IdentifiantMot de passe
Loading...
Mot de passe oublié ?Je m'inscris ! (gratuit)
Navigation

Inscrivez-vous gratuitement
pour pouvoir participer, suivre les réponses en temps réel, voter pour les messages, poser vos propres questions et recevoir la newsletter

Mathématiques - Sciences Discussion :

Carte mentale et matrice


Sujet :

Mathématiques - Sciences

  1. #1
    Candidat au Club
    Homme Profil pro
    Collégien
    Inscrit en
    Juillet 2019
    Messages
    8
    Détails du profil
    Informations personnelles :
    Sexe : Homme
    Localisation : France, Paris (Île de France)

    Informations professionnelles :
    Activité : Collégien

    Informations forums :
    Inscription : Juillet 2019
    Messages : 8
    Points : 3
    Points
    3
    Par défaut Carte mentale et matrice
    Bonjour,

    je suis en train de faire une fiche de synthèse avec texmaker dont voici le code :
    Code : Sélectionner tout - Visualiser dans une fenêtre à part
    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    \documentclass[a4paper,12pt,french]{article}
    \usepackage{lscape}
    \usepackage{tikz}
    \usetikzlibrary{mindmap}
    \pagestyle{empty}
    \begin{document}
    \tikzstyle{style1}=[draw,rounded corners=3pt,thick,fill=gray!35,text width=8cm, text centered]
    \tikzstyle{style2}=[rounded corners=3pt,thick,fill=gray!15,text width=7cm, text centered]
    \tikzstyle{style3}=[rounded corners=3pt,thick,fill=gray!2,text width=4cm, text centered]
     
    %\begin{landscape}
     
    \begin{tikzpicture}
    [scale=1]
    \node[style1](G) at (0,0){Groupe des permutations d'un ensemble fini. Applications.}; 
    \node[style2](S) at (1,3){I - Permutations d'un ensemble fini};
    \node[style2](D) at (-3,-4){II-D\'ecomposition};
    \node[style2](A) at (4,-2){Applications};
     
    \draw[->,>=latex,] (G) edge [bend left] (S);
    \draw[->,>=latex,] (G) edge [bend left] (D);
    \draw[->,>=latex,] (G) edge [bend right] (A);
    \end{tikzpicture}
     
    %\end{landscape}
     
    \end{document}
    J'aimerais pouvoir écrire une matrice à l'intérieur du I - Permutations d'un ensemble fini ligne 16 mais je n'y arrive pas :
    Code : Sélectionner tout - Visualiser dans une fenêtre à part
    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    \documentclass[a4paper,12pt,french]{article}
    \usepackage{lscape}
    \usepackage{tikz}
    \usetikzlibrary{mindmap}
    \pagestyle{empty}
    \begin{document}
    \tikzstyle{style1}=[draw,rounded corners=3pt,thick,fill=gray!35,text width=8cm, text centered]
    \tikzstyle{style2}=[rounded corners=3pt,thick,fill=gray!15,text width=7cm, text centered]
    \tikzstyle{style3}=[rounded corners=3pt,thick,fill=gray!2,text width=4cm, text centered]
     
    %\begin{landscape}
     
    \begin{tikzpicture}
    [scale=1]
    \node[style1](G) at (0,0){Groupe des permutations d'un ensemble fini. Applications.}; 
    \node[style2](S) at (1,3){I - Permutations d'un ensemble fini $\displaystyle\newline\begin{pmatrix}0 &-i \\ i & 0\end{pmatrix}$};
    \node[style2](D) at (-3,-4){II-D\'ecomposition};
    \node[style2](A) at (4,-2){Applications};
     
    \draw[->,>=latex,] (G) edge [bend left] (S);
    \draw[->,>=latex,] (G) edge [bend left] (D);
    \draw[->,>=latex,] (G) edge [bend right] (A);
    \end{tikzpicture}
     
    %\end{landscape}
     
    \end{document}
    Voici le log :
    Misplaced alignment tab character &.
    l.16 ...i $\displaystyle\newline\begin{pmatrix}0 &
    -i \\ i & 0\end{pmatrix}$};
    I can't figure out why you would want to use a tab mark
    here. If you just want an ampersand, the remedy is
    simple: Just type `I\&' now. But if some right brace
    up above has ended a previous alignment prematurely,
    you're probably due for more error messages, and you
    might try typing `S' now just to see what is salvageable.
    ! LaTeX Error: There's no line here to end.
    See the LaTeX manual or LaTeX Companion for explanation.
    Type H <return> for immediate help.
    ...
    l.16 ...isplaystyle\newline\begin{pmatrix}0 &-i \\
    i & 0\end{pmatrix}$};
    Your command was ignored.
    Type I <command> <return> to replace it with another command,
    or <return> to continue without it.
    ! Missing $ inserted.
    <inserted text>
    $
    l.16 ...isplaystyle\newline\begin{pmatrix}0 &-i \\
    i & 0\end{pmatrix}$};
    I've inserted a begin-math/end-math symbol since I think
    you left one out. Proceed, with fingers crossed.
    ! Missing \endgroup inserted.
    <inserted text>
    \endgroup
    l.16 ...isplaystyle\newline\begin{pmatrix}0 &-i \\
    i & 0\end{pmatrix}$};
    I've inserted something that you may have forgotten.
    (See the <inserted text> above.)
    With luck, this will get me unwedged. But if you
    really didn't forget anything, try typing `2' now; then
    my insertion and my current dilemma will both disappear.
    ! Misplaced alignment tab character &.
    l.16 ...aystyle\newline\begin{pmatrix}0 &-i \\ i &
    0\end{pmatrix}$};
    I can't figure out why you would want to use a tab mark
    here. If you just want an ampersand, the remedy is
    simple: Just type `I\&' now. But if some right brace
    up above has ended a previous alignment prematurely,
    you're probably due for more error messages, and you
    might try typing `S' now just to see what is salvageable.
    ! LaTeX Error: \begin{tikzpicture} on input line 13 ended by \end{pmatrix}.
    See the LaTeX manual or LaTeX Companion for explanation.
    Type H <return> for immediate help.
    ...
    l.16 ...\begin{pmatrix}0 &-i \\ i & 0\end{pmatrix}
    $};
    Your command was ignored.
    Type I <command> <return> to replace it with another command,
    or <return> to continue without it.
    ! Missing } inserted.
    <inserted text>
    }
    l.16 ...\begin{pmatrix}0 &-i \\ i & 0\end{pmatrix}
    $};
    I've inserted something that you may have forgotten.
    (See the <inserted text> above.)
    With luck, this will get me unwedged. But if you
    really didn't forget anything, try typing `2' now; then
    my insertion and my current dilemma will both disappear.
    ! Package tikz Error: Giving up on this path. Did you forget a semicolon?.
    See the tikz package documentation for explanation.
    Type H <return> for immediate help.
    ...
    l.16 ...\begin{pmatrix}0 &-i \\ i & 0\end{pmatrix}
    $};
    This error message was generated by an \errmessage
    command, so I can't give any explicit help.
    Pretend that you're Hercule Poirot: Examine all clues,
    and deduce the truth by order and method.
    ! Extra }, or forgotten $.
    <recently read> }
    l.16 ...egin{pmatrix}0 &-i \\ i & 0\end{pmatrix}$}
    ;
    I've deleted a group-closing symbol because it seems to be
    spurious, as in `$x}$'. But perhaps the } is legitimate and
    you forgot something else, as in `\hbox{$x}'. In such cases
    the way to recover is to insert both the forgotten and the
    deleted material, e.g., by typing `I$}'.
    ! Missing $ inserted.
    <inserted text>
    $
    l.19
    I've inserted a begin-math/end-math symbol since I think
    you left one out. Proceed, with fingers crossed.
    Overfull \hbox (33.7957pt too wide) in paragraph at lines 23--24
    [][]
    []
    [1
    {/Users/laafar/Library/Application Support/MiKTeX/texmfs/data/pdftex/config/pdf
    tex.map}] ("105 - Groupe des permutations.aux") )
    Here is how much of TeX's memory you used:
    12278 strings out of 494857
    264742 string characters out of 3176484
    289727 words of memory out of 3000000
    15719 multiletter control sequences out of 15000+200000
    6376 words of font info for 23 fonts, out of 3000000 for 9000
    0 hyphenation exceptions out of 8191
    55i,15n,65p,439b,772s stack positions out of 5000i,500n,10000p,200000b,50000s
    </Users/laafar/Library/Applica
    tion Support/MiKTeX/texmfs/install/fonts/type1/public/amsfonts/cm/cmmi12.pfb></
    Users/laafar/Library/Application Support/MiKTeX/texmfs/install/fonts/type1/publ
    ic/amsfonts/cm/cmr12.pfb></Users/laafar/Library/Application Support/MiKTeX/texm
    fs/install/fonts/type1/public/amsfonts/cm/cmsy10.pfb>
    Output written on "105 - Groupe des permutations.pdf" (1 page, 31233 bytes).
    PDF statistics:
    21 PDF objects out of 1000 (max. 8388607)
    0 named destinations out of 1000 (max. 500000)
    13 words of extra memory for PDF output out of 10000 (max. 10000000)
    Pouvez-vous m'aidez ?
    Merci d'avance !

