// xcas version=1.2.2-53 fontsize=18 font=0 currentlevel=9
// fltk 7Fl_Tile 23 -792 993 425 18 0
[
// fltk N4xcas7EditeurE 23 -792 993 311 18 0
970 ,
croissant(t):={
local j,n;
n:=size(t);
pour j de 1 jusque n-1 faire
si t[j-1]>t[j] alors return false; fsi;
fpour;
return true;
}:;
f(n,s):={
local cur,j,k,v,phis,t,S,m,M;
v:=[];
// liste des generateurs de Z/sZ
pour k de 1 jusque s-1 faire
si gcd(k,s)=1 alors v:=append(v,k); fsi;
fpour;
phis:=size(v);
S:=phis^n;
M:=0;
pour j de 0 jusque S-1 faire
// choix des realproot primitives s-ieme valeurs propres
// par ordre croissant
t:=convert(j,base,phis); // genere tous les n-uplets de t possible
si non croissant(t) alors continue; fsi;// reflection du probleme
t:=[0$(n-size(t)),op(t)]; // on rajoute en tete des 0 si necessaire
m:=1;
pour k de 1 jusque s/2 faire
cur:=abs(product(sin(pi*evalf(k)*v[t[J]]/s),J,0,n-1));
m:=min(m,cur);
fpour;
si m>M alors M:=m; choix:=seq(v[t[J]],J,0,n-1); fsi;
si irem(j,64)==0 alors print(j,M); fsi;
fpour;
retourne 2*M^(1/n),choix;
}:;
,
// fltk N4xcas10Log_OutputE 23 -481 993 90 18 0
// InterprÃ¨te croissant£// SuccÃ¨s lors de la compilation croissant£// InterprÃ¨te f£// Attention: J,choix, dÃ©clarÃ©e(s) comme variable(s) globale(s) lors de la compilation f£
,
// fltk N4xcas8EquationE 23 -391 993 24 18 0 1
"Done","Done"
]
,
// fltk 7Fl_Tile 23 -365 993 304 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 -365 993 36 18 0
7 ,
f(3,64),
// fltk N4xcas10Log_OutputE 23 -329 993 244 18 0
0,0.000118137131723£64,0.00238157763246£128,0.00401655995718£192,0.00984714874234£256,0.0140887253573£320,0.0211451329301£384,0.0211451329301£448,0.0211451329301£512,0.0211451329301£576,0.0211451329301£640,0.0211451329301£704,0.0211451329301£768,0.0211451329301£832,0.0211451329301£896,0.0211451329302£960,0.0211451329302£1024,0.0211451329302£2048,0.0211451329302£2112,0.0211451329302£3072,0.0211451329302£3136,0.0211451329302£4096,0.0211451329302£4160,0.0211451329302£4224,0.0211451329302£5120,0.0211451329302£5184,0.0211451329302£5248,0.0211451329302£6144,0.0211451329302£6208,0.0211451329302£6272,0.0211451329302£6336,0.0211451329302£7168,0.0211451329302£7232,0.0211451329302£7296,0.0211451329302£7360,0.0211451329302£8192,0.0211451329302£8256,0.0211451329302£8320,0.0211451329302£8384,0.0211451329302£8448,0.0211451329302£9216,0.0211451329302£9280,0.0211451329302£9344,0.0211451329302£9408,0.0211451329302£9472,0.0211451329302£10240,0.0211451329302£10304,0.0211451329302£10368,0.0211451329302£10432,0.0211451329302£10496,0.0211451329302£10560,0.0211451329302£11264,0.0211451329302£11328,0.0211451329302£11392,0.0211451329302£11456,0.0211451329302£11520,0.0211451329302£11584,0.0211451329302£12288,0.0211451329302£12352,0.0211451329302£12416,0.0211451329302£12480,0.0211451329302£12544,0.0211451329302£12608,0.0211451329302£12672,0.0211451329302£13312,0.0211451329302£