// xcas version=0.6.3 fontsize=25
// fltk N4xcas12History_FoldE 32 -44 1063 394 25
Partie I
// fltk N4xcas12History_PackE 32 -13 1047 1650 25
[
// fltk 7Fl_Tile 60 -13 1019 540 25
[
// fltk N4xcas7EditeurE 60 -13 1019 368 25
538 ,
inversG(a,N):={
  local b,x,N1;
  N1:=N-1;
  b:=a;
  a:=1;
  while (N1!=0) {
    x:=irem(N1,2);
    N1:=iquo(N1,2);
    a:=a*b^x;
    b:=b^2;
  }
  return a;
}:;

inverseG(a,N):={
  local b,N1;
  N1:=N-1;
  b:=a;
  a:=1;
  while (N1!=0) {
    if (irem(N1,2)) a:=a*b;
    b:=b*b;
    N1:=iquo(N1,2);
  }
  return a;
}:;

// cf. aussi la fonction interne powmod
puissmod(a,k,p):={
  local b;
  b:=a;
  a:=1;
  k:=irem(k,euler(p));
  while (k!=0) {
    if (irem(k,2)) a:=irem(a*b,p);
    b:=irem(b*b,p);
    k:=iquo(k,2);
  }
  return a;
}:;,
// fltk N4xcas10Log_OutputE 60 355 1019 129 25
// Parsing inversG£// Success compiling inversG£// Parsing inverseG£// Success compiling inverseG£// Parsing puissmod£// Success compiling puissmod£
,
// fltk N4xcas8EquationE 60 484 1019 43 25
"Done","Done","Done"
]
,
// fltk 7Fl_Tile 60 529 1019 35 25
[
// fltk N4xcas19Multiline_Input_tabE 60 529 1019 34 25

,
// fltk N4xcas10Log_OutputE 60 563 1019 1 25

]
,
// fltk 7Fl_Tile 60 566 1019 433 25
[
// fltk N4xcas7EditeurE 60 566 1019 345 25
191 ,
puissrapide(a,k,mult,unit,ordre):={
  local b;
  b:=a;
  a:=unit;
  k:=irem(k,ordre);
  while (k!=0) {
    if (irem(k,2)) a:=mult(a,b);
    b:=mult(b,b);
    k:=iquo(k,2);
  }
  return a;
}:;,
// fltk N4xcas10Log_OutputE 60 911 1019 45 25
// Parsing puissrapide£// Success compiling puissrapide£
,
// fltk N4xcas8EquationE 60 956 1019 43 25
"Done"
]
,
// fltk 7Fl_Tile 60 1001 1019 105 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1001 1019 61 25
multmod71(a,b):=irem(a*b,71);£puissrapide(47,50,multmod71,1,0)
,
// fltk N4xcas10Log_OutputE 60 1062 1019 1 25

,
// fltk N4xcas8EquationE 60 1063 1019 43 25
 (a,b)->irem(a*b,71),32
]
,
// fltk 7Fl_Tile 60 1108 1019 74 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1108 1019 30 25
p:=148
,
// fltk N4xcas10Log_OutputE 60 1138 1019 1 25

,
// fltk N4xcas8EquationE 60 1139 1019 43 25
148
]
,
// fltk 7Fl_Tile 60 1184 1019 74 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1184 1019 30 25
puissmod(5,71,148)
,
// fltk N4xcas10Log_OutputE 60 1214 1019 1 25

,
// fltk N4xcas8EquationE 60 1215 1019 43 25
89
]
,
// fltk 7Fl_Tile 60 1260 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1260 1019 30 25
powmod(5,71,148)
,
// fltk N4xcas10Log_OutputE 60 1290 1019 1 25

,
// fltk N4xcas8EquationE 60 1291 1019 53 25
89
]
,
// fltk 7Fl_Tile 60 1346 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1346 1019 30 25
multmod148(a,b):=irem(a*b,148);puissrapide(5,71,multmod148,1,euler(148))
,
// fltk N4xcas10Log_OutputE 60 1376 1019 1 25

,
// fltk N4xcas8EquationE 60 1377 1019 53 25
 (a,b)->irem(a*b,148),puissrapide(5,71, (a,b)->irem(a*b,148),1,72)
]
,
// fltk 7Fl_Tile 60 1432 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1432 1019 30 25
iegcd(5,148)
,
// fltk N4xcas10Log_OutputE 60 1462 1019 1 25

,
// fltk N4xcas8EquationE 60 1463 1019 53 25
[-59,2,1]
]
,
// fltk 7Fl_Tile 60 1518 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1518 1019 30 25
-59+148
,
// fltk N4xcas10Log_OutputE 60 1548 1019 1 25

,
// fltk N4xcas8EquationE 60 1549 1019 53 25
89
]
,
// fltk 7Fl_Tile 60 1604 1019 31 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1604 1019 30 25

,
// fltk N4xcas10Log_OutputE 60 1634 1019 1 25

]
]
,
// fltk N4xcas12History_FoldE 32 -11 1063 402 25
Partie II
// fltk N4xcas12History_PackE 32 20 1047 1287 25
[
// fltk 7Fl_Tile 47 20 1032 541 25
[
// fltk N4xcas7EditeurE 47 20 1032 329 25
365 ,
decod28(p):={
  local r;
  r:=irem(p,29);
  if (r==0) return "erreur";
  if (r<27) return char(p+64);
  if (r==27) return char(32);
  return char(46);
}:;

decode(a,b):={
  local c;
  c:=powmod(a,17,29);
  return irem(b*c,29);
}:;

decodel(L):={
  local s,M;
  s:=size(L);
  M:=NULL;
  for (k:=0;k<s;k++) {
    M:= M,decod28(decode(op(L[k])));
  }
  return [M];
}:;,
// fltk N4xcas10Log_OutputE 47 349 1032 159 25
// Parsing decod28£// Success compiling decod28£// Parsing decode£// Success compiling decode£// Parsing decodel£// Warning: k decod28 decode  declared as global variable(s) compiling decodel£
,
// fltk N4xcas8EquationE 47 508 1032 53 25
"Done","Done","Done"
]
,
// fltk 7Fl_Tile 47 563 1032 90 25
[
// fltk N4xcas19Multiline_Input_tabE 47 563 1032 36 25
puissmod(2,11,29)
,
// fltk N4xcas10Log_OutputE 47 599 1032 1 25

,
// fltk N4xcas8EquationE 47 600 1032 53 25
puissmod(2,11,29)
]
,
// fltk 7Fl_Tile 47 655 1032 84 25
[
// fltk N4xcas19Multiline_Input_tabE 47 655 1032 30 25
decode(3,1)
,
// fltk N4xcas10Log_OutputE 47 685 1032 1 25

,
// fltk N4xcas8EquationE 47 686 1032 53 25
decode(3,1)
]
,
// fltk 7Fl_Tile 47 741 1032 109 25
[
// fltk N4xcas19Multiline_Input_tabE 47 741 1032 55 25
multmod29(a,b):=irem(a*b,29);£puissrapide(3,17,multmod29,1,0)
,
// fltk N4xcas10Log_OutputE 47 796 1032 1 25