  2. #2
    Expert éminent sénior

    Avatar de -Nikopol-
    Homme Profil pro
    Développeur Web
    Inscrit en
    Mai 2013
    Messages
    2 174
    Détails du profil
    Informations personnelles :
    Sexe : Homme
    Âge : 48
    Localisation : France, Haute Marne (Champagne Ardenne)

    Informations professionnelles :
    Activité : Développeur Web
    Secteur : Enseignement

    Informations forums :
    Inscription : Mai 2013
    Messages : 2 174
    Points : 11 290
    Points
    11 290
    Billets dans le blog
    5
    Par défaut
    Bonjour, pour utiliser pmatrix il faut l'extension amsmath.

  3. #3
    Candidat au Club
    Homme Profil pro
    Collégien
    Inscrit en
    Juillet 2019
    Messages
    8
    Détails du profil
    Informations personnelles :
    Sexe : Homme
    Localisation : France, Paris (Île de France)

    Informations professionnelles :
    Activité : Collégien

    Informations forums :
    Inscription : Juillet 2019
    Messages : 8
    Points : 3
    Points
    3
    Par défaut
    Merci beaucoup.
    J'ai bien avancé et j'obtiens ceci :
    Nom : 1565523725-capture-d-ecran-2019-08-11-a-13-41-54.png
Affichages : 585
Taille : 101,7 Ko

    Je voudrais ceci :
    Nom : 1565523701-capture-d-ecran-2019-08-11-a-13-38-47.png
Affichages : 554
Taille : 132,0 Ko

    Voici le code :
    Code : Sélectionner tout - Visualiser dans une fenêtre à part
    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    51
    52
    53
    54
    55
    56
    57
    58
    59
    60
    61
    62
    63
    64
    65
    66
    67
    68
    69
    70
    71
    72
    73
    74
    75
    76
    77
    78
     
    \documentclass[landscape,20pt,french]{article}
    \usepackage{graphicx}
    \usepackage{pbox}
    \usepackage{lscape}
    \usepackage{geometry}
    \geometry{hmargin=1cm,vmargin=1cm}
    \usepackage{tikz}
    \usepackage{amsmath}
    \usepackage{amsfonts}
    \usetikzlibrary{mindmap}
    \pagestyle{empty}
    \begin{document}
    \tikzstyle{style1}=[draw,rounded corners=3pt,thick,fill=gray!35,text width=8cm, text centered]
    \tikzstyle{style2}=[rounded corners=3pt,thick,fill=gray!15,text width=7cm, text centered]
    \tikzstyle{style31}=[rounded corners=3pt,thick,fill=gray!2,text width=1cm, text centered]
    \tikzstyle{style32}=[rounded corners=3pt,thick,fill=gray!2,text width=2cm, text centered]
    \tikzstyle{style325}=[rounded corners=3pt,thick,fill=gray!2,text width=2.5cm, text centered]
    \tikzstyle{style33}=[rounded corners=3pt,thick,fill=gray!2,text width=3cm, text centered]
    \tikzstyle{style335}=[rounded corners=3pt,thick,fill=gray!2,text width=3.5cm, text centered]
    \tikzstyle{style34}=[rounded corners=3pt,thick,fill=gray!2,text width=4cm, text centered]
    \tikzstyle{style345}=[rounded corners=3pt,thick,fill=gray!2,text width=4.5cm, text centered]
    \tikzstyle{style35}=[rounded corners=3pt,thick,fill=gray!2,text width=5cm, text centered]
    \tikzstyle{style355}=[rounded corners=3pt,thick,fill=gray!2,text width=5.5cm, text centered]
    \tikzstyle{style36}=[rounded corners=3pt,thick,fill=gray!2,text width=6cm, text centered]
     
    \begin{tikzpicture}
    [scale=1]
    \node[style1](A) at (-3,-0.5){Groupe des permutations d'un ensemble fini. Applications.};
    %Partie 1
     
    \node[style2](B) at (-9,0.8){I - Permutations d'un ensemble fini};
    %1.1-Generalites
     
    \node[style31](I) at (-17,1.2){$\displaystyle S(E)$};
    \node[style32](I) at (-15.2,1.2){$\displaystyle (S(E),\circ)$};
    \node[style31](I) at (-17.1,3.2){\begin{huge}$S_n$\end{huge}};
    \node[style31](I) at (-15.7,4){$\displaystyle (S_n,\circ)$};
    \node[style325](I) at (-15,3.3){$\displaystyle card(S_n)=n!$};
    \node[style35](I) at (-13.7,2.4){$
    Z(S_n) = \left\{
        \begin{array}{ll}
            S_n,&si\,\,n=2 \\
            \{Id\},&si\,\,n\ge3
        \end{array}
    \right
    $};
    %1.2-Support
     
