(* 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 *)
Shuffle="true";Numbering="abc";
(* Numbers of select options and questions *)
SELNUM=6;Single="true";NUM=400;Title="2次行列式とスカラー倍";
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]])]];
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=Range[-6,6];
QtList={}; For[ct=1,ct≤NUM*1.05,ct++,
Cn=RandomChoice[{2,2,3,3,3}];
prm=RandomChoice[Prime[Range[4]]];
MAL={};
While[Length[MAL]<Cn,
While[Det[Tmp=Table[Table[Rnz[3],2],2]]==0];
MP=GetQnic[2,RandomChoice[Range[2]],prm];
MA=RandomChoice[{MP.Tmp,Tmp.MP}];MAL=Append[MAL,MA];MAL=DeleteDuplicates[MAL]];
QtList=Append[QtList,{Cn,prm,MAL}]];
(* QtList=DeleteDuplicates[QtList]; *)
QtList=RandomSample[QtList,NUM];Length[QtList]

MatrixForm[#] &/@ MAL

Clear[QtextF];QtextF[mm_]:=Module[{Cn,prm,MAL,ret},
{Cn,prm,MAL}=QtList[[mm]];ret=IfDeb[{prm,MatrixForm[#] &/@ MAL},
"以下の2次行列式のうち\\("<>TOT[prm]<>"\\)の倍数となるものを<u>1つ</u>を選びなさい."];
Return[ret]];

AListF[mm_]:=Module[{Cn,prm,MAL,MA,ct,Tmp,fsL={},retC={},retI={}},
{Cn,prm,MAL}=QtList[[mm]];
fsL=Append[fsL,"正解です."];fsL=Append[fsL,"行列式の性質を考えるとすぐに1つ見つけることができます."];
For[ct=1,ct≤Cn,ct++,MA=MAL[[ct]];
retC=Append[retC,{"C",IfDeb[{Det[MA],MF[MA]},"\\("<>TeXArray2Matrix[TOT[MA],"vmatrix"]<>"\\)"],fsL[[1]]}]];
While[Length[retI]<SELNUM-Cn,
While[Mod[Det[MA=Table[Table[Rnz[3],2],2]],prm]==0];
retI=Append[retI,{"I",IfDeb[{Det[MA],MF[MA]},"\\("<>TeXArray2Matrix[TOT[MA],"vmatrix"]<>"\\)"],fsL[[2]]}];
retI=DeleteDuplicates[retI]];
Return[Join[{{1,SELNUM-1}},retC,retI]]];

DebOff[];Print[QtextF[7]];AListF[7]

(* 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]

#->Nothing &/@ Permutations[{1,2,3},{2}]