////////// KETlib //////////
use("KetCindyPlugin");
Dircdy=loaddirectory;
setdirectory(gethome());
import("ketcindy.ini");

ansflg=0;
resetflg=0;

////////// figure //////////
Ketinit();
Setketcindyjs(["Label=[]","Color=offwhite"]);//no ketjs
Seteditable(50,["","Size=18","Width=30"]);
Seteditable(51,["","Size=18","Width=50"]);

Setwindow([-0.2,1.1],[-0.2,1.1]);
Setmarklen(0.1);

Slider("N",[0,YMIN-0.1],[1,YMIN-0.1]);
Expr([0,YMIN-0.2+0.01],"w1","n=");
forall(0..10,
  Listplot("t"+text(#),[[#/10,YMIN-0.1+0.02],[#/10,YMIN-0.1-0.02]],["Num=1"]);
  Expr([#/10,YMIN-0.2],"c",text(#));
);

Deffun("f(x)",["regional(y)","y=x^2","y"]);

if(resetflg==1,
  Subsedit(50,"");
  Subsedit(51,"");
  resetflg=0;
);

str1="0";//no ketjs
//str1=Textedit(50); //only ketjs
if(length(str1)>0,
  N.x=parse(str1)/10;
);

str2="2";//no ketjs
//str2=Textedit(51); //only ketjs
if(length(str2)>0,
  ans=parse(str2);
);

Mf(ss):=(
  regional(nn);
  nn=floor(ss);
  if(ss>0,
    forall(1..nn,
      Framedata("u"+text(#),[[(#-1)/nn,0],[#/nn,f(#/nn)]],["corner","Color=blue"]);
      Framedata("l1",[[0,0],[1/nn,f(0)]],["corner","Color=red"]);
      if(nn>1,
        Framedata("l"+text(#),[[(#-1)/nn,0],[#/nn,f((#-1)/nn)]],["corner","Color=red"]);
      );
      if(nn<18,
        if(#<nn,
          Expr([#/nn,0],"s2","\dfrac{"+text(#)+"}{"+text(nn)+"}");
        );
      );
    );
  );
);

ss=Animationparam(N.x*10,4,200);
Mf(ss);

Plotdata("1","f(x)","x=[XMIN,sqrt(XMAX)]");
Expr([sqrt(YMAX),YMAX],"n1","y=x^2",["Size=1.3"]);

Expr([1.2,1.2],"n1e","{\color{red}n}=",["Size=1.3"]);
Letter([1.52,1.2],"n1e","$(\leq 4)$のとき，$S_n$を計算すると",["Size=1.3"]);
if(length(str1)==0,
  Expr([1.2,1.02],"n1e","\displaystyle S_n=\sum_{k=1}^{\color{red}n}f(x_k)\Delta x_k\ ,\ \ x_k=\dfrac{k}{\color{red}n}\ ,\ \ \Delta x_k=\dfrac{1}{\color{red}n}",["Size=1.3"]);
  Expr([1.2,0.8],"n1e","\phantom{S_n}=\left(\dfrac{1}{\color{red}n}\right)^2\cdot\dfrac{1}{\color{red}n}+\left(\dfrac{2}{\color{red}n}\right)^2\cdot\dfrac{1}{\color{red}n}+\cdots+\left(\dfrac{\color{red}n}{\color{red}n}\right)^2\cdot\dfrac{1}{\color{red}n}",["Size=1.3"]);
,
  nn=parse(str1);
  Expr([1.2,1.02],"n1e","\displaystyle S_n=\sum_{k=1}^{\color{red}"+str1+"}f(x_k)\Delta x_k\ ,\ \ x_k=\dfrac{k}{\color{red}"+str1+"}\ ,\ \ \Delta x_k=\dfrac{1}{\color{red}"+str1+"}",["Size=1.3"]);
  Expr([1.2,0.8],"n1e","\phantom{S_n}=\left(\dfrac{\color{red}1}{\color{red}"+str1+"}\right)^2\cdot\dfrac{1}{\color{red}"+str1+"}",["Size=1.3"]);
  forall(2..nn,
    Expr([1.75+(#-2)*0.42,0.8],"n1e","+\left(\dfrac{"+text(#)+"}{\color{red}"+str1+"}\right)^2\cdot\dfrac{1}{\color{red}"+str1+"}",["Size=1.3"]);
  );
  Expr([1.2,0.6],"n1e","\phantom{S_n}=\dfrac{\color{red}1}{{\color{red}"+str1+"}^3}",["Size=1.3"]);
  forall(2..nn,
    Expr([1.5+(#-2)*0.15,0.6],"n1e","+\dfrac{"+text(#^2)+"}{{\color{red}"+str1+"}^3}",["Size=1.3"]);
  );
  Expr([1.2,0.4],"n1e","\displaystyle \phantom{S_n}=",["Size=1.3"]);
  Letter([1.6,0.4],"n1e","(四捨五入して小数第3位まで)",["Size=1.3"]);
);