    \node[style32](I) at (-11.5,3.9){$\displaystyle supp(\sigma)$};
    \node[style34](I) at (-11.5,8){$\displaystyle (1)\,supp(\sigma)=\emptyset \Leftrightarrow \sigma=Id$};
    \node[style34](I) at (-11.5,7.3){$\displaystyle (2)\,supp(\sigma)=supp(\sigma^{-1})$};
    \node[style34](I) at (-11.5,6.5){$\displaystyle (3)\,\sigma(supp(\sigma))=supp(\sigma)$};
    \node[style34](I) at (-11.5,5.7){$\displaystyle (4)\,supp(\sigma^r)\subset supp(\sigma)$};
    \node[style36](I) at (-11.5,5){$\displaystyle (5)\,supp(\sigma)\cap supp(\rho)=\emptyset \\ \Rightarrow \sigma\circ\rho = \rho\circ\sigma$};
    %1.3-Relation d'équivalence
    \node[style34](I) at (-3,3.2){$x R y \Leftrightarrow \exists k\in\mathbb{Z}\,,y=\sigma^k(x)$};
    \node[style34](I) at (-3,4.5){$O_\sigma(x)=\{\sigma^k(x)\,,k\in\mathbb{Z}\}$};
    \node[style35](I) at (-3,5.8){$card(O)=r \Rightarrow \exists x\in E\,, \\ O=\{x,\sigma(x),...,\sigma^{r-1}(x)\}$};
    %Partie 2
    \node[style2](C) at (1,2){II-D\'ecomposition d'une permutation};
    %2.1-Généralités
    \node[style33](I) at (4,3.2){$\sigma\in S_n\,:\,r-cycle$};
    \node[style32](I) at (5,6.2){\underline{caract\'erisation}};
    \node[style32](I) at (1,5.2){$1-cycle=\emptyset$};
    \node[style32](I) at (1,4.2){$2-cycle=transposition$};
    \node[style36](I) at (5,5.2){$\sigma\in S_n\,:\,r-cycle\\ \Leftrightarrow \exists x\in E_n\,,supp(\sigma)=O_\sigma(x) \\ \Leftrightarrow \sigma\,a\,une\,seule\,orbite\,et\,une\,seule $};
     
    \node[style32](I) at (7,3.2){$\sigma=\prod c_i$};
    \node[style2](E) at (1,-3){III - Signature d'une permutation};
    \node[style2](F) at (-7,-3){IV - Le groupe altern\'e};
     
    %\draw[->,>=latex,] (A) edge [right] (B);
    %\draw[->,>=latex,] (A) edge [left] (C);
    %\draw[->,>=latex,] (A) edge [right] (D);
    \end{tikzpicture}
     
    \end{document}
    Qu'en pensez-vous ?
    Comment faire un encadrement en pointillée comme sur l'image ?

    Encore merci de l'aide.

  4. #4
    Candidat au Club
    Homme Profil pro
    Collégien
    Inscrit en
    Juillet 2019
    Messages
    8
    Détails du profil
    Informations personnelles :
    Sexe : Homme
    Localisation : France, Paris (Île de France)