13376,0.0211451329302£13440,0.0211451329302£13504,0.0211451329302£13568,0.0211451329302£13632,0.0211451329302£13696,0.0211451329302£14336,0.0211451329302£14400,0.0211451329302£14464,0.0211451329302£14528,0.0211451329302£14592,0.0211451329302£14656,0.0211451329302£14720,0.0211451329302£14784,0.0211451329302£15360,0.0211451329302£15424,0.0211451329302£15488,0.0211451329302£15552,0.0211451329302£15616,0.0211451329302£15680,0.0211451329302£15744,0.0211451329302£15808,0.0211451329302£16384,0.0211451329302£16448,0.0211451329302£16512,0.0211451329302£16576,0.0211451329302£16640,0.0211451329302£16704,0.0211451329302£16768,0.0211451329302£16832,0.0211451329302£16896,0.0211451329302£17408,0.0211451329302£17472,0.0211451329302£17536,0.0211451329302£17600,0.0211451329302£17664,0.0211451329302£17728,0.0211451329302£17792,0.0211451329302£17856,0.0211451329302£17920,0.0211451329302£18432,0.0211451329302£18496,0.0211451329302£18560,0.0211451329302£18624,0.0211451329302£18688,0.0211451329302£18752,0.0211451329302£18816,0.0211451329302£18880,0.0211451329302£18944,0.0211451329302£19008,0.0211451329302£19456,0.0211451329302£19520,0.0211451329302£19584,0.0211451329302£19648,0.0211451329302£19712,0.0211451329302£19776,0.0211451329302£19840,0.0211451329302£19904,0.0211451329302£19968,0.0211451329302£20032,0.0211451329302£20480,0.0211451329302£20544,0.0211451329302£20608,0.0211451329302£20672,0.0211451329302£20736,0.0211451329302£20800,0.0211451329302£20864,0.0211451329302£20928,0.0211451329302£20992,0.0211451329302£21056,0.0211451329302£21120,0.0211451329302£21504,0.0211451329302£21568,0.0211451329302£21632,0.0211451329302£21696,0.0211451329302£21760,0.0211451329302£21824,0.0211451329302£21888,0.0211451329302£21952,0.0211451329302£22016,0.0211451329302£22080,0.0211451329302£22144,0.0211451329302£22528,0.0211451329302£22592,0.0211451329302£22656,0.0211451329302£22720,0.0211451329302£22784,0.0211451329302£22848,0.0211451329302£22912,0.0211451329302£22976,0.0211451329302£23040,0.0211451329302£23104,0.0211451329302£23168,0.0211451329302£23232,0.0211451329302£23552,0.0211451329302£23616,0.0211451329302£23680,0.0211451329302£23744,0.0211451329302£23808,0.0211451329302£23872,0.0211451329302£23936,0.0211451329302£24000,0.0211451329302£24064,0.0211451329302£24128,0.0211451329302£24192,0.0211451329302£24256,0.0211451329302£24576,0.0211451329302£24640,0.0211451329302£24704,0.0211451329302£24768,0.0211451329302£24832,0.0211451329302£24896,0.0211451329302£24960,0.0211451329302£25024,0.0211451329302£25088,0.0211451329302£25152,0.0211451329302£25216,0.0211451329302£25280,0.0211451329302£25344,0.0211451329302£25600,0.0211451329302£25664,0.0211451329302£25728,0.0211451329302£25792,0.0211451329302£25856,0.0211451329302£25920,0.0211451329302£25984,0.0211451329302£26048,0.0211451329302£26112,0.0211451329302£26176,0.0211451329302£26240,0.0211451329