From: Bjørn Rustad Date: Mon, 31 Oct 2011 14:30:23 +0000 (+0100) Subject: Finito X-Git-Url: http://git.rustad.me/?a=commitdiff_plain;h=refs%2Fheads%2Fmaster;p=stokpros1 Finito --- diff --git a/figur.eps b/figur.eps new file mode 100644 index 0000000..3323ecf --- /dev/null +++ b/figur.eps @@ -0,0 +1,4787 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Title: /home/edv4rd/School/Stokastisk - TMA4265/figur.eps +%%Creator: matplotlib version 0.99.3, http://matplotlib.sourceforge.net/ +%%CreationDate: Mon Oct 31 14:32:51 2011 +%%Orientation: portrait +%%BoundingBox: -53 190 665 601 +%%EndComments +%%BeginProlog +/mpldict 8 dict def +mpldict begin +/m { moveto } bind def +/l { lineto } bind def +/r { rlineto } bind def +/c { curveto } bind def +/cl { closepath } bind def +/box { +m +1 index 0 r +0 exch r +neg 0 r +cl +} bind def +/clipbox { +box +clip +newpath +} bind def +%!PS-Adobe-3.0 Resource-Font +%%Title: DejaVu Sans +%%Copyright: Copyright (c) 2003 by Bitstream, Inc. All Rights Reserved. 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\exp_args:Nccc on line 140 -Defining \exp_args:Nco on line 143 -Defining \exp_not:o on line 192 -Defining \exp_not:d on line 193 -Defining \exp_not:f on line 196 -Defining \exp_not:v on line 199 -Defining \exp_not:V on line 202 -Defining \exp_not:c on line 205 -Defining \cs_generate_variant:Nn on line 206 -Defining \cs_generate_internal_variant:n on line 242 -Defining \cs_generate_internal_variant_aux:n on line 248 -Defining \exp_arg_last_unbraced:nn on line 255 -Defining \::f_unbraced on line 256 -Defining \::o_unbraced on line 260 -Defining \::V_unbraced on line 263 -Defining \::v_unbraced on line 267 -Defining \exp_last_unbraced:Nf on line 273 -Defining \exp_last_unbraced:NV on line 274 -Defining \exp_last_unbraced:Nv on line 275 -Defining \exp_last_unbraced:NcV on line 276 -Defining \exp_last_unbraced:NNo on line 279 -Defining \exp_last_unbraced:NNV on line 282 -Defining \exp_last_unbraced:NNNo on line 285 -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3tl.sty -Package: l3tl 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\tl_gset_eq:NN on line 86 -Defining \tl_set_eq:Nc on line 87 -Defining \tl_set_eq:cN on line 87 -Defining \tl_set_eq:cc on line 87 -Defining \tl_gset_eq:Nc on line 88 -Defining \tl_gset_eq:cN on line 88 -Defining \tl_gset_eq:cc on line 88 -Defining \tl_clear:N on line 89 -Defining \tl_clear:c on line 90 -Defining \tl_gclear:N on line 91 -Defining \tl_gclear:c on line 92 -Defining \tl_clear_new:N on line 93 -Defining \tl_clear_new:c on line 94 -Defining \tl_gclear_new:N on line 95 -Defining \tl_gclear_new:c on line 96 -Defining \tl_put_left:Nn on line 97 -Defining \tl_put_left:NV on line 101 -Defining \tl_put_left:No on line 104 -Defining \tl_put_left:Nx on line 108 -Defining \tl_gput_left:Nn on line 111 -Defining \tl_gput_left:NV on line 115 -Defining \tl_gput_left:No on line 118 -Defining \tl_gput_left:Nx on line 122 -Defining \tl_put_left:cn on line 125 -Defining \tl_put_left:co on line 125 -Defining \tl_put_left:cV on line 125 -Defining \tl_gput_left:cn on line 126 -Defining \tl_gput_left:co on line 126 -Defining \tl_gput_left:cV on line 127 -Defining \tl_put_right:Nn on line 128 -Defining \tl_gput_right:Nn on line 132 -Defining \tl_put_right:NV on line 136 -Defining \tl_put_right:No on line 139 -Defining \tl_gput_right:NV on line 143 -Defining \tl_gput_right:No