    Informations professionnelles :
    Activité : Collégien

    Informations forums :
    Inscription : Juillet 2019
    Messages : 8
    Points : 3
    Points
    3
    Par défaut
    Voici le log :
    Code : Sélectionner tout - Visualiser dans une fenêtre à part
    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16
    17
    18
    19
    20
    21
    22
    23
    24
    25
    26
    27
    28
    29
    30
    31
    32
    33
    34
    35
    36
    37
    38
    39
    40
    41
    42
    43
    44
    45
    46
    47
    48
    49
    50
    51
    52
    53
    54
    55
    56
    57
    58
    59
    60
    61
    62
    63
    64
    65
    66
    67
    68
    69
    70
    71
    72
    73
    74
    75
    76
    77
    78
    79
    80
    81
    82
    83
    84
    85
    86
    87
    88
    89
    90
    91
    92
    93
    94
    95
    96
    97
    98
    99
    100
    101
    102
    103
    104
    105
    106
    107
    108
    109
    110
    111
    112
    113
    114
    115
    116
    117
    118
    119
    120
    121
    122
    123
    124
    125
    126
    127
    128
    129
    130
    131
    132
    133
    134
    135
    136
    137
    138
    139
    140
    141
    142
    143
    144
    145
    146
    147
    148
    149
    150
    151
    152
    153
    154
    155
    156
    157
    158
    159
    160
    161
    162
    163
    164
    165
    166
    167
    168
    169
    170
    171
    172
    173
    174
    175
    176
    177
    178
    179
    180
    181
    182
    183
    184
    185
    186
    187
    188
    189
    190
    191
    192
    193
    194
    195
    196
    197
    198
    199
    200
    201
    202
    203
    204
    205
    206
    207
    208
    209
    210
    211
    212
    213
    214
    215
    216
    217
    218
    219
    220
    221
    222
    223
    224
    225
    226
    227
    228
    229
    230
    231
    232
    233
    234
    235
    236
    237
    238
    239
    240
    241
    242
    243
    244
    245
    246
    247
    248
    249
    250
    251
    252
    253
    254
    255
    256
    257
    258
    259
    260
    261
    262
    263
    264
    265
    266
    267
    268
    269
    270
    271
    272
    273
    274
    275
    276
    277
    278
    279
    280
    281
    282
    283
    284
    285
    286
    287
    288
    289
    290
    291
    292
    293
    294
    295
    296
    297
    298
    299
    300
    301
    302
    303
    304
    305
    306
    307
    308
    309
    310
    311
    312
    313
    314
    315
    316
    317
    318
    319
    320
    321
    322
    323
    324
    325
    326
    327
    328
    329
    330
    331
    332
    333
    334
    335
    336
    337
    338
    339
    340
    341
    342
    343
    344
    345
    346
    347
    348
    349
    350
    351
    352
    353
    354
    355
    356
    357
    358
    359
    360
    361
    362
    363
    364
    365
    366
    367
    368
    369
    370
    371
    372
    373
    374
    375
    376
    377
    378
    379
    380
    381
    382
    383
    384
    385
    386
    387
    388
    389
    390
    391
    392
    393
    394
    395
    396
    397
    398
    399
    400
    401
    402
    403
    404
    405
    406
    407
    408
    409
    410
    411
    412
    413
    414
    415
    416
    417
    418
    419
    420
    421
    422
    423
    424
    425
    426
    427
    428
    429
    430
    431
    432
    433
    434
    435
    436
    437
    438
    439
    440
    441
    442
    443
    444
    445
    446
    447
    448
    449
    450
    451
    452
    453
    454
    455
    456
    457
    458
    459
    460
    461
    462
    463
    464
    465
    466
    467
    468
    469
    470
    471
    472
    473
    474
    475
    476
    477
    478
    479
    480
    481
    482
    483
    484
    485
    486
    487
    488
    489
    490
    491
    492
    493
    494
    495
    496
    497
    498
    499
    500
    501
    502
    503
    504
    505
    506
    507
    508
    509
    510
    511
    512
    513
    514
    515
    516
    517
    518
    519
    520
    521
    522
    523
    524
    525
    526
    527
    528
    529
    530
    531
    532
    533
    534
    535
    536
    537
    538
    539
    540
    541
    542
    543
    544
    545
    546
    547
    548
    549
    550
    551
    552
    553
    554
    555
    556
    557
    558
    559
    560
    561
    562
    563
    564
    565
    566
    567
    568
    569
    570
    571
    572
    573
    574
    575
    576
    577
    578
    579
    580
    581
    582
    583
    584
    585
    586
    587
    588
    589
    590
    591
    592
    593
    594
    595
    596
    597
    598
    599
    600
    601
    602
    603
    604
    605
    606
    607
    608
    609
    610
    611
    612
    613
    614
    615
    616
    617
    618
    619
    620
    621
    622
    623
    624
    625
    626
    627
    628
    629
    630
    631
    632
    633
    634
    635
    636
    637
    638
    639
    640
    641
    642
    643
    644
    645
    646
    647
    648
    649
    650
    651
    652
    653
    654
    655
    656
    657
    658
    659
    660
    661
    662
    663
    664
    665
    666
    667
    668
    669
    670
    671
    672
    673
    674
    675
    676
    677
    678
    679
    680
    681
    682
    683
    684
    685
    686
    687
    688
    689
    690
    691
    692
    693
    694
    695
    696
    697
    698
    699
    700
    701
    702
    703
    704
    705
    706
    707
    708
    709
    710
    711
    712
    713
    714
    715
    716
    717
    718
    719
    720
    721
    722
    723
    724
    725
    726
    727
    728
    729
    730
    731
    732
    733
    734
    735
    736
    737
    738
    739
    740
    741
    742
    743
    744
    745
    746
    747
    748
    749
    750
    751
    752
    753
    754
    755
    756
    757
    758
    759
    760
    761
    762
    763
    764
    765
    766
    767
    768
    769
    770
    771
    772
    773
    774
    775
    776
    777
    778
    779
    780
    781
    782
    783
    784
    785
    786
    787
    788
    LOG FILE :
    This is pdfTeX, Version 3.14159265-2.6-1.40.20 (MiKTeX 2.9.7050) (preloaded format=pdflatex 2019.7.28) 11 AUG 2019 13:45
    entering extended mode
    **"./105 - Groupe des permutations.tex"
    ("105 - Groupe des permutations.tex"
    LaTeX2e <2018-12-01>
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/bas
    e/article.cls"
    Document Class: article 2018/09/03 v1.4i Standard LaTeX document class
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/bas
    e/size10.clo"
    File: size10.clo 2018/09/03 v1.4i Standard LaTeX file (size option)
    )
    \c@part=\count80
    \c@section=\count81
    \c@subsection=\count82
    \c@subsubsection=\count83
    \c@paragraph=\count84
    \c@subparagraph=\count85
    \c@figure=\count86
    \c@table=\count87
    \abovecaptionskip=\skip41
    \belowcaptionskip=\skip42
    \bibindent=\dimen102
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/gra
    phics/graphicx.sty"
    Package: graphicx 2017/06/01 v1.1a Enhanced LaTeX Graphics (DPC,SPQR)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/gra
    phics/keyval.sty"
    Package: keyval 2014/10/28 v1.15 key=value parser (DPC)
    \KV@toks@=\toks14
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/gra
    phics/graphics.sty"
    Package: graphics 2017/06/25 v1.2c Standard LaTeX Graphics (DPC,SPQR)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/gra
    phics/trig.sty"
    Package: trig 2016/01/03 v1.10 sin cos tan (DPC)
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/gra
    phics-cfg/graphics.cfg"
    File: graphics.cfg 2016/06/04 v1.11 sample graphics configuration
    )
    Package graphics Info: Driver file: pdftex.def on input line 99.
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/gra
    phics-def/pdftex.def"
    File: pdftex.def 2018/01/08 v1.0l Graphics/color driver for pdftex
    ))
    \Gin@req@height=\dimen103
    \Gin@req@width=\dimen104
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/pbo
    x/pbox.sty"
    Package: pbox 2011/12/07 v1.2 Dynamic parboxes
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/too
    ls/calc.sty"
    Package: calc 2017/05/25 v4.3 Infix arithmetic (KKT,FJ)
    \calc@Acount=\count88
    \calc@Bcount=\count89
    \calc@Adimen=\dimen105
    \calc@Bdimen=\dimen106
    \calc@Askip=\skip43
    \calc@Bskip=\skip44
    LaTeX Info: Redefining \setlength on input line 80.
    LaTeX Info: Redefining \addtolength on input line 81.
    \calc@Ccount=\count90
    \calc@Cskip=\skip45
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/bas
    e/ifthen.sty"
    Package: ifthen 2014/09/29 v1.1c Standard LaTeX ifthen package (DPC)
    )
    \pb@xlen=\skip46
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/gra