302£26304,0.0211451329302£26368,0.0211451329302£26624,0.0211451329302£26688,0.0211451329302£26752,0.0211451329302£26816,0.0211451329302£26880,0.0211451329302£26944,0.0211451329302£27008,0.0211451329302£27072,0.0211451329302£27136,0.0211451329302£27200,0.0211451329302£27264,0.0211451329302£27328,0.0211451329302£27392,0.0211451329302£27456,0.0211451329302£27648,0.0211451329302£27712,0.0211451329302£27776,0.0211451329302£27840,0.0211451329302£27904,0.0211451329302£27968,0.0211451329302£28032,0.0211451329302£28096,0.0211451329302£28160,0.0211451329302£28224,0.0211451329302£28288,0.0211451329302£28352,0.0211451329302£28416,0.0211451329302£28480,0.0211451329302£28672,0.0211451329302£28736,0.0211451329302£28800,0.0211451329302£28864,0.0211451329302£28928,0.0211451329302£28992,0.0211451329302£29056,0.0211451329302£29120,0.0211451329302£29184,0.0211451329302£29248,0.0211451329302£29312,0.0211451329302£29376,0.0211451329302£29440,0.0211451329302£29504,0.0211451329302£29568,0.0211451329302£29696,0.0211451329302£29760,0.0211451329302£29824,0.0211451329302£29888,0.0211451329302£29952,0.0211451329302£30016,0.0211451329302£30080,0.0211451329302£30144,0.0211451329302£30208,0.0211451329302£30272,0.0211451329302£30336,0.0211451329302£30400,0.0211451329302£30464,0.0211451329302£30528,0.0211451329302£30592,0.0211451329302£30720,0.0211451329302£30784,0.0211451329302£30848,0.0211451329302£30912,0.0211451329302£30976,0.0211451329302£31040,0.0211451329302£31104,0.0211451329302£31168,0.0211451329302£31232,0.0211451329302£31296,0.0211451329302£31360,0.0211451329302£31424,0.0211451329302£31488,0.0211451329302£31552,0.0211451329302£31616,0.0211451329302£31680,0.0211451329302£31744,0.0211451329302£31808,0.0211451329302£31872,0.0211451329302£31936,0.0211451329302£32000,0.0211451329302£32064,0.0211451329302£32128,0.0211451329302£32192,0.0211451329302£32256,0.0211451329302£32320,0.0211451329302£32384,0.0211451329302£32448,0.0211451329302£32512,0.0211451329302£32576,0.0211451329302£32640,0.0211451329302£32704,0.0211451329302££Temps mis pour l'Ã©valuation: 5.37£
,
// fltk N4xcas8EquationE 23 -85 993 24 18 0 1
0.553053063372,[11,41,57]
]
,
// fltk 7Fl_Tile 23 -59 993 137 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 -59 993 36 18 0
48 ,
restart;S:=[[s0,s1],[s2,s3]]; factor(S^2+idn(S)),
// fltk N4xcas10Log_OutputE 23 -23 993 1 18 0
,
// fltk N4xcas8EquationE 23 -22 993 100 18 0 1
[Es,Fs,G,Gs,M,S,T,alpha,choix,croissant,eta,f,g,n,s,s3,simplif,sl2,t],[[s0,s1],[s2,s3]],[[s1*s2+s0^2+1,s1*(s0+s3)],[s2*(s0+s3),s1*s2+s3^2+1]]
]
,
// fltk 7Fl_Tile 23 80 993 119 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 80 993 36 18 0
11 ,
s3:=-s0;S^2,
// fltk N4xcas10Log_OutputE 23 116 993 1 18 0
,
// fltk N4xcas8EquationE 23 117 993 82 18 0 1
-s0,[[s0^2+s1*s2,0],[0,s0^2+s1*s2]]
]
,
// fltk 7Fl_Tile 23 201 993 119 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 201 993 36 18 0