,
// fltk N4xcas8EquationE 47 797 1032 53 25
 (a,b)->irem(a*b,29),puissrapide(3,17, (a,b)->irem(a*b,29),1,0)
]
,
// fltk 7Fl_Tile 47 852 1032 334 25
[
// fltk N4xcas19Multiline_Input_tabE 47 852 1032 30 25
L:=[[16,17],[18,24],[28,22],[17,21],[23,23],[24,8]]
,
// fltk N4xcas10Log_OutputE 47 882 1032 1 25

,
// fltk N4xcas8EquationE 47 883 1032 303 25
[[16,17],[18,24],[28,22],[17,21],[23,23],[24,8]]
]
,
// fltk 7Fl_Tile 47 1188 1032 84 25
[
// fltk N4xcas19Multiline_Input_tabE 47 1188 1032 30 25
decodel(L)
,
// fltk N4xcas10Log_OutputE 47 1218 1032 1 25

,
// fltk N4xcas8EquationE 47 1219 1032 53 25
["C","O","G","I","T","O"]
]
,
// fltk 7Fl_Tile 47 1274 1032 31 25
[
// fltk N4xcas19Multiline_Input_tabE 47 1274 1032 30 25

,
// fltk N4xcas10Log_OutputE 47 1304 1032 1 25

]
]
,
// fltk N4xcas12History_FoldE 32 22 1063 398 25
Partie III
// fltk N4xcas12History_PackE 32 53 1047 2647 25
[
// fltk 7Fl_Tile 60 53 1019 102 25
[
// fltk N4xcas19Multiline_Input_tabE 60 53 1019 34 25
F16:=GF(2,4,['t','F16'])
,
// fltk N4xcas10Log_OutputE 60 87 1019 1 25

,
// fltk N4xcas8EquationE 60 88 1019 67 25
GF(2,t^4+t^3+1,[t,F16],undef)
]
,
// fltk 7Fl_Tile 60 157 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 157 1019 30 25
F16(t^4)
,
// fltk N4xcas10Log_OutputE 60 187 1019 1 25

,
// fltk N4xcas8EquationE 60 188 1019 67 25
F16(t^3+1)
]
,
// fltk 7Fl_Tile 60 257 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 257 1019 30 25
F16(t^5)
,
// fltk N4xcas10Log_OutputE 60 287 1019 1 25

,
// fltk N4xcas8EquationE 60 288 1019 67 25
F16(t^3+t+1)
]
,
// fltk 7Fl_Tile 60 357 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 357 1019 30 25
w:=F16(t)
,
// fltk N4xcas10Log_OutputE 60 387 1019 1 25

,
// fltk N4xcas8EquationE 60 388 1019 53 25
F16(t)
]
,
// fltk 7Fl_Tile 60 443 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 443 1019 30 25
w^4+w^3+1
,
// fltk N4xcas10Log_OutputE 60 473 1019 1 25

,
// fltk N4xcas8EquationE 60 474 1019 53 25
F16(0)
]
,
// fltk 7Fl_Tile 60 529 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 529 1019 30 25
K:=append(seq(w^k,k,1,15),F16(0))
,
// fltk N4xcas10Log_OutputE 60 559 1019 1 25

,
// fltk N4xcas8EquationE 60 560 1019 67 25
[F16(t),F16(t^2),F16(t^3),F16(t^3+1),F16(t^3+t+1),F16(t^3+t^2+t+1),F16(t^2+t+1),F16(t^3+t^2+t),F16(t^2+1),F16(t^3+t),F16(t^3+t^2+1),F16(t+1),F16(t^2+t),F16(t^3+t^2),F16(1),F16(0)]
]
,
// fltk 7Fl_Tile 60 629 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 629 1019 30 25
P(x):=x^4+x^3+1
,
// fltk N4xcas10Log_OutputE 60 659 1019 1 25

,
// fltk N4xcas8EquationE 60 660 1019 67 25
 (x)->x^4+x^3+1
]
,
// fltk 7Fl_Tile 60 729 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 729 1019 30 25
seq(P(w^(2^k)),k,0,3)
,
// fltk N4xcas10Log_OutputE 60 759 1019 1 25

,
// fltk N4xcas8EquationE 60 760 1019 53 25
[F16(0),F16(0),F16(0),F16(0)]
]
,
// fltk 7Fl_Tile 60 815 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 815 1019 30 25
seq(w^(2^k),k,0,3)
,
// fltk N4xcas10Log_OutputE 60 845 1019 1 25

,
// fltk N4xcas8EquationE 60 846 1019 67 25
[F16(t),F16(t^2),F16(t^3+1),F16(t^3+t^2+t)]
]
,
// fltk 7Fl_Tile 60 915 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 915 1019 30 25
w^16
,
// fltk N4xcas10Log_OutputE 60 945 1019 1 25

,
// fltk N4xcas8EquationE 60 946 1019 53 25
F16(t)
]
,
// fltk 7Fl_Tile 60 1001 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1001 1019 30 25
(w^3+w)^3
,
// fltk N4xcas10Log_OutputE 60 1031 1019 1 25

,
// fltk N4xcas8EquationE 60 1032 1019 53 25
F16(1)
]
,
// fltk 7Fl_Tile 60 1087 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1087 1019 30 25
A:=seq(K[k]^5,k,0,14)
,
// fltk N4xcas10Log_OutputE 60 1117 1019 1 25

,
// fltk N4xcas8EquationE 60 1118 1019 67 25
[F16(t^3+t+1),F16(t^3+t),F16(1),F16(t^3+t+1),F16(t^3+t),F16(1),F16(t^3+t+1),F16(t^3+t),F16(1),F16(t^3+t+1),F16(t^3+t),F16(1),F16(t^3+t+1),F16(t^3+t),F16(1)]
]
,
// fltk 7Fl_Tile 60 1187 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1187 1019 30 25
B:=set[op(A)]
,
// fltk N4xcas10Log_OutputE 60 1217 1019 1 25

,
// fltk N4xcas8EquationE 60 1218 1019 67 25
set[F16(t^3+t+1),F16(t^3+t),F16(1)]
]
,
// fltk 7Fl_Tile 60 1287 1019 36 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1287 1019 35 25

,
// fltk N4xcas10Log_OutputE 60 1322 1019 1 25

]
,
// fltk 7Fl_Tile 60 1325 1019 340 25
[
// fltk N4xcas7EditeurE 60 1325 1019 252 25
113 ,
sol(p):={
  local s,k;
  s:=[];
  for (k:=0;k<15;k++){
    if (A[k]==B[p]) s:=append(s,K[k]);
  }
  return s;
}:;,
// fltk N4xcas10Log_OutputE 60 1577 1019 45 25
// Parsing sol£// Warning: A B K  declared as global variable(s) compiling sol£
,
// fltk N4xcas8EquationE 60 1622 1019 43 25
"Done"
]
,
// fltk 7Fl_Tile 60 1667 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1667 1019 30 25
S0:=sol(0)
,
// fltk N4xcas10Log_OutputE 60 1697 1019 1 25