    phics/lscape.sty"
    Package: lscape 2000/10/22 v3.01 Landscape Pages (DPC)
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/geo
    metry/geometry.sty"
    Package: geometry 2018/04/16 v5.8 Page Geometry
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/o
    berdiek/ifpdf.sty"
    Package: ifpdf 2018/09/07 v3.3 Provides the ifpdf switch
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/o
    berdiek/ifvtex.sty"
    Package: ifvtex 2016/05/16 v1.6 Detect VTeX and its facilities (HO)
    Package ifvtex Info: VTeX not detected.
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/i
    fxetex/ifxetex.sty"
    Package: ifxetex 2010/09/12 v0.6 Provides ifxetex conditional
    )
    \Gm@cnth=\count91
    \Gm@cntv=\count92
    \c@Gm@tempcnt=\count93
    \Gm@bindingoffset=\dimen107
    \Gm@wd@mp=\dimen108
    \Gm@odd@mp=\dimen109
    \Gm@even@mp=\dimen110
    \Gm@layoutwidth=\dimen111
    \Gm@layoutheight=\dimen112
    \Gm@layouthoffset=\dimen113
    \Gm@layoutvoffset=\dimen114
    \Gm@dimlist=\toks15
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/geo
    metry/geometry.cfg"))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/pgf
    /frontendlayer/tikz.sty"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/pgf
    /basiclayer/pgf.sty"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/pgf
    /utilities/pgfrcs.sty"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/utilities/pgfutil-common.tex"
    \pgfutil@everybye=\toks16
    \pgfutil@tempdima=\dimen115
    \pgfutil@tempdimb=\dimen116
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/utilities/pgfutil-common-lists.tex"))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/utilities/pgfutil-latex.def"
    \pgfutil@abb=\box27
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/ms/
    everyshi.sty"
    Package: everyshi 2001/05/15 v3.00 EveryShipout Package (MS)
    ))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/utilities/pgfrcs.code.tex"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/pgf.revision.tex")
    Package: pgfrcs 2019/07/17 v3.1.4a (3.1.4a)
    ))
    Package: pgf 2019/07/17 v3.1.4a (3.1.4a)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/pgf
    /basiclayer/pgfcore.sty"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/pgf
    /systemlayer/pgfsys.sty"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/systemlayer/pgfsys.code.tex"
    Package: pgfsys 2019/07/17 v3.1.4a (3.1.4a)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/utilities/pgfkeys.code.tex"
    \pgfkeys@pathtoks=\toks17
    \pgfkeys@temptoks=\toks18
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/utilities/pgfkeysfiltered.code.tex"
    \pgfkeys@tmptoks=\toks19
    ))
    \pgf@x=\dimen117
    \pgf@y=\dimen118
    \pgf@xa=\dimen119
    \pgf@ya=\dimen120
    \pgf@xb=\dimen121
    \pgf@yb=\dimen122
    \pgf@xc=\dimen123
    \pgf@yc=\dimen124
    \pgf@xd=\dimen125
    \pgf@yd=\dimen126
    \w@pgf@writea=\write3
    \r@pgf@reada=\read1
    \c@pgf@counta=\count94
    \c@pgf@countb=\count95
    \c@pgf@countc=\count96
    \c@pgf@countd=\count97
    \t@pgf@toka=\toks20
    \t@pgf@tokb=\toks21
    \t@pgf@tokc=\toks22
    \pgf@sys@id@count=\count98
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/systemlayer/pgf.cfg"
    File: pgf.cfg 2019/07/17 v3.1.4a (3.1.4a)
    )
    Driver file for pgf: pgfsys-pdftex.def
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/systemlayer/pgfsys-pdftex.def"
    File: pgfsys-pdftex.def 2019/07/17 v3.1.4a (3.1.4a)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/systemlayer/pgfsys-common-pdf.def"
    File: pgfsys-common-pdf.def 2019/07/17 v3.1.4a (3.1.4a)
    )))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/systemlayer/pgfsyssoftpath.code.tex"
    File: pgfsyssoftpath.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgfsyssoftpath@smallbuffer@items=\count99
    \pgfsyssoftpath@bigbuffer@items=\count100
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/systemlayer/pgfsysprotocol.code.tex"
    File: pgfsysprotocol.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    ))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/xco
    lor/xcolor.sty"
    Package: xcolor 2016/05/11 v2.12 LaTeX color extensions (UK)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/gra
    phics-cfg/color.cfg"
    File: color.cfg 2016/01/02 v1.6 sample color configuration
    )
    Package xcolor Info: Driver file: pdftex.def on input line 225.
    Package xcolor Info: Model `cmy' substituted by `cmy0' on input line 1348.
    Package xcolor Info: Model `hsb' substituted by `rgb' on input line 1352.
    Package xcolor Info: Model `RGB' extended on input line 1364.
    Package xcolor Info: Model `HTML' substituted by `rgb' on input line 1366.
    Package xcolor Info: Model `Hsb' substituted by `hsb' on input line 1367.
    Package xcolor Info: Model `tHsb' substituted by `hsb' on input line 1368.
    Package xcolor Info: Model `HSB' substituted by `hsb' on input line 1369.
    Package xcolor Info: Model `Gray' substituted by `gray' on input line 1370.
    Package xcolor Info: Model `wave' substituted by `hsb' on input line 1371.
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcore.code.tex"
    Package: pgfcore 2019/07/17 v3.1.4a (3.1.4a)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmath.code.tex"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathcalc.code.tex"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathutil.code.tex")
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathparser.code.tex"
    \pgfmath@dimen=\dimen127
    \pgfmath@count=\count101
    \pgfmath@box=\box28
    \pgfmath@toks=\toks23
    \pgfmath@stack@operand=\toks24
    \pgfmath@stack@operation=\toks25
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathfunctions.code.tex"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathfunctions.basic.code.tex")
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathfunctions.trigonometric.code.tex")
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathfunctions.random.code.tex")
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathfunctions.comparison.code.tex")
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathfunctions.base.code.tex")
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathfunctions.round.code.tex")
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathfunctions.misc.code.tex")
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathfunctions.integerarithmetics.code.tex")))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmathfloat.code.tex"
    \c@pgfmathroundto@lastzeros=\count102
    ))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfint.code.tex")
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcorepoints.code.tex"
    File: pgfcorepoints.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgf@picminx=\dimen128
    \pgf@picmaxx=\dimen129
    \pgf@picminy=\dimen130
    \pgf@picmaxy=\dimen131
    \pgf@pathminx=\dimen132
    \pgf@pathmaxx=\dimen133
    \pgf@pathminy=\dimen134
    \pgf@pathmaxy=\dimen135
    \pgf@xx=\dimen136
    \pgf@xy=\dimen137
    \pgf@yx=\dimen138
    \pgf@yy=\dimen139
    \pgf@zx=\dimen140
    \pgf@zy=\dimen141
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcorepathconstruct.code.tex"
    File: pgfcorepathconstruct.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgf@path@lastx=\dimen142
    \pgf@path@lasty=\dimen143
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcorepathusage.code.tex"
    File: pgfcorepathusage.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgf@shorten@end@additional=\dimen144
    \pgf@shorten@start@additional=\dimen145
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcorescopes.code.tex"
    File: pgfcorescopes.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgfpic=\box29
    \pgf@hbox=\box30
    \pgf@layerbox@main=\box31
    \pgf@picture@serial@count=\count103
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcoregraphicstate.code.tex"
    File: pgfcoregraphicstate.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgflinewidth=\dimen146
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcoretransformations.code.tex"
    File: pgfcoretransformations.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgf@pt@x=\dimen147
    \pgf@pt@y=\dimen148
    \pgf@pt@temp=\dimen149
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcorequick.code.tex"
    File: pgfcorequick.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcoreobjects.code.tex"
    File: pgfcoreobjects.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcorepathprocessing.code.tex"
    File: pgfcorepathprocessing.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcorearrows.code.tex"
    File: pgfcorearrows.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgfarrowsep=\dimen150
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcoreshade.code.tex"
    File: pgfcoreshade.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgf@max=\dimen151
    \pgf@sys@shading@range@num=\count104
    \pgf@shadingcount=\count105
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcoreimage.code.tex"
