(* Require XMLgen_MC.nb ver >=0.24 *)
SetDirectory[NotebookDirectory[]];
<<XMLgenMC.mx;
DebugMode=False;
ThisNo=StringReplace[StringSplit[ NotebookFileName[],"/"][[-1]],{"LA_"->"",".nb"->"","_"->"-"}];
Category="LA/"<>ThisNo<>".";

(* Global Options *)
Numbering="abc";Title="3次行列式の形";
(* Numbers of select options and questions *)
Shuffle="true";Single="true";SELNUM=6;NUM=300;
GeneralFeedback="";

TOT[mt_]:=ToString[OneLineTeXForm[mt]];
TOTT[mt_]:=ToString[OneLineTeXForm[Transpose[mt]]];
TTSt[eq_]:=ToString[TeXForm[StandardForm[eq]]];
TOC[mt_,c_]:=TOTT[{Transpose[mt][[c]]}];
TTD[r_]:=StringReplace[TT[r],"\\frac"->"\\dfrac"];
MFT[m_]:=MatrixForm[Transpose[m]];
MF[m_]:=MatrixForm[m];
Rnz[m_]:=(RandomInteger[m]+1)*(2*RandomInteger[1]-1); (* \\pm 1,\pm2,...,\pm(m+1) *)
Rpos[m_]:=RandomInteger[m]+1; (* 1,2,...,m+1 *)
Rbtw[m_]:=RandomInteger[2m]-m;
TTC[A_,n_]:=TOTT[{(Transpose[A])[[n]]}];
PtString[M_]:=StringReplace[ToString[M],{"{"->"(","}"->")"}];
ai2tex[s_]:=StringReplace[TOT[s],Table["\\text{a"<>TOT[i]<>"}"->"{\\mathbf a}_"<>TOT[i],{i,1,8}]];
ci2tex[c_,s_]:=StringReplace[s,Table["\\text{"<>c<>TOT[i]<>"}"->"{\\mathbf "<>c<>"}_"<>TOT[i],{i,1,5}]];
ci2tex[c_,s_,tx_]:=StringReplace[s,Table["\\text{"<>c<>TOT[i]<>"}"->"{"<>tx<>c<>"}_"<>TOT[i],{i,1,8}]];
TOTci2tex[c_,s_]:=StringReplace[TOT[s],Table["\\text{"<>c<>TOT[i]<>"}"->"{\\mathbf "<>c<>"}_"<>TOT[i],{i,1,8}]];
TeXArray2Matrix[s_,mtx_]:=StringReplace[s,Join[{"array"->mtx,"\\left("->"","\\right)"->""},#->"" &/@ ("{"<>StringRepeat["c",#]<>"}" &/@ Reverse[Range[20]])]];
TAM[s_,mtx_]:=TeXArray2Matrix[TOT[s],mtx];
TpStr[L_]:="\\("<>TOT[L[[1]]]<>"\\times"<>TOT[L[[2]]]<>"\\)";
TpTpse[L_]:=If[L=={},{},{L[[2]],L[[1]]}];
PType[A_,B_]:=If[A=={}||B=={},Return[{}],
If[A[[2]]===B[[1]],Return[{A[[1]],B[[2]]}],Return[{}]]];
PTypeL[L_]:=Module[{ct,len,tmp},len=Length[L];
Which[len==0,Return[{}],len==1,Return[L[[1]]],
len==2,Return[PType[L[[1]],L[[2]]]],
True,tmp=L[[1]];For[ct=2,ct≤len,ct++,tmp=PType[tmp,L[[ct]]]];Return[tmp]]];
GCDL[L_]:=Module[{ct,ret=0},For[ct=1,ct≤Length[L],ct++,ret=GCD[ret,L[[ct]]]];Return[ret]];

Clear[p,q,r,s,t,u,v,x,y,z]

(* select pairs of matrices *)
MAList=Join[Range[-9,-1],Range[2,12]];sz=3;
QtList={}; For[ct=1,ct≤NUM*1.02,ct++,
Cn=1;
MA=ArrayReshape[RandomSample[MAList,sz*sz],{sz,sz}];
QtList=Append[QtList,{Cn,sz,MA}]];
(* QtList=DeleteDuplicates[QtList]; *)
QtList=RandomSample[QtList,NUM];Length[QtList]