if(ansflg==1,
  if(parse(str1)==1,
    if(ans==1,
      Letter([1.5,0.2],"n1e","正解",["Size=1.3","Color=red"]);
    ,
      Letter([1.5,0.2],"n1e","間違い",["Size=1.3","Color=red"]);
      Letter([1.85,0.2],"n1e","正解は $1$",["Size=1.3","Color=red"]);
    );
  ); 
  if(parse(str1)==2,
    if(ans==0.625,
      Letter([1.5,0.2],"n1e","正解",["Size=1.3","Color=red"]);
    ,
      Letter([1.5,0.2],"n1e","間違い",["Size=1.3","Color=red"]);
      Letter([1.85,0.2],"n1e","正解は $0.625$",["Size=1.3","Color=red"]);
    );
  );
  if(parse(str1)==3,
    if(ans==0.519,
      Letter([1.5,0.2],"n1e","正解",["Size=1.3","Color=red"]);
    ,
      Letter([1.5,0.2],"n1e","間違い",["Size=1.3","Color=red"]);
      Letter([1.85,0.2],"n1e","正解は $0.519$",["Size=1.3","Color=red"]);
    );
  );
  if(parse(str1)==4,
    if(ans==0.469,
      Letter([1.5,0.2],"n1e","正解",["Size=1.3","Color=red"]);
    ,
      Letter([1.5,0.2],"n1e","間違い",["Size=1.3","Color=red"]);
      Letter([1.85,0.2],"n1e","正解は $0.469$",["Size=1.3","Color=red"]);
    );
  );
);

Letter([1.2,0],"n1e","Playボタンを押して，一般に$S_n$を計算すると",["Size=1.3"]);
if((Animeflg==1)%(Animeflg==0),
  Expr([1.2,-0.2],"n1e","\displaystyle \overline{S}_n=\dfrac{1}{n^3}\sum_{k=1}^n k^2=\dfrac{(n+1)(2n+1)}{6n^2}=\dfrac{1}{6}\left(1+\dfrac{1}{n}\right)\left(2+\dfrac{1}{n}\right)",["Size=1.3"]);
  ns=floor(ss);
  Expr([1.2,-0.4],"n1e","\displaystyle \phantom{\overline{S}_n}="+format((ns+1)*(2*ns+1)/(6*ns^2),4),["Size=1.3"]);
  Expr([1.8,-0.4],"n1e","(n="+text(ns)+")",["Size=1.3"]);
  if(ss==200,
    Expr([1.2,-0.6],"n1e","\displaystyle \int_0^1 x^2\,dx=\lim_{n\to\infty}S_n=\dfrac{1}{6}\cdot1\cdot2=\dfrac{1}{3}=0.3333\cdots",["Size=1.3"]);
  );
  Expr([1.2,-0.8],"n1e","\displaystyle \underline{S}_n=\dfrac{1}{n^3}\sum_{k=1}^{n-1} k^2=\dfrac{(n-1)(2n-1)}{6n^2}=\dfrac{1}{6}\left(1-\dfrac{1}{n}\right)\left(2-\dfrac{1}{n}\right)",["Size=1.3"]);
  ns=floor(ss);
  Expr([1.2,-1],"n1e","\displaystyle \phantom{\underline{S}_n}="+format((ns-1)*(2*ns-1)/(6*ns^2),4),["Size=1.3"]);
  Expr([1.8,-1],"n1e","(n="+text(ns)+")",["Size=1.3"]);
);

Listplot("do1",[[1,0],[1,f(1)],[0,f(1)]],["do"]);
Htickmark([1,"1"]);
Vtickmark([f(1),text(f(1))]);

Windispg();

//Help("Subsedit");