    File: pgfcoreimage.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcoreexternal.code.tex"
    File: pgfcoreexternal.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgfexternal@startupbox=\box32
    ))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcorelayers.code.tex"
    File: pgfcorelayers.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcoretransparency.code.tex"
    File: pgfcoretransparency.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcorepatterns.code.tex"
    File: pgfcorepatterns.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/basiclayer/pgfcorerdf.code.tex"
    File: pgfcorerdf.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    )))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/modules/pgfmoduleshapes.code.tex"
    File: pgfmoduleshapes.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgfnodeparttextbox=\box33
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/modules/pgfmoduleplot.code.tex"
    File: pgfmoduleplot.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/pgf
    /compatibility/pgfcomp-version-0-65.sty"
    Package: pgfcomp-version-0-65 2019/07/17 v3.1.4a (3.1.4a)
    \pgf@nodesepstart=\dimen152
    \pgf@nodesepend=\dimen153
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/pgf
    /compatibility/pgfcomp-version-1-18.sty"
    Package: pgfcomp-version-1-18 2019/07/17 v3.1.4a (3.1.4a)
    ))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/pgf
    /utilities/pgffor.sty"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/pgf
    /utilities/pgfkeys.sty"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/utilities/pgfkeys.code.tex"))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/pgf
    /math/pgfmath.sty"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmath.code.tex"))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/utilities/pgffor.code.tex"
    Package: pgffor 2019/07/17 v3.1.4a (3.1.4a)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/math/pgfmath.code.tex")
    \pgffor@iter=\dimen154
    \pgffor@skip=\dimen155
    \pgffor@stack=\toks26
    \pgffor@toks=\toks27
    ))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/frontendlayer/tikz/tikz.code.tex"
    Package: tikz 2019/07/17 v3.1.4a (3.1.4a)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/libraries/pgflibraryplothandlers.code.tex"
    File: pgflibraryplothandlers.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgf@plot@mark@count=\count106
    \pgfplotmarksize=\dimen156
    )
    \tikz@lastx=\dimen157
    \tikz@lasty=\dimen158
    \tikz@lastxsaved=\dimen159
    \tikz@lastysaved=\dimen160
    \tikz@lastmovetox=\dimen161
    \tikz@lastmovetoy=\dimen162
    \tikzleveldistance=\dimen163
    \tikzsiblingdistance=\dimen164
    \tikz@figbox=\box34
    \tikz@figbox@bg=\box35
    \tikz@tempbox=\box36
    \tikz@tempbox@bg=\box37
    \tikztreelevel=\count107
    \tikznumberofchildren=\count108
    \tikznumberofcurrentchild=\count109
    \tikz@fig@count=\count110
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/modules/pgfmodulematrix.code.tex"
    File: pgfmodulematrix.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    \pgfmatrixcurrentrow=\count111
    \pgfmatrixcurrentcolumn=\count112
    \pgf@matrix@numberofcolumns=\count113
    )
    \tikz@expandcount=\count114
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/frontendlayer/tikz/libraries/tikzlibrarytopaths.code.tex"
    File: tikzlibrarytopaths.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    )))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/ams
    math/amsmath.sty"
    Package: amsmath 2018/12/01 v2.17b AMS math features
    \@mathmargin=\skip47
    For additional information on amsmath, use the `?' option.
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/ams
    math/amstext.sty"
    Package: amstext 2000/06/29 v2.01 AMS text
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/ams
    math/amsgen.sty"
    File: amsgen.sty 1999/11/30 v2.0 generic functions
    \@emptytoks=\toks28
    \ex@=\dimen165
    ))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/ams
    math/amsbsy.sty"
    Package: amsbsy 1999/11/29 v1.2d Bold Symbols
    \pmbraise@=\dimen166
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/ams
    math/amsopn.sty"
    Package: amsopn 2016/03/08 v2.02 operator names
    )
    \inf@bad=\count115
    LaTeX Info: Redefining \frac on input line 223.
    \uproot@=\count116
    \leftroot@=\count117
    LaTeX Info: Redefining \overline on input line 385.
    \classnum@=\count118
    \DOTSCASE@=\count119
    LaTeX Info: Redefining \ldots on input line 482.
    LaTeX Info: Redefining \dots on input line 485.
    LaTeX Info: Redefining \cdots on input line 606.
    \Mathstrutbox@=\box38
    \strutbox@=\box39
    \big@size=\dimen167
    LaTeX Font Info: Redeclaring font encoding OML on input line 729.
    LaTeX Font Info: Redeclaring font encoding OMS on input line 730.
    \macc@depth=\count120
    \c@MaxMatrixCols=\count121
    \dotsspace@=\muskip10
    \c@parentequation=\count122
    \dspbrk@lvl=\count123
    \tag@help=\toks29
    \row@=\count124
    \column@=\count125
    \maxfields@=\count126
    \andhelp@=\toks30
    \eqnshift@=\dimen168
    \alignsep@=\dimen169
    \tagshift@=\dimen170
    \tagwidth@=\dimen171
    \totwidth@=\dimen172
    \lineht@=\dimen173
    \@envbody=\toks31
    \multlinegap=\skip48
    \multlinetaggap=\skip49
    \mathdisplay@stack=\toks32
    LaTeX Info: Redefining \[ on input line 2844.
    LaTeX Info: Redefining \] on input line 2845.
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/ams
    fonts/amsfonts.sty"
    Package: amsfonts 2013/01/14 v3.01 Basic AMSFonts support
    \symAMSa=\mathgroup4
    \symAMSb=\mathgroup5
    LaTeX Font Info: Overwriting math alphabet `\mathfrak' in version `bold'
    (Font) U/euf/m/n --> U/euf/b/n on input line 106.
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/frontendlayer/tikz/libraries/tikzlibrarymindmap.code.tex"
    File: tikzlibrarymindmap.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/frontendlayer/tikz/libraries/tikzlibrarytrees.code.tex"
    File: tikzlibrarytrees.code.tex 2019/07/17 v3.1.4a (3.1.4a)
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/frontendlayer/tikz/libraries/tikzlibrarydecorations.code.tex"
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/p
    gf/modules/pgfmoduledecorations.code.tex"
    \pgfdecoratedcompleteddistance=\dimen174
    \pgfdecoratedremainingdistance=\dimen175
    \pgfdecoratedinputsegmentcompleteddistance=\dimen176
    \pgfdecoratedinputsegmentremainingdistance=\dimen177
    \pgf@decorate@distancetomove=\dimen178
    \pgf@decorate@repeatstate=\count127
    \pgfdecorationsegmentamplitude=\dimen179
    \pgfdecorationsegmentlength=\dimen180
    )
    \tikz@lib@dec@box=\box40
    ))
    LaTeX Warning: Unused global option(s):
    [20pt,french].
    ("105 - Groupe des permutations.aux")
    \openout1 = `"105 - Groupe des permutations.aux"'.
    LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 12.
    LaTeX Font Info: ... okay on input line 12.
    LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 12.
    LaTeX Font Info: ... okay on input line 12.
    LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 12.
    LaTeX Font Info: ... okay on input line 12.
    LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 12.
    LaTeX Font Info: ... okay on input line 12.
    LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 12.
    LaTeX Font Info: ... okay on input line 12.
    LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 12.
    LaTeX Font Info: ... okay on input line 12.
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/context/b
    ase/mkii/supp-pdf.mkii"
    [Loading MPS to PDF converter (version 2006.09.02).]
    \scratchcounter=\count128
    \scratchdimen=\dimen181
    \scratchbox=\box41
    \nofMPsegments=\count129
    \nofMParguments=\count130
    \everyMPshowfont=\toks33
    \MPscratchCnt=\count131
    \MPscratchDim=\dimen182
    \MPnumerator=\count132
    \makeMPintoPDFobject=\count133
    \everyMPtoPDFconversion=\toks34
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/obe
    rdiek/epstopdf-base.sty"
    Package: epstopdf-base 2016/05/15 v2.6 Base part for package epstopdf
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/o
    berdiek/infwarerr.sty"
    Package: infwarerr 2016/05/16 v1.4 Providing info/warning/error messages (HO)
    )
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/obe
    rdiek/grfext.sty"
    Package: grfext 2016/05/16 v1.2 Manage graphics extensions (HO)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/o
    berdiek/kvdefinekeys.sty"
    Package: kvdefinekeys 2016/05/16 v1.4 Define keys (HO)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/o
    berdiek/ltxcmds.sty"
    Package: ltxcmds 2016/05/16 v1.23 LaTeX kernel commands for general use (HO)
    )))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/obe
    rdiek/kvoptions.sty"
    Package: kvoptions 2016/05/16 v3.12 Key value format for package options (HO)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/o
    berdiek/kvsetkeys.sty"