,
// fltk N4xcas8EquationE 60 1698 1019 53 25
sol(0)
]
,
// fltk 7Fl_Tile 60 1753 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1753 1019 30 25
S1:=sol(1)
,
// fltk N4xcas10Log_OutputE 60 1783 1019 1 25

,
// fltk N4xcas8EquationE 60 1784 1019 53 25
sol(1)
]
,
// fltk 7Fl_Tile 60 1839 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1839 1019 30 25
S2:=sol(2)
,
// fltk N4xcas10Log_OutputE 60 1869 1019 1 25

,
// fltk N4xcas8EquationE 60 1870 1019 53 25
sol(2)
]
,
// fltk 7Fl_Tile 60 1925 1019 36 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1925 1019 35 25

,
// fltk N4xcas10Log_OutputE 60 1960 1019 1 25

]
,
// fltk 7Fl_Tile 60 1963 1019 426 25
[
// fltk N4xcas7EditeurE 60 1963 1019 338 25
453 ,
multi(a,b):={
  local c,ci,k,j,p,u;
  c:=[];
  for (j:=3;j>=0;j--){
    ci:=[0];
    for (k:=3;k>=0;k--){
      ci:=prepend(ci,(a[k] and b[j]));
    };
    for (p:=0;p<=3-j;p++){
      ci:=append(tail(ci),head(ci));
    }
    u:=ci[4];
    for (p:=0;p<4;p++){
      ci[p]:=ci[p] xor u;
    }
    ci[4]:=0;
    c:=append(c,mid(ci,0,4));
  }
  for (j:=3;j>0;j--){
    for (k:=3;k>=0;k--){
      c[j-1,k]:=c[j,k] xor c[j-1,k];
    }
  }
  return c[0];
}:;
,
// fltk N4xcas10Log_OutputE 60 2301 1019 45 25
// Parsing multi£// Success compiling multi£
,
// fltk N4xcas8EquationE 60 2346 1019 43 25
"Done"
]
,
// fltk 7Fl_Tile 60 2391 1019 74 25
[
// fltk N4xcas19Multiline_Input_tabE 60 2391 1019 30 25
multi([1,0,1,1],[0,1,1,1])
,
// fltk N4xcas10Log_OutputE 60 2421 1019 1 25

,
// fltk N4xcas8EquationE 60 2422 1019 43 25
[0,0,0,1]
]
,
// fltk 7Fl_Tile 60 2467 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 2467 1019 30 25
c:=w^3;
,
// fltk N4xcas10Log_OutputE 60 2497 1019 1 25

,
// fltk N4xcas8EquationE 60 2498 1019 67 25
F16(t^3)
]
,
// fltk 7Fl_Tile 60 2567 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 2567 1019 30 25
(c^4+c^2+c)*(c^3+c^2+c)
,
// fltk N4xcas10Log_OutputE 60 2597 1019 1 25

,
// fltk N4xcas8EquationE 60 2598 1019 67 25
F16(t^3)
]
,
// fltk 7Fl_Tile 60 2667 1019 31 25
[
// fltk N4xcas19Multiline_Input_tabE 60 2667 1019 30 25

,
// fltk N4xcas10Log_OutputE 60 2697 1019 1 25

]
]
,
// fltk N4xcas12History_FoldE 32 55 1063 529 25
Partie IV
// fltk N4xcas12History_PackE 32 -677 1047 1277 25
[
// fltk 7Fl_Tile 47 -677 1032 381 25
[
// fltk N4xcas19Multiline_Input_tabE 47 -677 1032 36 25
plot(x^3,x)
,
// fltk N4xcas10Log_OutputE 47 -641 1032 1 25