Clear[a,b,c,QtextF];QtextF[mm_]:=Module[{Cn,sz,MA,ret,ct},
{Cn,sz,MA}=QtList[[mm]];
ret="以下の3次行列式に対するサラスの式として正しいものを選べ."
<>"\\("<>TOT[MA]<>"\\)";
Return[IfDeb[{MF[MA]},ret]]];

DspNumMult[nL_]:=Module[{ct,x,ret=""},
For[ct=1,ct≤Length[nL],ct++,x=nL[[ct]];
If[ct>1,ret=ret<>"\\cdot"];
ret=ret<>If[x<0,"("<>TOT[x]<>")",TOT[x]]];Return[ret]];

SR[L_,c_]:=StringRiffle[L,c];
Rg[a_,b_]:=Range[a,b];

AListF[mm_]:=Module[{Cn,sz,MA,MA1,Trm={},Rg,i,j,ct,fsL={},ret={},IL={}},
{Cn,sz,MA}=QtList[[mm]];
fsL=Append[fsL,"正解です."];fsL=Append[fsL,"違います. 公式を線形性と交代性で自分で作ってみよう!"];
fsL=Append[fsL,"すべての成分を使っていません. 2次の行列式と混同しないようにしよう."];
Trm=Append[Trm,DspNumMult[{MA[[1,1]],MA[[2,2]],MA[[3,3]]}]];
Trm=Append[Trm,DspNumMult[{MA[[1,2]],MA[[2,3]],MA[[3,1]]}]];
Trm=Append[Trm,DspNumMult[{MA[[1,3]],MA[[2,1]],MA[[3,2]]}]];
Trm=Append[Trm,DspNumMult[{MA[[1,3]],MA[[2,2]],MA[[3,1]]}]];
Trm=Append[Trm,DspNumMult[{MA[[1,2]],MA[[2,1]],MA[[3,3]]}]];
Trm=Append[Trm,DspNumMult[{MA[[1,1]],MA[[2,3]],MA[[3,2]]}]];
ret=Append[ret,{"C","\\("<>SR[Trm[[{1,2,3}]],"+"]<>"-"<>SR[Trm[[{4,5,6}]],"-"]<>"\\)",fsL[[1]]}];
IL=Append[IL,{"I","\\("<>SR[Trm[[{1,2,3}]],"+"]<>"+"<>SR[Trm[[{4,5,6}]],"+"]<>"\\)",fsL[[2]]}];
IL=Append[IL,{"I","\\("<>SR[Trm[[{4,5,6}]],"+"]<>"-"<>SR[Trm[[{1,2,3}]],"-"]<>"\\)",fsL[[2]]}];IL=Append[IL,{"I","\\("<>SR[Trm[[{1,3,5}]],"+"]<>"-"<>SR[Trm[[{2,4,6}]],"-"]<>"\\)",fsL[[2]]}];IL=Append[IL,{"I","\\("<>SR[Trm[[{1,2,4}]],"+"]<>"-"<>SR[Trm[[{3,5,6}]],"-"]<>"\\)",fsL[[2]]}];
IL=Append[IL,{"I","\\("<>SR[Trm[[{1,2,3,4,5}]],"+"]<>"-"<>Trm[[6]]<>"\\)",fsL[[2]]}];
IL=Append[IL,{"I","\\("<>Trm[[1]]<>"-"<>Trm[[6]]<>"\\)",fsL[[3]]}];
ret=RandomSample[Join[ret,RandomSample[IL,SELNUM-Cn]]];
Return[Join[{{Cn,SELNUM-Cn}},ret]]];

AListF[8]

QtextF[3]

DebOn[];AListF[3]

DebOn[];For[ct=1,ct≤NUM,ct++,PrintTemporary[ct];QtextF[ct];AListF[ct]]

(* For[ct=1,ct≤NUM,ct++,Print[ct];QtextF[ct];AListF[ct]]; (* Error Check *) *)

DebOff[];GenMCxmlV2[DFname[1],Category<>Title<>"(MC1)",Title,NUM,Single,QtextF,AListF]