(* 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次行列式の交代性";
(* Numbers of select options and questions *)
Shuffle="true";Single="false";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=Range[-9,9];sz=3;
QtList={}; For[ct=1,ct≤NUM*1.02,ct++,
Cn=RandomChoice[{2,2,2,3,3,3,3,4,4}]; (* 1/8 *)
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,MA1,We,WR,ret,ct},
{Cn,sz,MA}=QtList[[mm]];
ret="\\("<>TOT[sz]<>"\\)次行列式は列ベクトル・行ベクトルについて交代性(入れ替えると符号が反転する)を持つ."
<>"行列式\\("<>TAM[MA,"vmatrix"]<>"\\)と同じ値を持つ行列式をすべて選べ";
Return[IfDeb[{MF[MA]},ret]]];

QtextF[3]

AListF[mm_]:=Module[{Cn,sz,MA,MAL={},Prm,ct,pm,R,CL={},IL={},aret,fsL={},ret={}},
{Cn,sz,MA}=QtList[[mm]];
Prm=Permutations[Range[sz]] /. Range[sz]->Nothing;
For[ct=1,ct≤Length[Prm],ct++,pm=Prm[[ct]];R=IdentityMatrix[sz][[pm]];
If[Signature[pm]==1,CL=Join[CL,{R.MA,MA.R}],IL=Join[IL,{R.MA,MA.R}]]];
CL=RandomSample[CL,Cn];
IL=RandomSample[IL,SELNUM-Cn];
fsL=Append[fsL,"正解です."];fsL=Append[fsL,"違います. \\(-1\\)倍になります."];
For[ct=1,ct≤Length[CL],ct++,
ret=Append[ret,{"C",IfDeb[MF[CL[[ct]]],"\\("<>TAM[CL[[ct]],"vmatrix"]<>"\\)"],fsL[[1]]}]];
For[ct=1,ct≤Length[IL],ct++,
ret=Append[ret,{"I",IfDeb[MF[IL[[ct]]],"\\("<>TAM[IL[[ct]],"vmatrix"]<>"\\)"],fsL[[2]]}]];
ret=RandomSample[ret];Return[Join[{{Cn,SELNUM-Cn}},ret]]];

(* 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]