,
// fltk 7Fl_Tile 47 -640 1032 344 25
[
// fltk N4xcas7Graph2dE 47 -640 882 344 25
-10,9.95,-1000,985.07,[pnt(pnt[curve(group[pnt[x+(i)*x^3,x,-10.0,10.0],group[-10.0-1000*(i),-9.95-985.074875*(i),-9.9-970.299*(i),-9.85-955.671625*(i),-9.8-941.192*(i),-9.75-926.859375*(i),-9.7-912.673*(i),-9.65-898.632125*(i),-9.6-884.736*(i),-9.55-870.983875*(i),-9.5-857.375*(i),-9.45-843.908625*(i),-9.4-830.584*(i),-9.35-817.400375*(i),-9.3-804.357*(i),-9.25-791.453125*(i),-9.2-778.688*(i),-9.15-766.060875*(i),-9.1-753.571*(i),-9.05-741.217625*(i),-9-729*(i),-8.95-716.917375*(i),-8.9-704.969*(i),-8.85-693.154125*(i),-8.8-681.472*(i),-8.75-669.921875*(i),-8.7-658.503*(i),-8.65-647.214625*(i),-8.6-636.056*(i),-8.55-625.026375*(i),-8.5-614.125*(i),-8.45-603.351125*(i),-8.4-592.704*(i),-8.35-582.182875*(i),-8.3-571.787*(i),-8.25-561.515625*(i),-8.2-551.368*(i),-8.15-541.343375*(i),-8.1-531.441*(i),-8.05-521.660125*(i),-8-512*(i),-7.95-502.459875*(i),-7.9-493.039*(i),-7.85-483.736625*(i),-7.8-474.552*(i),-7.75-465.484375*(i),-7.7-456.533*(i),-7.65-447.697125*(i),-7.6-438.976*(i),-7.55-430.368875*(i),-7.5-421.875*(i),-7.45-413.493625*(i),-7.4-405.224*(i),-7.35-397.065375*(i),-7.3-389.017*(i),-7.25-381.078125*(i),-7.2-373.248*(i),-7.15-365.525875*(i),-7.1-357.911*(i),-7.05-350.402625*(i),-7-343*(i),-6.95-335.702375*(i),-6.9-328.509*(i),-6.85-321.419125*(i),-6.8-314.432*(i),-6.75-307.546875*(i),-6.7-300.763*(i),-6.65-294.079625*(i),-6.6-287.496*(i),-6.55-281.011375*(i),-6.5-274.625*(i),-6.45-268.336125*(i),-6.4-262.144*(i),-6.35-256.047875*(i),-6.3-250.047*(i),-6.25-244.140625*(i),-6.2-238.328*(i),-6.15-232.608375*(i),-6.1-226.981*(i),-6.05-221.445125*(i),-6-216*(i),-5.95-210.644875*(i),-5.9-205.379*(i),-5.85-200.201625*(i),-5.8-195.112*(i),-5.75-190.109375*(i),-5.7-185.193*(i),-5.65-180.362125*(i),-5.6-175.616*(i),-5.55-170.953875*(i),-5.5-166.375*(i),-5.45-161.878625*(i),-5.4-157.464*(i),-5.35-153.130375*(i),-5.3-148.877*(i),-5.25-144.703125*(i),-5.2-140.608*(i),-5.15-136.590875*(i),-5.1-132.651*(i),-5.05-128.787625*(i),-5-125*(i),-4.95-121.287375*(i),-4.9-117.649*(i),-4.85-114.084125*(i),-4.8-110.592*(i),-4.75-107.171875*(i),-4.7-103.823*(i),-4.65-100.544625*(i),-4.6-97.336*(i),-4.55-94.196375*(i),-4.5-91.125*(i),-4.45-88.121125*(i),-4.4-85.184*(i),-4.35-82.312875*(i),-4.3-79.507*(i),-4.25-76.765625*(i),-4.2-74.088*(i),-4.15-71.473375*(i),-4.1-68.921*(i),-4.05-66.430125*(i),-4-64*(i),-3.95-61.629875*(i),-3.9-59.319*(i),-3.85-57.066625*(i),-3.8-54.872*(i),-3.75-52.734375*(i),-3.7-50.653*(i),-3.65-48.627125*(i),-3.6-46.656*(i),-3.55-44.738875*(i),-3.5-42.875*(i),-3.45-41.063625*(i),-3.4-39.304*(i),-3.35-37.595375*(i),-3.3-35.937*(i),-3.25-34.328125*(i),-3.2-32.768*(i),-3.15-31.255875*(i),-3.1-29.791*(i),-3.05-28.372625*(i),-3-27*(i),-2.95-25.672375*(i),-2.9-24.389*(i),-2.85-23.149125*(i),-2.8-21.952*(i),-2.75-20.796875*(i),-2.7-19.683*(i),-2.65-18.609625*(i),-2.6-17.576*(i),-2.55-16.581375*(i),-2.5-15.625*(i),-2.45-14.706125*(i),-2.4-13.824*(i),-2.35-12.977875*(i),-2.3-12.167*(i),-2.25-11.390625*(i),-2.2-10.648*(i),-2.15-9.938375*(i),-2.1-9.261*(i),-2.05-8.615125*(i),-2-8*(i),-1.95-7.414875*(i),-1.9-6.859*(i),-1.85-6.331625*(i),-1.8-5.832*(i),-1.75-5.359375*(i),-1.7-4.913*(i),-1.65-4.492125*(i),-1.6-4.096*(i),-1.55-3.723875*(i),-1.5-3.375*(i),-1.45-3.048625*(i),-1.4-2.744*(i),-1.35-2.460375*(i),-1.3-2.197*(i),-1.25-1.953125*(i),-1.2-1.728*(i),-1.15-1.520875*(i),-1.1-1.331*(i),-1.05-1.157625*(i),-1-1*(i),-0.95-0.857375*(i),-0.9-0.729*(i),-0.85-0.614125*(i),-0.8-0.512*(i),-0.75-0.421875*(i),-0.7-0.343*(i),-0.65-0.274625*(i),-0.6-0.216*(i),-0.55-0.166375*(i),-0.5-0.125*(i),-0.45-0.091125*(i),-0.4-0.064*(i),-0.35-0.042875*(i),-0.3-0.027*(i),-0.25-0.015625*(i),-0.2-0.008*(i),-0.15-0.003375*(i),-0.1-0.001*(i),-0.05-0.000125*(i),7.64666108211e-15,0.05+0.000125*(i),0.1+0.001*(i),0.15+0.003375*(i),0.2+0.008*(i),0.25+0.015625*(i),0.3+0.027*(i),0.35+0.042875*(i),0.4+0.064*(i),0.45+0.091125*(i),0.5+0.125*(i),0.55+0.166375*(i),0.6+0.216*(i),0.65+0.274625*(i),0.7+0.343*(i),0.75+0.421875*(i),0.8+0.512*(i),0.85+0.614125*(i),0.9+0.729*(i),0.95+0.857375*(i),1+1*(i),1.05+1.157625*(i),1.1+1.331*(i),1.15+1.520875*(i),1.2+1.728*(i),1.25+1.953125*(i),1.3+2.197*(i),1.35+2.460375*(i),1.4+2.744*(i),1.45+3.048625*(i),1.5+3.375*(i),1.55+3.723875*(i),1.6+4.096*(i),1.65+4.492125*(i),1.7+4.913*(i),1.75+5.359375*(i),1.8+5.832*(i),1.85+6.331625*(i),1.9+6.859*(i),1.95+7.414875*(i),2+8*(i),2.05+8.615125*(i),2.1+9.261*(i),2.15+9.938375*(i),2.2+10.648*(i),2.25+11.390625*(i),2.3+12.167*(i),2.35+12.977875*(i),2.4+13.824*(i),2.45+14.706125*(i),2.5+15.625*(i),2.55+16.581375*(i),2.6+17.576*(i),2.65+18.609625*(i),2.7+19.683*(i),2.75+20.796875*(i),2.8+21.952*(i),2.85+23.149125*(i),2.9+24.389*(i),2.95+25.672375*(i),3+27*(i),3.05+28.372625*(i),3.1+29.791*(i),3.15+31.255875*(i),3.2+32.768*(i),3.25+34.328125*(i),3.3+35.937*(i),3.35+37.595375*(i),3.4+39.304*(i),3.45+41.063625*(i),3.5+42.875*(i),3.55+44.738875*(i),3.6+46.656*(i),3.65+48.627125*(i),3.7+50.653*(i),3.75+52.734375*(i),3.8+54.872*(i),3.85+57.066625*(i),3.9+59.319*(i),3.95+61.629875*(i),4+64*(i),4.0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,
// fltk 7Fl_Tile 929 -640 150 344 25
[
// fltk N4xcas14Mouse_PositionE 929 -640 150 50 25
[]
,
// fltk 8Fl_Group 929 -590 150 140 25
[
// fltk 9Fl_Button 929 -590 50 28 25
[]
,
// fltk 9Fl_Button 979 -590 50 28 25
[]
,
// fltk 9Fl_Button 1029 -590 50 28 25
[]
,
// fltk 9Fl_Button 929 -562 50 28 25
[]
,
// fltk 9Fl_Button 979 -562 50 28 25
[]
,
// fltk 9Fl_Button 1029 -562 50 28 25
[]
,
// fltk 9Fl_Button 929 -534 50 28 25
[]
,
// fltk 9Fl_Button 979 -534 50 28 25
[]
,
// fltk 9Fl_Button 1029 -534 50 28 25
[]
,
// fltk 9Fl_Button 929 -506 50 28 25
[]
,
// fltk 9Fl_Button 979 -506 50 28 25
[]
,
// fltk 9Fl_Button 1029 -506 50 28 25
[]
,
// fltk 9Fl_Button 929 -478 50 28 25
[]
,
// fltk 11Fl_Menu_Bar 979 -478 100 28 25
[]
]
,
// fltk 8Fl_Group 929 -450 150 154 25
[
]
]
]
]
,
// fltk 7Fl_Tile 47 -294 1032 380 25
[
// fltk N4xcas19Multiline_Input_tabE 47 -294 1032 35 25
plotpolar(1/sin(t)^3,t,0,pi)
,
// fltk N4xcas10Log_OutputE 47 -259 1032 1 25

