// xcas version=0.9.0 fontsize=18 font=0 currentlevel=14
// fltk 7Fl_Tile 25 -451 976 31 18 0
[
// fltk N4xcas23Comment_Multiline_InputE 25 -451 976 30 18 0
x^n/n! tend vers 0 lorsque n->l'infini, mais il faut un peu attendre lorsque x est grand
,
// fltk N4xcas10Log_OutputE 25 -421 976 1 18 0

]
,
// fltk 7Fl_Tile 25 -418 976 356 18 0
[
// fltk N4xcas19Multiline_Input_tabE 25 -418 976 30 18 0
plot([seq(x^n/Gamma(n+1),x=1..10)],n=1..10)
,
// fltk N4xcas10Log_OutputE 25 -388 976 1 18 0

,
// fltk 7Fl_Tile 25 -387 976 325 18 0
[
// fltk N4xcas7Graph2dE 25 -387 814 325 18 0
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,
// fltk 8Fl_Group 839 -387 162 325 18 0
[
// fltk N4xcas14Mouse_PositionE 839 -387 162 36 18 0
[]
,
// fltk 8Fl_Group 839 -351 162 105 18 0
[
// fltk 9Fl_Button 839 -351 54 21 18 0
[]
,
// fltk 9Fl_Button 893 -351 54 21 18 0
[]
,
// fltk 9Fl_Button 947 -351 54 21 18 0
[]
,
// fltk 9Fl_Button 839 -330 54 21 18 0
[]
,
// fltk 9Fl_Button 893 -330 54 21 18 0
[]
,
// fltk 9Fl_Button 947 -330 54 21 18 0
[]
,
// fltk 9Fl_Button 839 -309 54 21 18 0
[]
,
// fltk 9Fl_Button 893 -309 54 21 18 0
[]
,
// fltk 9Fl_Button 947 -309 54 21 18 0
[]
,
// fltk 9Fl_Button 839 -288 54 21 18 0
[]
,
// fltk 9Fl_Button 893 -288 54 21 18 0
[]
,
// fltk 9Fl_Button 947 -288 54 21 18 0
[]
,
// fltk 9Fl_Button 893 -267 54 21 18 0
[]
,
// fltk 9Fl_Button 947 -267 54 21 18 0
[]
,
// fltk 11Fl_Menu_Bar 839 -267 54 21 18 0
[]
]
,
// fltk 8Fl_Group 839 -246 162 184 18 0
[
]
]
]
]
,
// fltk 7Fl_Tile 25 -60 976 72 18 0
[
// fltk N4xcas23Comment_Multiline_InputE 25 -60 976 71 18 0
On utilise lorsque x est grand la reduction d'argument (division par ln(2)),£il faut donc connaitre ln(2) avec une grande precision. Ci-dessous, une valeur £approchee dont on peut montrer qu'elle approche ln(2) avec une erreur < 1/100/2^100
,
// fltk N4xcas10Log_OutputE 25 11 976 1 18 0

]
,
// fltk 7Fl_Tile 25 14 976 75 18 0
[
// fltk N4xcas19Multiline_Input_tabE 25 14 976 30 18 0
a:=sum((1/2)^k/k,k=1..100)
,
// fltk N4xcas10Log_OutputE 25 44 976 1 18 0

,
// fltk N4xcas8EquationE 25 45 976 44 18 0 1
3828818331455184422344627831213909151314102123988311058781117587039581/5523817219255149938494401971202337010699973469474412780567055355084800
]
,
// fltk 7Fl_Tile 25 91 976 53 18 0
[
// fltk N4xcas19Multiline_Input_tabE 25 91 976 30 18 0
evalf(a,30)
,
// fltk N4xcas10Log_OutputE 25 121 976 1 18 0

,
// fltk N4xcas8EquationE 25 122 976 22 18 0 1
0.6931471805599453094172321214580
]
,
// fltk 7Fl_Tile 25 146 976 53 18 0
[
// fltk N4xcas19Multiline_Input_tabE 25 146 976 30 18 0
evalf(ln(2),30)
,
// fltk N4xcas10Log_OutputE 25 176 976 1 18 0

