ \itemtomacro\MAMATRICEA[2,2]\MatF
+ \itemtomacro\MAMATRICEA[2,3]\MatG
+ \itemtomacro\MAMATRICEA[2,4]\MatH
+ \itemtomacro\MAMATRICEA[3,1]\MatI
+ \itemtomacro\MAMATRICEA[3,2]\MatJ
+ \itemtomacro\MAMATRICEA[3,3]\MatK
+ \itemtomacro\MAMATRICEA[3,4]\MatL
+ \itemtomacro\MAMATRICEA[4,1]\MatM
+ \itemtomacro\MAMATRICEA[4,2]\MatN
+ \itemtomacro\MAMATRICEA[4,3]\MatO
+ \itemtomacro\MAMATRICEA[4,4]\MatP
+ %le déterminant
+ \def\DETMATRICE{\xinteval{\MatA*\MatF*\MatK*\MatP-\MatA*\MatF*\MatL*\MatO-\MatA*\MatG*\MatJ*\MatP+\MatA*\MatG*\MatL*\MatN+\MatA*\MatH*\MatJ*\MatO-\MatA*\MatH*\MatK*\MatN-\MatB*\MatE*\MatK*\MatP+\MatB*\MatE*\MatL*\MatO+\MatB*\MatG*\MatI*\MatP-\MatB*\MatG*\MatL*\MatM-\MatB*\MatH*\MatI*\MatO+\MatB*\MatH*\MatK*\MatM+\MatC*\MatE*\MatJ*\MatP-\MatC*\MatE*\MatL*\MatN-\MatC*\MatF*\MatI*\MatP+\MatC*\MatF*\MatL*\MatM+\MatC*\MatH*\MatI*\MatN-\MatC*\MatH*\MatJ*\MatM-\MatD*\MatE*\MatJ*\MatO+\MatD*\MatE*\MatK*\MatN+\MatD*\MatF*\MatI*\MatO-\MatD*\MatF*\MatK*\MatM-\MatD*\MatG*\MatI*\MatN+\MatD*\MatG*\MatJ*\MatM}}%
+ %les coeffs de B
+ \itemtomacro\MAMATRICEB[1]\MatBA
+ \itemtomacro\MAMATRICEB[2]\MatBB
+ \itemtomacro\MAMATRICEB[3]\MatBC
+ \itemtomacro\MAMATRICEB[4]\MatBD
+ %matrice inverse, si elle existe...
+ \xintifboolexpr{\DETMATRICE == 0}%
+ {\text{Matrice non inversible}}%
+ {%
+ \def\MatInvA{(\MatF*\MatK*\MatP+\MatG*\MatL*\MatN+\MatH*\MatJ*\MatO-\MatF*\MatL*\MatO-\MatG*\MatJ*\MatP-\MatH*\MatK*\MatN)/\DETMATRICE}%
+ \def\MatInvB{(\MatB*\MatL*\MatO+\MatC*\MatJ*\MatP+\MatD*\MatK*\MatN-\MatB*\MatK*\MatP-\MatC*\MatL*\MatN-\MatD*\MatJ*\MatO)/\DETMATRICE}%
+ \def\MatInvC{(\MatB*\MatG*\MatP+\MatC*\MatH*\MatN+\MatD*\MatF*\MatO-\MatB*\MatH*\MatO-\MatC*\MatF*\MatP-\MatD*\MatG*\MatN)/\DETMATRICE}%
+ \def\MatInvD{(\MatB*\MatH*\MatK+\MatC*\MatF*\MatL+\MatD*\MatG*\MatJ-\MatB*\MatG*\MatL-\MatC*\MatH*\MatJ-\MatD*\MatF*\MatK)/\DETMATRICE}%
+ \def\MatInvE{(\MatE*\MatL*\MatO+\MatG*\MatI*\MatP+\MatH*\MatK*\MatM-\MatE*\MatK*\MatP-\MatG*\MatL*\MatM-\MatH*\MatI*\MatO)/\DETMATRICE}%
+ \def\MatInvF{(\MatA*\MatK*\MatP+\MatC*\MatL*\MatM+\MatD*\MatI*\MatO-\MatA*\MatL*\MatO-\MatC*\MatI*\MatP-\MatD*\MatK*\MatM)/\DETMATRICE}%
+ \def\MatInvG{(\MatA*\MatH*\MatO+\MatC*\MatE*\MatP+\MatD*\MatG*\MatM-\MatA*\MatG*\MatP-\MatC*\MatH*\MatM-\MatD*\MatE*\MatO)/\DETMATRICE}%
+ \def\MatInvH{(\MatA*\MatG*\MatL+\MatC*\MatH*\MatI+\MatD*\MatE*\MatK-\MatA*\MatH*\MatK-\MatC*\MatE*\MatL-\MatD*\MatG*\MatI)/\DETMATRICE}%