,
// fltk 7Fl_Tile 47 -258 1032 344 25
[
// fltk N4xcas7Graph2dE 47 -258 882 344 25
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),-2.34779357116+2.17027805356*(i),-2.42630695633+2.20776946008*(i),-2.50818778688+2.24652036456*(i),-2.59362169178+2.28658510503*(i),-2.68280666009+2.32802103128*(i),-2.77595401327+2.37088870647*(i),-2.87328946581+2.41525212476*(i),-2.97505428341+2.46117894641*(i),-3.08150654875+2.50874075181*(i),-3.19292254654+2.55801331637*(i),-3.30959828024+2.60907690815*(i),-3.43185113513+2.66201661049*(i),-3.56002170346+2.71692267197*(i),-3.69447578985+2.77389088644*(i),-3.83560661718+2.83302300611*(i),-3.98383725581+2.894427191*(i),-4.13962330191+2.9582184985*(i),-4.30345583391+3.02451941708*(i),-4.47586468014+3.09346044892*(i),-4.6574220349+3.16518074645*(i),-4.84874646536+3.23982880884*(i),-5.05050735743+3.31756324467*(i),-5.26342985547+3.39855360831*(i),-5.48830035846+3.4829813182*(i),-5.72597264408+3.57104066622*(i),-5.97737470264+3.66293992878*(i),-6.24351637471+3.75890259143*(i),-6.52549790046+3.85916870039*(i),-6.8245195049+3.96399635643*(i),-7.14189216246+4.07366336828*(i),-7.4790497067+4.18846908556*(i),-7.83756247713+4.30873643365*(i),-8.21915272637+4.43481417646*(i),-8.62571204704+4.5670794367*(i),-9.05932112141+4.70594050777*(i),-9.52227214781+4.85183999632*(i),-10.0170943591+5.00525834079*(i),-10.5465831211+5.16671775829*(i),-11.1138331861+5.33678668027*(i),-11.722276781+5.51608474762*(i),-12.3757273353+5.70528844718*(i),-13.0784298064+5.90513748558*(i),-13.8351187435+6.11644201271*(i),-14.651085454+6.34009082683*(i),-15.5322559113+6.57706071675*(i),-16.4852813742+6.82842712475*(i),-17.5176441012+7.09537634809*(i),-18.6377810467+7.37921953821*(i),-19.8552290559+7.68140880661*(i),-21.180795855+8.00355580794*(i),-22.6267621072+8.34745324527*(i),-24.207121034+8.71509983491*(i),-25.9378636422+9.10872938168*(i),-27.8373195602+9.53084475661*(i),-29.9265659827+9.98425774529*(i),-32.2299204278+10.472135955*(i),-34.775537133+10.998058247*(i),-37.5961322756+11.5660805118*(i),-40.7298701846+12.1808140527*(i),-44.221451892+12.8475194183*(i),-48.1234595169+13.5722192634*(i),-52.4980261598+14.3618347802*(i),-57.4189227261+15.2243514984*(i),-62.9741825397+16.169021906*(i),-69.2694248221+17.2066145455*(i),-76.4320935556+18.3497221747*(i),-84.6169054186+19.6131455628*(i),-94.0129090278+21.0143749019*(i),-104.852712071+22.5741982779*(i),-117.424655+24.3174770208*(i),-132.089033554+26.2741423691*(i),-149.299950235+28.4804886981*(i),-169.635090901+30.9808686278*(i),-193.836812332+33.8299393382*(i),-222.869613354+37.0956748762*(i),-258.001721036+40.8634581891*(i),-300.922799703+45.2417189473*(i),-353.916818966+50.3698223846*(i),-420.120949279+56.4292981203*(i),-503.921805801+63.6601285122*(i),-611.576764267+72.3848801301*(i),-752.215018861+83.0453112207*(i),-939.500773609+96.2594104328*(i),-1194.49497437+112.913019281*(i),-1550.78175772+134.312256167*(i),-2064.09295747+162.447638798*(i),-2831.40571048+200.474276361*(i),-4031.4376101+253.636555794*(i),-6017.77535089+331.178216215*(i),-9556.00705861+450.649853173*(i),-16512.7830105+648.789011477*(i),-32251.5323381+1013.54523556*(i),-76448.0800482+1801.59885732*(i),-258012.274418+4053.18069547*(i),-2064098.20319+16211.7227202*(i),-3.39594018435e+41]]),0])],-5,5,1,0,0,0,10,5,1,0,1,1.7857,0,0,1
,
// fltk 7Fl_Tile 929 -258 150 344 25
[
// fltk N4xcas14Mouse_PositionE 929 -258 150 50 25
[]
,
// fltk 8Fl_Group 929 -208 150 140 25
[
// fltk 9Fl_Button 929 -208 50 28 25
[]
,
// fltk 9Fl_Button 979 -208 50 28 25
[]
,
// fltk 9Fl_Button 1029 -208 50 28 25
[]
,
// fltk 9Fl_Button 929 -180 50 28 25
[]
,
// fltk 9Fl_Button 979 -180 50 28 25
[]
,
// fltk 9Fl_Button 1029 -180 50 28 25
[]
,
// fltk 9Fl_Button 929 -152 50 28 25
[]
,
// fltk 9Fl_Button 979 -152 50 28 25
[]
,
// fltk 9Fl_Button 1029 -152 50 28 25
[]
,
// fltk 9Fl_Button 929 -124 50 28 25
[]
,
// fltk 9Fl_Button 979 -124 50 28 25
[]
,
// fltk 9Fl_Button 1029 -124 50 28 25
[]
,
// fltk 9Fl_Button 929 -96 50 28 25
[]
,
// fltk 11Fl_Menu_Bar 979 -96 100 28 25
[]
]
,
// fltk 8Fl_Group 929 -68 150 154 25
[
]
]
]
]
,
// fltk 7Fl_Tile 47 88 1032 36 25
[
// fltk N4xcas19Multiline_Input_tabE 47 88 1032 35 25

,
// fltk N4xcas10Log_OutputE 47 123 1032 1 25

]
,
// fltk 7Fl_Tile 47 126 1032 439 25
[
// fltk N4xcas6FigureE 47 126 1032 439 25
// fltk N4xcas12History_PackE 49 -569 217 1134 25
[
// fltk 7Fl_Tile 77 -569 189 116 25
[
// fltk N4xcas19Multiline_Input_tabE 77 -569 189 56 25
F:=plotpolar(1/(sin(t)^3),t=(0 .. pi),'affichage'=(rouge+line_width_2+quadrant4))
,
// fltk N4xcas10Log_OutputE 77 -513 189 1 25