    Package: kvsetkeys 2016/05/16 v1.17 Key value parser (HO)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/o
    berdiek/etexcmds.sty"
    Package: etexcmds 2016/05/16 v1.6 Avoid name clashes with e-TeX commands (HO)
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/o
    berdiek/ifluatex.sty"
    Package: ifluatex 2016/05/16 v1.4 Provides the ifluatex switch (HO)
    Package ifluatex Info: LuaTeX not detected.
    ))))
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/generic/o
    berdiek/pdftexcmds.sty"
    Package: pdftexcmds 2018/09/10 v0.29 Utility functions of pdfTeX for LuaTeX (HO
    )
    Package pdftexcmds Info: LuaTeX not detected.
    Package pdftexcmds Info: \pdf@primitive is available.
    Package pdftexcmds Info: \pdf@ifprimitive is available.
    Package pdftexcmds Info: \pdfdraftmode found.
    )
    Package epstopdf-base Info: Redefining graphics rule for `.eps' on input line 4
    38.
    Package grfext Info: Graphics extension search list:
    (grfext) [.pdf,.png,.jpg,.mps,.jpeg,.jbig2,.jb2,.PDF,.PNG,.JPG,.JPE
    G,.JBIG2,.JB2,.eps]
    (grfext) \AppendGraphicsExtensions on input line 456.
    )
    *geometry* driver: auto-detecting
    *geometry* detected driver: pdftex
    *geometry* verbose mode - [ preamble ] result:
    * driver: pdftex
    * paper: <default>
    * layout: <same size as paper>
    * layoutoffset:(h,v)=(0.0pt,0.0pt)
    * modes: landscape
    * h-part:(L,W,R)=(28.45274pt, 738.0645pt, 28.45274pt)
    * v-part:(T,H,B)=(28.45274pt, 557.38951pt, 28.45274pt)
    * \paperwidth=794.96999pt
    * \paperheight=614.295pt
    * \textwidth=738.0645pt
    * \textheight=557.38951pt
    * \oddsidemargin=-43.81725pt
    * \evensidemargin=-43.81725pt
    * \topmargin=-80.81725pt
    * \headheight=12.0pt
    * \headsep=25.0pt
    * \topskip=10.0pt
    * \footskip=30.0pt
    * \marginparwidth=144.0pt
    * \marginparsep=11.0pt
    * \columnsep=10.0pt
    * \skip\footins=9.0pt plus 4.0pt minus 2.0pt
    * \hoffset=0.0pt
    * \voffset=0.0pt
    * \mag=1000
    * \@twocolumnfalse
    * \@twosidefalse
    * \@mparswitchfalse
    * \@reversemarginfalse
    * (1in=72.27pt=25.4mm, 1cm=28.453pt)
    ABD: EveryShipout initializing macros
    LaTeX Font Info: Try loading font information for U+msa on input line 34.
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/ams
    fonts/umsa.fd"
    File: umsa.fd 2013/01/14 v3.01 AMS symbols A
    )
    LaTeX Font Info: Try loading font information for U+msb on input line 34.
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/ams
    fonts/umsb.fd"
    File: umsb.fd 2013/01/14 v3.01 AMS symbols B
    )
    ! Missing delimiter (. inserted).
    <to be read again>
    $
    l.46 $
    };
    I was expecting to see something like `(' or `\{' or
    `\}' here. If you typed, e.g., `{' instead of `\{', you
    should probably delete the `{' by typing `1' now, so that
    braces don't get unbalanced. Otherwise just proceed.
    Acceptable delimiters are characters whose \delcode is
    nonnegative, or you can use `\delimiter <delimiter code>'.
    ! LaTeX Error: There's no line here to end.
    See the LaTeX manual or LaTeX Companion for explanation.
    Type H <return> for immediate help.
    ...
    l.54 ...\,supp(\sigma)\cap supp(\rho)=\emptyset \\
    \Rightarrow \sigma\circ\r...
    Your command was ignored.
    Type I <command> <return> to replace it with another command,
    or <return> to continue without it.
    ! Missing $ inserted.
    <inserted text>
    $
    l.54 ...\,supp(\sigma)\cap supp(\rho)=\emptyset \\
    \Rightarrow \sigma\circ\r...
    I've inserted a begin-math/end-math symbol since I think
    you left one out. Proceed, with fingers crossed.
    ! Missing $ inserted.
    <inserted text>
    $
    l.54 ...a)\cap supp(\rho)=\emptyset \\ \Rightarrow
    \sigma\circ\rho = \rho\ci...
    I've inserted a begin-math/end-math symbol since I think
    you left one out. Proceed, with fingers crossed.
    ! LaTeX Error: There's no line here to end.
    See the LaTeX manual or LaTeX Companion for explanation.
    Type H <return> for immediate help.
    ...
    l.58 ...card(O)=r \Rightarrow \exists x\in E\,, \\
    O=\{x,\sigma(x),...,\sigm...
    Your command was ignored.
    Type I <command> <return> to replace it with another command,
    or <return> to continue without it.
    ! Missing $ inserted.
    <inserted text>
    $
    l.58 ...card(O)=r \Rightarrow \exists x\in E\,, \\
    O=\{x,\sigma(x),...,\sigm...
    I've inserted a begin-math/end-math symbol since I think
    you left one out. Proceed, with fingers crossed.
    LaTeX Font Info: Try loading font information for OMS+cmr on input line 58.
    ("/Users/laafar/Library/Application Support/MiKTeX/texmfs/install/tex/latex/bas
    e/omscmr.fd"
    File: omscmr.fd 2014/09/29 v2.5h Standard LaTeX font definitions
    )
    LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <10> not available
    (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 58.
    ! Missing $ inserted.
    <inserted text>
    $
    l.58 ...ghtarrow \exists x\in E\,, \\ O=\{x,\sigma
    (x),...,\sigma^{r-1}(x)\}$};
    I've inserted a begin-math/end-math symbol since I think
    you left one out. Proceed, with fingers crossed.
    Overfull \hbox (7.09462pt too wide) in paragraph at lines 63--63
    [][]$[]$
    []
    Overfull \hbox (3.38765pt too wide) in paragraph at lines 65--65
    \OML/cmm/m/it/10 transposition$
    []
    ! LaTeX Error: There's no line here to end.
    See the LaTeX manual or LaTeX Companion for explanation.
    Type H <return> for immediate help.
    ...
    l.66 ...I) at (5,5.2){$\sigma\in S_n\,:\,r-cycle\\
    \Leftrightarrow \exists x...
    Your command was ignored.
    Type I <command> <return> to replace it with another command,
    or <return> to continue without it.
    ! Missing $ inserted.
    <inserted text>
    $
    l.66 ...I) at (5,5.2){$\sigma\in S_n\,:\,r-cycle\\
    \Leftrightarrow \exists x...
    I've inserted a begin-math/end-math symbol since I think
    you left one out. Proceed, with fingers crossed.
    ! Missing $ inserted.
    <inserted text>
    $
    l.66 ...sigma\in S_n\,:\,r-cycle\\ \Leftrightarrow
    \exists x\in E_n\,,supp(\...
    I've inserted a begin-math/end-math symbol since I think
    you left one out. Proceed, with fingers crossed.
    ! LaTeX Error: There's no line here to end.
    See the LaTeX manual or LaTeX Companion for explanation.
    Type H <return> for immediate help.
    ...
    l.66 ...sts x\in E_n\,,supp(\sigma)=O_\sigma(x) \\
    \Leftrightarrow \sigma\,a...
    Your command was ignored.
    Type I <command> <return> to replace it with another command,
    or <return> to continue without it.
    ! Missing $ inserted.
    <inserted text>
    $
    l.66 ...sts x\in E_n\,,supp(\sigma)=O_\sigma(x) \\
    \Leftrightarrow \sigma\,a...
    I've inserted a begin-math/end-math symbol since I think
    you left one out. Proceed, with fingers crossed.
    ! Missing $ inserted.
    <inserted text>
    $
    l.66 ...upp(\sigma)=O_\sigma(x) \\ \Leftrightarrow
    \sigma\,a\,une\,seule\,or...
    I've inserted a begin-math/end-math symbol since I think
    you left one out. Proceed, with fingers crossed.
    Overfull \hbox (11.99188pt too wide) in paragraph at lines 75--76
    [][]
    []
    [1
    {/Users/laafar/Library/Application Support/MiKTeX/texmfs/data/pdftex/config/pdf
    tex.map}] ("105 - Groupe des permutations.aux") )
    Here is how much of TeX's memory you used:
    13620 strings out of 494857
    283719 string characters out of 3176484
    334184 words of memory out of 3000000
    17007 multiletter control sequences out of 15000+200000
    9975 words of font info for 40 fonts, out of 3000000 for 9000
    0 hyphenation exceptions out of 8191
    55i,12n,65p,435b,711s stack positions out of 5000i,500n,10000p,200000b,50000s
    </Users/laafar/Library/Applica
    tion Support/MiKTeX/texmfs/install/fonts/type1/public/amsfonts/cm/cmex10.pfb></
    Users/laafar/Library/Application Support/MiKTeX/texmfs/install/fonts/type1/publ
    ic/amsfonts/cm/cmmi10.pfb></Users/laafar/Library/Application Support/MiKTeX/tex
    mfs/install/fonts/type1/public/amsfonts/cm/cmmi12.pfb></Users/laafar/Library/Ap
    plication Support/MiKTeX/texmfs/install/fonts/type1/public/amsfonts/cm/cmmi7.pf
    b></Users/laafar/Library/Application Support/MiKTeX/texmfs/install/fonts/type1/
    public/amsfonts/cm/cmr10.pfb></Users/laafar/Library/Application Support/MiKTeX/
    texmfs/install/fonts/type1/public/amsfonts/cm/cmr7.pfb></Users/laafar/Library/A
    pplication Support/MiKTeX/texmfs/install/fonts/type1/public/amsfonts/cm/cmsy10.
    pfb></Users/laafar/Library/Application Support/MiKTeX/texmfs/install/fonts/type
    1/public/amsfonts/cm/cmsy7.pfb></Users/laafar/Library/Application Support/MiKTe
    X/texmfs/install/fonts/type1/public/amsfonts/symbols/msbm10.pfb>
    Output written on "105 - Groupe des permutations.pdf" (1 page, 90338 bytes).
    PDF statistics:
    45 PDF objects out of 1000 (max. 8388607)
    0 named destinations out of 1000 (max. 500000)
    13 words of extra memory for PDF output out of 10000 (max. 10000000)