,
// fltk N4xcas8EquationE 25 177 976 22 18 0 1
0.6931471805599453094172321214580
]
,
// fltk 7Fl_Tile 25 201 976 31 18 0
[
// fltk N4xcas23Comment_Multiline_InputE 25 201 976 30 18 0
En pratique, on calcule la mantisse de a, cela se fait de maniere exacte:
,
// fltk N4xcas10Log_OutputE 25 231 976 1 18 0

]
,
// fltk 7Fl_Tile 25 234 976 53 18 0
[
// fltk N4xcas19Multiline_Input_tabE 25 234 976 30 18 0
b:=iquo(numer(a)*2^100,denom(a))
,
// fltk N4xcas10Log_OutputE 25 264 976 1 18 0

,
// fltk N4xcas8EquationE 25 265 976 22 18 0 1
878668439483319573618263538048
]
,
// fltk 7Fl_Tile 25 289 976 53 18 0
[
// fltk N4xcas19Multiline_Input_tabE 25 289 976 30 18 0
evalf(b/2^100,30)
,
// fltk N4xcas10Log_OutputE 25 319 976 1 18 0

,
// fltk N4xcas8EquationE 25 320 976 22 18 0 1
0.6931471805599453094172321214580
]
,
// fltk 7Fl_Tile 25 344 976 31 18 0
[
// fltk N4xcas23Comment_Multiline_InputE 25 344 976 30 18 0
Comparaison entre la valeur renvoyee par la machine et la serie de exp
,
// fltk N4xcas10Log_OutputE 25 374 976 1 18 0

]
,
// fltk 7Fl_Tile 25 377 976 53 18 0
[
// fltk N4xcas19Multiline_Input_tabE 25 377 976 30 18 0
c:=exp(0.5)
,
// fltk N4xcas10Log_OutputE 25 407 976 1 18 0

,
// fltk N4xcas8EquationE 25 408 976 22 18 0 1
1.6487212707
]
,
// fltk 7Fl_Tile 25 432 976 53 18 0
[
// fltk N4xcas19Multiline_Input_tabE 25 432 976 30 18 0
d:=sum(0.5^n/n!,n=0..8)
,
// fltk N4xcas10Log_OutputE 25 462 976 1 18 0

,
// fltk N4xcas8EquationE 25 463 976 22 18 0 1
1.64872126504
]
,
// fltk 7Fl_Tile 25 487 976 31 18 0
[
// fltk N4xcas23Comment_Multiline_InputE 25 487 976 30 18 0
Si on s'arrete a 8 l'erreur relative est majoree par 0.5^9/9!
,
// fltk N4xcas10Log_OutputE 25 517 976 1 18 0

]
,
// fltk 7Fl_Tile 25 520 976 53 18 0
[
// fltk N4xcas19Multiline_Input_tabE 25 520 976 30 18 0
0.5^9/9!,abs(c-d)/c
,
// fltk N4xcas10Log_OutputE 25 550 976 1 18 0

,
// fltk N4xcas8EquationE 25 551 976 22 18 0 1
5.38228891093e-09,3.43555715565e-09
]
,
// fltk 7Fl_Tile 25 575 976 31 18 0
[
// fltk N4xcas19Multiline_Input_tabE 25 575 976 30 18 0

,
// fltk N4xcas10Log_OutputE 25 605 976 1 18 0

]
// context 666 giac archive
7 0 9 8 0 0 'cas_setup' 7 0 11 0 0 0
0 0 0
0 0 0
0 1 0
0 0 0
7 0 2 1 
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1 
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0 12 0
7 0 4 0 1 0
0 50 0
0 0 0
0 25 0
0 0 0
0 0 0
0 0 0
8 0 0 'xyztrange' 7 0 16 1 
$À
1 
$@
1 
$À
1 
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1 
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1 
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1 
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1 
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1 
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1 
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1 
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0 1 0
1 

1 
ð?
0 1 0
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2 5523817219255149938494401971202337010699973469474412780567055355084800
6 1 a 8 0 15 7 0 2 2 878668439483319573618263538048
6 1 b 8 0 15 7 0 2 1 
Ž)aú?
6 1 c 8 0 15 7 0 2 1 
ǘŒ)aú?
6 1 d 8 0 0 'xcas_mode' 0 0 0