,
// fltk 9Fl_Scroll 77 -512 189 59 25
[
// fltk N4xcas10Gen_OutputE 77 -512 794 32 25
plotparam(re(1/(sin(t)^3))*exp((i)*t),t=0.00785398163397..3.14159265359)
,
// fltk 12Fl_Scrollbar 77 298 173 25 25
[]
,
// fltk 12Fl_Scrollbar 250 266 16 43 25
[]
]
]
,
// fltk 7Fl_Tile 77 -451 189 90 25
[
// fltk N4xcas19Multiline_Input_tabE 77 -451 189 30 25
assume(ta:=[1.350884861,0,pi])
,
// fltk N4xcas10Log_OutputE 77 -421 189 1 25

,
// fltk 9Fl_Scroll 77 -420 189 59 25
[
// fltk N4xcas10Gen_OutputE 77 -420 501 32 25
parameter(ta,0.0,3.14159265359,1.350884861)
,
// fltk 12Fl_Scrollbar 77 272 173 25 25
[]
,
// fltk 12Fl_Scrollbar 250 240 16 43 25
[]
]
]
,
// fltk 7Fl_Tile 77 -359 189 90 25
[
// fltk N4xcas19Multiline_Input_tabE 77 -359 189 30 25
assume(tb:=[0.911061883,0,pi])
,
// fltk N4xcas10Log_OutputE 77 -329 189 1 25

,
// fltk 9Fl_Scroll 77 -328 189 59 25
[
// fltk N4xcas10Gen_OutputE 77 -328 502 32 25
parameter(tb,0.0,3.14159265359,0.911061883)
,
// fltk 12Fl_Scrollbar 77 272 173 25 25
[]
,
// fltk 12Fl_Scrollbar 250 240 16 43 25
[]
]
]
,
// fltk 7Fl_Tile 77 -267 189 123 25
[
// fltk N4xcas19Multiline_Input_tabE 77 -267 189 63 25
A:=point(exp(i*ta)/sin(ta)^3£,affichage=quadrant4);
,
// fltk N4xcas10Log_OutputE 77 -204 189 1 25

,
// fltk 9Fl_Scroll 77 -203 189 59 25
[
// fltk N4xcas10Gen_OutputE 77 -203 284 32 25
point(exp((i)*ta)/sin(ta)^3)
,
// fltk 12Fl_Scrollbar 77 305 173 25 25
[]
,
// fltk 12Fl_Scrollbar 250 273 16 43 25
[]
]
]
,
// fltk 7Fl_Tile 77 -142 189 121 25
[
// fltk N4xcas19Multiline_Input_tabE 77 -142 189 61 25
B:=point(exp(i*tb)/sin(tb)^3£,affichage=quadrant4);
,
// fltk N4xcas10Log_OutputE 77 -81 189 1 25

,
// fltk 9Fl_Scroll 77 -80 189 59 25
[
// fltk N4xcas10Gen_OutputE 77 -80 286 32 25
point(exp((i)*tb)/sin(tb)^3)
,
// fltk 12Fl_Scrollbar 77 303 173 25 25
[]
,
// fltk 12Fl_Scrollbar 250 271 16 43 25
[]
]
]
,
// fltk 7Fl_Tile 77 -19 189 90 25
[
// fltk N4xcas19Multiline_Input_tabE 77 -19 189 30 25
E:=droite(A,B,'affichage'=(bleu+hidden_name))
,
// fltk N4xcas10Log_OutputE 77 11 189 1 25

,
// fltk 9Fl_Scroll 77 12 189 59 25
[
// fltk N4xcas10Gen_OutputE 77 12 1659 32 25
droite(y=((-sin(ta)^3*sin(tb)+sin(ta)*sin(tb)^3)/(cos(ta)*sin(tb)^3-cos(tb)*sin(ta)^3)*x+(cos(ta)*sin(tb)-cos(tb)*sin(ta))/(cos(ta)*sin(tb)^3-cos(tb)*sin(ta)^3)))
,
// fltk 12Fl_Scrollbar 77 272 173 25 25
[]
,
// fltk 12Fl_Scrollbar 250 240 16 43 25
[]
]
]
,
// fltk 7Fl_Tile 77 73 189 63 25
[
// fltk N4xcas19Multiline_Input_tabE 77 73 189 30 25
tc:=normal(pi-ta-tb)
,
// fltk N4xcas10Log_OutputE 77 103 189 1 25

,
// fltk N4xcas10Gen_OutputE 77 104 189 32 25
pi-ta-tb
]
,
// fltk 7Fl_Tile 77 138 189 116 25
[
// fltk N4xcas19Multiline_Input_tabE 77 138 189 56 25
C:=point(exp(i*tc)/sin(tc)^3,£affichage=quadrant2);
,
// fltk N4xcas10Log_OutputE 77 194 189 1 25

,
// fltk 9Fl_Scroll 77 195 189 59 25
[
// fltk N4xcas10Gen_OutputE 77 195 416 32 25
point(exp((i)*(pi-ta-tb))/sin(pi-ta-tb)^3)
,
// fltk 12Fl_Scrollbar 77 229 189 25 25
[]
,
// fltk 12Fl_Scrollbar 266 195 16 34 25
[]
]
]
,
// fltk 7Fl_Tile 77 256 189 90 25
[
// fltk N4xcas19Multiline_Input_tabE 77 256 189 30 25
D:=point(exp(i*(pi-tc))/sin(tc)^3);
,
// fltk N4xcas10Log_OutputE 77 286 189 1 25

,
// fltk 9Fl_Scroll 77 287 189 59 25
[
// fltk N4xcas10Gen_OutputE 77 287 456 32 25
point(exp((i)*(pi-pi+ta+tb))/sin(pi-ta-tb)^3)
,
// fltk 12Fl_Scrollbar 77 321 189 25 25
[]
,
// fltk 12Fl_Scrollbar 266 287 16 34 25
[]
]
]
,
// fltk 7Fl_Tile 77 348 189 90 25
[
// fltk N4xcas19Multiline_Input_tabE 77 348 189 30 25
equation(droite(0,D)
,
// fltk N4xcas10Log_OutputE 77 378 189 1 25

,
// fltk 9Fl_Scroll 77 379 189 59 25
[
// fltk N4xcas10Gen_OutputE 77 379 292 32 25
y=(sin(ta+tb)/cos(ta+tb)*x)
,
// fltk 12Fl_Scrollbar 77 413 189 25 25
[]
,
// fltk 12Fl_Scrollbar 266 379 16 34 25
[]
]
]
,
// fltk 7Fl_Tile 77 440 189 90 25
[
// fltk N4xcas19Multiline_Input_tabE 77 440 189 30 25
droite(C,D)
,
// fltk N4xcas10Log_OutputE 77 470 189 1 25

,
// fltk 9Fl_Scroll 77 471 189 59 25
[
// fltk N4xcas10Gen_OutputE 77 471 1807 32 25
droite(y=((sin(pi-ta-tb)-sin(ta+tb))/(cos(pi-ta-tb)-cos(ta+tb))*x+(cos(pi-ta-tb)*sin(ta+tb)-cos(ta+tb)*sin(pi-ta-tb))/(cos(pi-ta-tb)*sin(pi-ta-tb)^3-cos(ta+tb)*sin(pi-ta-tb)^3)))
,
// fltk 12Fl_Scrollbar 77 505 189 25 25
[]
,
// fltk 12Fl_Scrollbar 266 471 16 34 25
[]
]
]
,
// fltk 7Fl_Tile 77 532 189 31 25
[
// fltk N4xcas19Multiline_Input_tabE 77 532 189 30 25