  5. #5
    Rédacteur/Modérateur
    Avatar de Winnt
    Homme Profil pro
    budget et contrôle de gestion
    Inscrit en
    Décembre 2006
    Messages
    1 978
    Détails du profil
    Informations personnelles :
    Sexe : Homme
    Âge : 56
    Localisation : France

    Informations professionnelles :
    Activité : budget et contrôle de gestion
    Secteur : Administration - Collectivité locale

    Informations forums :
    Inscription : Décembre 2006
    Messages : 1 978
    Points : 4 130
    Points
    4 130
    Par défaut
    Bonjour,

    Vous chargez déjà l'extension TikZ.
    Regardez donc cette documentation sur TikZ qui est bourrée d'exemples. Je pense que vous y trouverez votre bonheur.
    Winnt
    Merci de lire les règles du forum LaTeX et Qu'est ce qu'un ECM ?.
    N'hésitez pas à parcourir la FAQ la réponse y est peut-être déjà.
    Pensez au bouton si votre problème est résolu.


    C'est en Linuxant qu'on devient .... geek
    Et c'est en LateXant qu'on devient flemmard
    Mon blog tout neuf.
    Articles : présentation de la distribution Gentoo, Les index sous LaTeX et leur personnalisation.

Discussions similaires

  1. Carte mentale pour Game concept document et GDD
    Par Bioshok dans le forum Création de jeux vidéo
    Réponses: 0
    Dernier message: 03/03/2019, 13h14
  2. Réponses: 5
    Dernier message: 31/01/2018, 18h23
  3. Réponses: 1
    Dernier message: 01/06/2017, 12h39
  4. Réponses: 6
    Dernier message: 06/07/2015, 17h14
  5. Détecter une zone précise dans une carte (matrice 2D)
    Par Aspic dans le forum Algorithmes et structures de données
    Réponses: 12
    Dernier message: 11/04/2015, 15h05

Partager

Partager
  • Envoyer la discussion sur Viadeo
  • Envoyer la discussion sur Twitter
  • Envoyer la discussion sur Google
  • Envoyer la discussion sur Facebook
  • Envoyer la discussion sur Digg
  • Envoyer la discussion sur Delicious
  • Envoyer la discussion sur MySpace
  • Envoyer la discussion sur Yahoo