40 ,
T:=[[t0,t1],[t2,t3]]; factor(T^3+idn(2)),
// fltk N4xcas10Log_OutputE 23 237 993 1 18 0
,
// fltk N4xcas8EquationE 23 238 993 82 18 0 1
[[t0,t1],[t2,t3]],[[2*t1*t0*t2+t1*t2*t3+t0^3+1,t1*(t2*t1+t3^2+t3*t0+t0^2)],[t2*(t1*t2+t0^2+t0*t3+t3^2),t2*t0*t1+2*t2*t1*t3+t3^3+1]]
]
,
// fltk 7Fl_Tile 23 322 993 29 18 0
[
// fltk N4xcas23Comment_Multiline_InputE 23 322 993 28 18 0
t1*t2=t0*t3-1, prendre le terme ligne 1 colonne 2
,
// fltk N4xcas10Log_OutputE 23 350 993 1 18 0
]
,
// fltk 7Fl_Tile 23 353 993 61 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 353 993 36 18 0
31 ,
factor(t0*t3-1+t3^2+t3*t0+t0^2),
// fltk N4xcas10Log_OutputE 23 389 993 1 18 0
,
// fltk N4xcas8EquationE 23 390 993 24 18 0 1
(t0+t3-1)*(t0+t3+1)
]
,
// fltk 7Fl_Tile 23 416 993 72 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 416 993 36 18 0
18 ,
t0:=1-t3; det(T)-1,
// fltk N4xcas10Log_OutputE 23 452 993 1 18 0
,
// fltk N4xcas8EquationE 23 453 993 35 18 0 1
-t3+1,-t3^2-t1*t2+t3-1
]
,
// fltk 7Fl_Tile 23 490 993 97 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 490 993 36 18 0
3 ,
S*T,
// fltk N4xcas10Log_OutputE 23 526 993 1 18 0
,
// fltk N4xcas8EquationE 23 527 993 60 18 0 1
[[s0*(-t3+1)+s1*t2,s0*t1+s1*t3],[-s0*t2+s2*(-t3+1),-s0*t3+s2*t1]]
]
,
// fltk 7Fl_Tile 23 589 993 31 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 589 993 30 18 0
0 ,
,
// fltk N4xcas10Log_OutputE 23 619 993 1 18 0
]
,
// fltk 7Fl_Tile 23 622 993 381 18 0
[
// fltk N4xcas7EditeurE 23 622 993 311 18 0
483 ,
sl2(S,T):={
local E,F,Es,Fs,j,f;
// on code les elements par des chaines
Es:=[""]; E:=[S*S*S*S];
tantque true faire
F:=E; Fs:=Es;
pour j de 0 jusque size(E)-1 faire
f:=E[j]*S;
si !contains(F,f) alors
F:=append(F,f); Fs:=append(Fs,Es[j]+"s");
fsi;
f:=E[j]*T;
si !contains(F,f) alors
F:=append(F,f); Fs:=append(Fs,Es[j]+"t");
fsi;
fpour;
si E==F alors return E,Es; fsi;
E:=F; Es:=Fs;
ftantque;
}:;
,
// fltk N4xcas10Log_OutputE 23 933 993 46 18 0
// InterprÃ¨te sl2£// SuccÃ¨s lors de la compilation sl2£
,
// fltk N4xcas8EquationE 23 979 993 24 18 0 1
"Done"
]
,
// fltk 7Fl_Tile 23 1005 993 97 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 1005 993 36 18 0
44 ,
S:=[[0,-1],[1,0]] % 5; T:=[[0,-1],[1,1]] % 5,
// fltk N4xcas10Log_OutputE 23 1041 993 1 18 0
,
// fltk N4xcas8EquationE 23 1042 993 60 18 0 1
[[0 % 5,(-1) % 5],[1 % 5,0 % 5]],[[0 % 5,(-1) % 5],[1 % 5,1 % 5]]
]
,
// fltk 7Fl_Tile 23 1104 993 115 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 1104 993 36 18 0
14 ,
G,Gs:=sl2(S,T),
// fltk N4xcas10Log_OutputE 23 1140 993 1 18 0
,
// fltk N4xcas8EquationE 23 1141 993 78 18 0 1
Done
]
,
// fltk 7Fl_Tile 23 1221 993 61 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 1221 993 36 18 0
8 ,
size(Gs),
// fltk N4xcas10Log_OutputE 23 1257 993 1 18 0
,
// fltk N4xcas8EquationE 23 1258 993 24 18 0 1