,
// fltk N4xcas10Log_OutputE 77 562 189 1 25

]
]
// fltk N4xcas5Geo2dE 284 157 611 408 25
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,
// fltk N4xcas10Log_OutputE 47 565 1032 0 25

]
,
// fltk 7Fl_Tile 47 567 1032 31 25
[
// fltk N4xcas19Multiline_Input_tabE 47 567 1032 30 25

,
// fltk N4xcas10Log_OutputE 47 597 1032 1 25

]
]
,
// fltk N4xcas12History_FoldE 32 586 1063 449 25
Partie V
// fltk N4xcas12History_PackE 32 617 1047 2464 25
[
// fltk 7Fl_Tile 60 617 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 617 1019 30 25
F16:=GF(2,4,['t','F16']);w:=F16(t)
,
// fltk N4xcas10Log_OutputE 60 647 1019 1 25

,
// fltk N4xcas8EquationE 60 648 1019 67 25
GF(2,t^4+t^3+1,[t,F16],undef),F16(t)
]
,
// fltk 7Fl_Tile 60 717 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 717 1019 30 25
Pv:=(x^3+x+y^2+y)
,
// fltk N4xcas10Log_OutputE 60 747 1019 1 25

,
// fltk N4xcas8EquationE 60 748 1019 67 25
x^3+x+y^2+y
]
,
// fltk 7Fl_Tile 60 817 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 817 1019 30 25
diff(Pv,x);diff(Pv,y)
,
// fltk N4xcas10Log_OutputE 60 847 1019 1 25

,
// fltk N4xcas8EquationE 60 848 1019 67 25
3*x^2+1,2*y+1
]
,
// fltk 7Fl_Tile 60 917 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 917 1019 30 25
K:=append(seq(w^k,k,1,15),F16(0))
,
// fltk N4xcas10Log_OutputE 60 947 1019 1 25

,
// fltk N4xcas8EquationE 60 948 1019 67 25
[F16(t),F16(t^2),F16(t^3),F16(t^3+1),F16(t^3+t+1),F16(t^3+t^2+t+1),F16(t^2+t+1),F16(t^3+t^2+t),F16(t^2+1),F16(t^3+t),F16(t^3+t^2+1),F16(t+1),F16(t^2+t),F16(t^3+t^2),F16(1),F16(0)]
]
,
// fltk 7Fl_Tile 60 1017 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1017 1019 30 25
La:=seq(K[k]^3+K[k],k,0,15)
,
// fltk N4xcas10Log_OutputE 60 1047 1019 1 25

,
// fltk N4xcas8EquationE 60 1048 1019 67 25
[F16(t^3+t),F16(t^3+t+1),F16(t^3+t^2+1),F16(t^3+t),F16(t^3+t),F16(t^2+t+1),F16(t^3),F16(t^3+t+1),F16(t^2+t),F16(t^3+t+1),F16(t^2+1),F16(t^3+t^2),F16(t+1),F16(t^3+t^2+t+1),F16(0),F16(0)]
]
,
// fltk 7Fl_Tile 60 1117 1019 98 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1117 1019 30 25
A:=set[op(La)]; size(A)
,
// fltk N4xcas10Log_OutputE 60 1147 1019 1 25

,
// fltk N4xcas8EquationE 60 1148 1019 67 25
set[F16(t^3+t),F16(t^3+t+1),F16(t^3+t^2+1),F16(t^2+t+1),F16(t^3),F16(t^2+t),F16(t^2+1),F16(t^3+t^2),F16(t+1),F16(t^3+t^2+t+1),F16(0)],11
]
,
// fltk 7Fl_Tile 60 1217 1019 36 25
[
// fltk N4xcas19Multiline_Input_tabE 60 1217 1019 35 25

,
// fltk N4xcas10Log_OutputE 60 1252 1019 1 25

]
,
// fltk 7Fl_Tile 60 1255 1019 992 25
[
// fltk N4xcas7EditeurE 60 1255 1019 264 25
2197 ,
// F16:=GF(2,4,['f','F16'])
// xa et ya sont dans F16 par ex xa:=F16(w^3) ...
estdansgamma(xa,ya):=(xa^3+xa+ya^2+ya==0):;

// a:=[xa,ya] b:=[xb,yb] ou xa,ya,xb,yb sont dans F16
etoile(a,b):={
 local xa,xb,ya,yb,xc,yc;
 if (a==infinity and b==infinity) return infinity;
 if (a==infinity) {
  if (estdansgamma(op(b))==0) return b+" pas dans gamma";
  return b;
 }
 if (b==infinity) {
  if (estdansgamma(op(a))==0) return a+" pas dans gamma";
  return a;
 }
 xa:=a[0]; xb:=b[0]; ya:=a[1]; yb:=b[1];
 if (estdansgamma(xa,ya)==0) return a+" pas dans gamma"; 
 if (estdansgamma(xb,yb)==0) return b+" pas dans gamma";
 if (xa!=xb) {
  xc:=(xa+xb)^13*(ya^2+yb^2)+xa+xb;
  yc:=(xa+xb)^14*((ya+yb)*xc+xa*yb+xb*ya)+F16(1);
  return [xc,yc];
 }
 if ((xa==xb) and (ya==yb)) {
  xc:=xa^4+F16(1);
  yc:=xa^4+ya^4;
  return [xc,yc];
 }
 return infinity;
}:;

puissrapide(a,k,mult,unit,ordre):={
  local b;
  b:=a;
  a:=unit;
  k:=irem(k,ordre);
  while (k!=0) {
    if (irem(k,2)) a:=mult(a,b);
    b:=mult(b,b);
    k:=iquo(k,2);
  }
  return a;
}:;

// tau est un element de G par ex tau:=lettre2G(a)
falpha(k,tau):={
 local a;
 return [puissrapide(pii,k,etoile,infinity,0), 
         etoile(puissrapide(alpha,k,etoile,infinity,0),tau)];
}:;

