rem  ---- P4iteration --------------------------------
rem   
rem      f(z)=z^4-2*p*z^2+4*q*z+b
rem
rem         p=(a1+a2)^2-a1*a2=pr+i*pi
rem         q=a1*a2*(a1+a2)  =qr+i*qi
rem       critical points: a1, a2, a3
rem                      a1+a2+a3=0     
rem
rem   初期値 or Critical point を与えての反復計算
rem
REM-------------------------------- 8.4 '08, Joe  ----------------
rem
print"初期値を与えて Zn+1=Zn^4-2*p*Zn^2+4*q*Zn+b の反復を計算"
input prompt"a1=a1r+i*a1i をinputせよ，a1r,a1i=":a1r,a1i
input prompt"a2=a2r+i*a2i をinputせよ，a2r,a2i=":a2r,a2i
input prompt"b=br+i*bi をinputせよ，br,bi=":br,bi
LET  a3r=-(a1r+a2r)
LET  a3i=-(a1i+a2i)
5 PRINT"初期値の選択（下の４つから）"
  print"1.... 初期値は a1"
  print"2.... 初期値は a2"
  print"3.... 初期値は a3"
  print"4---- x0,y0 をinput"
  print"----------------------"
  input prompt" 番号(1〜4)=":jo
  rem
  if jo=1 then goto 10
  if jo=2 then goto 20
  if jo=3 then goto 25
  input prompt"x0,y0=":x0,y0
  goto 30
10 LET  x0=a1r
   LET  y0=a1i
   goto 30
20 LET  x0=a2r
   LET  y0=a2i
   goto 30
25 LET  x0=a3r
   LET  y0=a3i
30 LET  r=36
   print"表示する数列の最小と最大の n をinputせよ"
   input prompt"nl,nu=":nl,nu
   rem
   rem   多項式の係数
   rem
   LET  c1=a1r+a2r
   LET  d1=a1i+a2i
   LET  c2=a1r*a2r
   LET  d2=a1i*a2i
   LET  d3=c2-d2
   LET  c3=a1r*a2i
   LET  c4=a2r*a1i
   LET  c5=c3+c4
   LET  pr=c1*c1-d1*d1-d3
   LET  ppi=2*c1*d1-c5
   LET  qr=d3*c1-c5*d1
   LET  qi=d3*d1+c5*c1
   rem
   LET  x=x0
   LET  y=y0
   rem
   rem     計算
   rem
   for n=1 to nu
      LET  xy2=(x+y)*(x-y)
      LET  xy=x*y
      LET  x1=xy2*(xy2-2*pr)+4*(xy*(ppi-xy)+qr*x-qi*y)+br
      LET  y1=2*xy2*(2*xy-ppi)+4*(x*(qi-pr*y)+qr*y)+bi
      LET  d=x1*x1+y1*y1
      if nl<=n and n<=nu then goto 32 else goto 35
32    print n;")";x1;" , ";y1
35    if d>r then goto 40 else goto 45
40    print"発散です d=";d;" n=";n
      goto 100
45    LET  x=x1
      LET  y=y1
   next n
   rem
100 INPUT PROMPT"別の臨界値でやる？ yes...1, no....2=":joe
    IF joe=1  THEN GOTO 5
 END