120
]
,
// fltk 7Fl_Tile 23 1284 993 87 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 1284 993 36 18 0
19 ,
eta:=exp(2*i*pi/10),
// fltk N4xcas10Log_OutputE 23 1320 993 1 18 0
,
// fltk N4xcas8EquationE 23 1321 993 50 18 0 1
(sqrt(5)+1)/4+sqrt(2)*1/4*i*sqrt(-(sqrt(5))+5)
]
,
// fltk 7Fl_Tile 23 1373 993 118 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 1373 993 36 18 0
38 ,
alpha:=normal(sqrt(1/abs(1-eta^2)^2-1),
// fltk N4xcas10Log_OutputE 23 1409 993 24 18 0
Warning adding 1 ) at end of input£
,
// fltk N4xcas8EquationE 23 1433 993 58 18 0 1
i*(sqrt(-(sqrt(5))+5))/(sqrt(10))
]
,
// fltk 7Fl_Tile 23 1493 993 165 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 1493 993 36 18 0
74 ,
S:=normal(1/(1-eta^2)*[[eta,-eta*alpha],[(eta^4-eta^2+1)/alpha/eta,-eta]]),
// fltk N4xcas10Log_OutputE 23 1529 993 1 18 0
,
// fltk N4xcas8EquationE 23 1530 993 128 18 0 1
[[i*(sqrt(sqrt(5)+5))/(sqrt(10)),1/(sqrt(5))],[(-(sqrt(5))+1)/2,(-(i))*(sqrt(sqrt(5)+5))/(sqrt(10))]]
]
,
// fltk 7Fl_Tile 23 1660 993 97 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 1660 993 36 18 0
11 ,
normal(S*S),
// fltk N4xcas10Log_OutputE 23 1696 993 1 18 0
,
// fltk N4xcas8EquationE 23 1697 993 60 18 0 1
[[-1,0],[0,-1]]
]
,
// fltk 7Fl_Tile 23 1759 993 175 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 1759 993 36 18 0
68 ,
T:=normal((1/(1-eta^2)*[[-eta^2,alpha],[-(eta^4-eta^2+1)/alpha,1]])),
// fltk N4xcas10Log_OutputE 23 1795 993 1 18 0
,
// fltk N4xcas8EquationE 23 1796 993 138 18 0 1
[[(sqrt(5)*(-(i))*sqrt(2*sqrt(5)+5)+5)/10,expr("rootof([[-5416-6408*i,-4558-22921*i,745640+875000*i,190630+2765325*i,-23158320-27844600*i,-6713480-90096070*i,148575200+206154200*i,-251884600+303587100*i],[1,0,-140,80,4540,-2400,-38000,33600,16400]])",0)/840511600],[(i*sqrt(-2*sqrt(5)+5)+1)/2,(sqrt(5)*i*sqrt(2*sqrt(5)+5)+5)/10]]
]
,
// fltk 7Fl_Tile 23 1936 993 97 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 1936 993 36 18 0
11 ,
normal(T^3),
// fltk N4xcas10Log_OutputE 23 1972 993 1 18 0
,
// fltk N4xcas8EquationE 23 1973 993 60 18 0 1
[[-1,0],[0,-1]]
]
,
// fltk 7Fl_Tile 23 2035 993 142 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 2035 993 36 18 0
15 ,
normal((S*T)^5),
// fltk N4xcas10Log_OutputE 23 2071 993 46 18 0
£Temps mis pour l'Ã©valuation: 1.24£
,
// fltk N4xcas8EquationE 23 2117 993 60 18 0 1
[[-1,0],[0,-1]]
]
,
// fltk 7Fl_Tile 23 2179 993 37 18 0
[
// fltk N4xcas16Xcas_Text_EditorE 23 2179 993 36 18 0
0 ,
,
// fltk N4xcas10Log_OutputE 23 2215 993 1 18 0
]
,
// fltk 7Fl_Tile 23 2218 993 381 18 0
[
// fltk N4xcas7EditeurE 23 2218 993 311 18 0
346 ,
g(S,T,Gs):={
local M,s,ss,P,j,m;
S:=evalf(S);
T:=evalf(T);
M:=2;
pour s in Gs faire
ss:=size(s);
si ss==0 alors continue; fsi;
P:=idn(S);
pour j de 0 jusque ss-1 faire
si s[j]=="s" alors P:=P*S; sinon P:=P*T; fsi;
fpour;
m:=abs(det(P-idn(S)));
si m