+ \def\MatInvI{(\MatE*\MatJ*\MatP+\MatF*\MatL*\MatM+\MatH*\MatI*\MatN-\MatE*\MatL*\MatN-\MatF*\MatI*\MatP-\MatH*\MatJ*\MatM)/\DETMATRICE}%
+ \def\MatInvJ{(\MatA*\MatL*\MatN+\MatB*\MatI*\MatP+\MatD*\MatJ*\MatM-\MatA*\MatJ*\MatP-\MatB*\MatL*\MatM-\MatD*\MatI*\MatN)/\DETMATRICE}%
+ \def\MatInvK{(\MatA*\MatF*\MatP+\MatB*\MatH*\MatM+\MatD*\MatE*\MatN-\MatA*\MatH*\MatN-\MatB*\MatE*\MatP-\MatD*\MatF*\MatM)/\DETMATRICE}%
+ \def\MatInvL{(\MatA*\MatH*\MatJ+\MatB*\MatE*\MatL+\MatD*\MatF*\MatI-\MatA*\MatF*\MatL-\MatB*\MatH*\MatI-\MatD*\MatE*\MatJ)/\DETMATRICE}%
+ \def\MatInvM{(\MatE*\MatK*\MatN+\MatF*\MatI*\MatO+\MatG*\MatJ*\MatM-\MatE*\MatJ*\MatO-\MatF*\MatK*\MatM-\MatG*\MatI*\MatN)/\DETMATRICE}%
+ \def\MatInvN{(\MatA*\MatJ*\MatO+\MatB*\MatK*\MatM+\MatC*\MatI*\MatN-\MatA*\MatK*\MatN-\MatB*\MatI*\MatO-\MatC*\MatJ*\MatM)/\DETMATRICE}%
+ \def\MatInvO{(\MatA*\MatG*\MatN+\MatB*\MatE*\MatO+\MatC*\MatF*\MatM-\MatA*\MatF*\MatO-\MatB*\MatG*\MatM-\MatC*\MatE*\MatN)/\DETMATRICE}%
+ \def\MatInvP{(\MatA*\MatF*\MatK+\MatB*\MatG*\MatI+\MatC*\MatE*\MatJ-\MatA*\MatG*\MatJ-\MatB*\MatE*\MatK-\MatC*\MatF*\MatI)/\DETMATRICE}%
+ %
+ \IfBooleanTF{#1}%version étoilée := moinsdevant
+ {%
+ \def\MatResA{\ConvVersFrac*[#2]{\MatInvA*\MatBA+\MatInvB*\MatBB+\MatInvC*\MatBC+\MatInvD*\MatBD}}%
+ \def\MatResB{\ConvVersFrac*[#2]{\MatInvE*\MatBA+\MatInvF*\MatBB+\MatInvG*\MatBC+\MatInvH*\MatBD}}%
+ \def\MatResC{\ConvVersFrac*[#2]{\MatInvI*\MatBA+\MatInvJ*\MatBB+\MatInvK*\MatBC+\MatInvL*\MatBD}}%
+ \def\MatResD{\ConvVersFrac*[#2]{\MatInvM*\MatBA+\MatInvN*\MatBB+\MatInvO*\MatBC+\MatInvP*\MatBD}}%
+ }%
+ {%
+ \def\MatResA{\ConvVersFrac[#2]{\MatInvA*\MatBA+\MatInvB*\MatBB+\MatInvC*\MatBC+\MatInvD*\MatBD}}%
+ \def\MatResB{\ConvVersFrac[#2]{\MatInvE*\MatBA+\MatInvF*\MatBB+\MatInvG*\MatBC+\MatInvH*\MatBD}}%
+ \def\MatResC{\ConvVersFrac[#2]{\MatInvI*\MatBA+\MatInvJ*\MatBB+\MatInvK*\MatBC+\MatInvL*\MatBD}}%
+ \def\MatResD{\ConvVersFrac[#2]{\MatInvM*\MatBA+\MatInvN*\MatBB+\MatInvO*\MatBC+\MatInvP*\MatBD}}%
+ }%
+ \IfStrEq{#6}{Matrice}%si matrice
+ {%
+ \begin{pNiceMatrix}[#3]
+ {\MatResA} \\
+ {\MatResB} \\
+ {\MatResC} \\
+ {\MatResD}
+ \end{pNiceMatrix}%
+ }%
+ {%
+ \left( {\MatResA} ; {\MatResB} ; {\MatResC} ; {\MatResD} \right)%
+ }%
+ }%
+ \fi
\ifnum \MAMATRICEAlen=3
\itemtomacro\MAMATRICEA[1,1]\MatA
\itemtomacro\MAMATRICEA[1,2]\MatB