// a et b sont des elements de G
phie(a,b,ex):={
 local inva;
 ex:=irem(ex,5);
 inva:=puissrapide(a,5-ex,etoile,infinity,0);
 return etoile(inva,b);
}:;
lettre2n(a):={
 local c;
 c:=op(asc(a));
 if (c==32) return 24;
 if (c<87) return c-65;
 if (c==87) return 21;
 if (c==88) return 22;
 if (c==89) return 7;
 if (c==90) return 23;
}:;

n2lettre(n):={
 if (n<22) return char(n+65);
 if (n==24) return " ";
 if (n==22) return "X";
 if (n==23) return "Z";
}:;

lettre2G(a,G):={
 local c;
 c:=lettre2n(a);
 return G[c];
};

codage(s,G):={
 local L,n,j,k,f;
 L:=[];
 n:=size(s);
 for (j:=0;j<n;j++){
  k:=rand(25);
  f:=falpha(k,lettre2G(s[j],G))
  L:=append(L,f);
 }
 return L;
}:;

indice(tau,G):={
 local n,k;
 n:=size(G);
 k:=0;
 while (tau!=G[k]){
  k:=k+1;
 }
 return k;
}:;

decodage(L,ex,G):={
 local n,j,M,tau,k,a,b;
 M:="";
 n:=size(L);
 for (j:=0;j<n;j++){
  a:=L[j,0];
  b:=L[j,1];
  tau:=phie(a,b,ex);
  k:=indice(tau,G);
  M:=M+n2lettre(k);
 }
 return M;
}:;,
// fltk N4xcas10Log_OutputE 60 1519 1019 575 25
// Parsing estdansgamma£// Success compiling estdansgamma£// Parsing etoile£// Warning: infinity estdansgamma F16  declared as global variable(s) compiling etoile£// Parsing puissrapide£// Success compiling puissrapide£// Parsing falpha£// Warning: puissrapide pii etoile infinity alpha  declared as global variable(s) compiling falpha£// Parsing phie£// Warning: puissrapide etoile infinity  declared as global variable(s) compiling phie£// Parsing lettre2n£// Success compiling lettre2n£// Parsing n2lettre£// Success compiling n2lettre£// Parsing lettre2G£// Warning: lettre2n  declared as global variable(s) compiling lettre2G£// Parsing codage£// Warning: falpha lettre2G  declared as global variable(s) compiling codage£// Parsing indice£// Success compiling indice£// Parsing decodage£// Warning: phie indice n2lettre  declared as global variable(s) compiling decodage£
,
// fltk N4xcas8EquationE 60 2094 1019 153 25
"Done","Done","Done","Done","Done","Done","Done",expr(" (a,G)-> £{ local c; £  c:=lettre2n(a);  £  return(G[c]);  £}",0),"Done","Done","Done"
]
,
// fltk 7Fl_Tile 60 2249 1019 150 25
[
// fltk N4xcas19Multiline_Input_tabE 60 2249 1019 82 25
u:=[F16(1),F16(0)]; v:=[F16(t^3),F16(t^9)];£G:=seq(seq(etoile(puissrapide(u,k,etoile,infinity,0), puissrapide(v,j,etoile,infinity,0)),k=1..5),j=1..5):;£G:=[G];
,
// fltk N4xcas10Log_OutputE 60 2331 1019 1 25

,
// fltk N4xcas8EquationE 60 2332 1019 67 25
[F16(1),F16(0)],[F16(t^3),F16(t^2+1)],"Done",[[F16(t+1),F16(t^3+t^2+t)],[F16(t^3+t^2+t),F16(t^2+t+1)],[F16(t^3+t+1),F16(t^3+t^2)],[F16(t^2),F16(t^2+t+1)],[F16(t^3),F16(t^2+1)],[F16(t^3+t),F16(t^2+t)],[F16(t^3+1),F16(t^3+t^2)],[F16(t^3+t^2+t+1),F16(t^3)],[F16(t^2+1),F16(t)],[F16(t),F16(t^3+t^2)],[F16(t^2+1),F16(t+1)],[F16(t^3+t^2+t+1),F16(t^3+1)],[F16(t^3+1),F16(t^3+t^2+1)],[F16(t^3+t),F16(t^2+t+1)],[F16(t),F16(t^3+t^2+1)],[F16(t^2),F16(t^2+t)],[F16(t^3+t+1),F16(t^3+t^2+1)],[F16(t^3+t^2+t),F16(t^2+t)],[F16(t+1),F16(t^3+t^2+t+1)],[F16(t^3),F16(t^2)],[F16(1),F16(0)],[F16(0),F16(1)],[F16(0),F16(0)],[F16(1),F16(1)],infinity]
]
,
// fltk 7Fl_Tile 60 2401 1019 89 25
[
// fltk N4xcas19Multiline_Input_tabE 60 2401 1019 35 25
size(set[op(G)])
,
// fltk N4xcas10Log_OutputE 60 2436 1019 1 25

,
// fltk N4xcas8EquationE 60 2437 1019 53 25
25
]
,
// fltk 7Fl_Tile 60 2492 1019 103 25
[
// fltk N4xcas19Multiline_Input_tabE 60 2492 1019 35 25
pii:=G[10]; ex:=3; alpha:=puissrapide(pii,ex,etoile,infinity,0)
,
// fltk N4xcas10Log_OutputE 60 2527 1019 1 25

,
// fltk N4xcas8EquationE 60 2528 1019 67 25
[F16(t^2+1),F16(t+1)],3,[F16(t^3+t^2+t),F16(t^2+t)]
]
,
// fltk 7Fl_Tile 60 2597 1019 167 25
[
// fltk N4xcas19Multiline_Input_tabE 60 2597 1019 35 25
message:=codage("COGITO",G)
,
// fltk N4xcas10Log_OutputE 60 2632 1019 1 25

,
// fltk N4xcas8EquationE 60 2633 1019 131 25
[[[F16(t^2+1),F16(t)],[F16(t),F16(t^3+t^2)]],[[F16(t^3+t^2+t),F16(t^2+t)],[F16(1),F16(1)]],[[F16(t^2+1),F16(t)],[F16(t^3+t),F16(t^2+t+1)]],[infinity,[F16(t^2+1),F16(t)]],[[F16(t^3+t^2+t),F16(t^2+t+1)],[F16(t^3+t),F16(t^2+t)]],[[F16(t^2+1),F16(t+1)],[F16(t^3+t^2+t+1),F16(t^3)]]]
]
,
// fltk 7Fl_Tile 60 2766 1019 89 25
[
// fltk N4xcas19Multiline_Input_tabE 60 2766 1019 35 25
decodage(message,ex,G)
,
// fltk N4xcas10Log_OutputE 60 2801 1019 1 25

,
// fltk N4xcas8EquationE 60 2802 1019 53 25
"COGITO"
]
,
// fltk 7Fl_Tile 60 2857 1019 103 25
[
// fltk N4xcas19Multiline_Input_tabE 60 2857 1019 35 25
messagel:=codage("C",G)
,
// fltk N4xcas10Log_OutputE 60 2892 1019 1 25

,
// fltk N4xcas8EquationE 60 2893 1019 67 25
[[[F16(t^2+1),F16(t+1)],[F16(1),F16(0)]]]
]
,
// fltk 7Fl_Tile 60 2962 1019 84 25
[
// fltk N4xcas19Multiline_Input_tabE 60 2962 1019 30 25
decodage(messagel,ex,G)
,
// fltk N4xcas10Log_OutputE 60 2992 1019 1 25

,
// fltk N4xcas8EquationE 60 2993 1019 53 25
"C"
]
,
// fltk 7Fl_Tile 60 3048 1019 31 25
[
// fltk N4xcas19Multiline_Input_tabE 60 3048 1019 30 25

,
// fltk N4xcas10Log_OutputE 60 3078 1019 1 25

]
]