on line 146 -Defining \tl_put_right:cn on line 156 -Defining \tl_put_right:co on line 156 -Defining \tl_put_right:cV on line 157 -Defining \tl_gput_right:cn on line 158 -Defining \tl_gput_right:co on line 158 -Defining \tl_gput_right:cV on line 158 -Defining \tl_gset:Nc on line 159 -Defining \tl_set:Nc on line 162 -Defining \c_job_name_tl on line 163 -Defining \c_empty_tl on line 164 -Defining \g_tmpa_tl on line 165 -Defining \g_tmpb_tl on line 166 -Defining \l_testa_tl on line 167 -Defining \l_testb_tl on line 168 -Defining \g_testa_tl on line 169 -Defining \g_testb_tl on line 170 -Defining \l_tmpa_tl on line 171 -Defining \l_tmpb_tl on line 172 -Defining \tl_if_empty_p:c on line 177 -Defining \tl_if_empty:cTF on line 178 -Defining \tl_if_empty:cT on line 179 -Defining \tl_if_empty:cF on line 180 -Defining \tl_if_eq_p:NN on line 183 -Defining \tl_if_eq:NNTF on line 183 -Defining \tl_if_eq:NNT on line 183 -Defining \tl_if_eq:NNF on line 183 -Defining \tl_if_eq_p:Nc on line 184 -Defining \tl_if_eq_p:cN on line 184 -Defining \tl_if_eq_p:cc on line 184 -Defining \tl_if_eq:NcTF on line 185 -Defining \tl_if_eq:cNTF on line 185 -Defining \tl_if_eq:ccTF on line 185 -Defining \tl_if_eq:NcT on line 186 -Defining \tl_if_eq:cNT on line 186 -Defining \tl_if_eq:ccT on line 186 -Defining \tl_if_eq:NcF on line 187 -Defining \tl_if_eq:cNF on line 187 -Defining \tl_if_eq:ccF on line 187 -Defining \tl_if_empty_p:n on line 191 -Defining \tl_if_empty:nTF on line 191 -Defining \tl_if_empty:nT on line 191 -Defining \tl_if_empty:nF on line 191 -Defining \tl_if_empty_p:V on line 192 -Defining \tl_if_empty:VTF on line 193 -Defining \tl_if_empty:VT on line 194 -Defining \tl_if_empty:VF on line 195 -Defining \tl_if_empty_p:o on line 196 -Defining \tl_if_empty:oTF on line 197 -Defining \tl_if_empty:oT on line 198 -Defining \tl_if_empty:oF on line 199 -Defining \tl_if_blank_p:n on line 202 -Defining \tl_if_blank:nTF on line 202 -Defining \tl_if_blank:nT on line 202 -Defining \tl_if_blank:nF on line 202 -Defining \tl_if_blank_p_aux:w on line 203 -Defining \tl_if_blank_p:V on line 206 -Defining \tl_if_blank:VTF on line 207 -Defining \tl_if_blank:VT on line 208 -Defining \tl_if_blank:VF on line 209 -Defining \tl_if_blank_p:o on line 210 -Defining \tl_if_blank:oTF on line 211 -Defining \tl_if_blank:oT on line 212 -Defining \tl_if_blank:oF on line 213 -Defining \tl_compare:xx on line 214 -Defining \tl_compare:nn on line 215 -Defining \tl_compare:nx on line 218 -Defining \tl_compare:xn on line 221 -Defining \tl_compare:nV on line 224 -Defining \tl_compare:no on line 227 -Defining \tl_compare:Vn on line 230 -Defining \tl_compare:on on line 233 -Defining \tl_compare:VV on line 236 -Defining \tl_compare:oo on line 239 -Defining \tl_compare:xV on line 242 -Defining \tl_compare:xo on line 245 -Defining \tl_compare:Vx on line 248 -Defining \tl_compare:ox on line 251 -Defining \tl_if_eq_p:xx on line 265 -Defining \tl_if_eq:xxTF on line 265 -Defining \tl_if_eq:xxT on line 265 -Defining \tl_if_eq:xxF on line 265 -Defining \tl_if_eq_p:nx on line 265 -Defining \tl_if_eq:nxTF on line 265 -Defining \tl_if_eq:nxT on line 265 -Defining \tl_if_eq:nxF on line 265 -Defining \tl_if_eq_p:ox on line 265 -Defining \tl_if_eq:oxTF on line 265 -Defining \tl_if_eq:oxT on line 265 -Defining \tl_if_eq:oxF on line 265 -Defining \tl_if_eq_p:Vx on line 265 -Defining \tl_if_eq:VxTF on line 265 -Defining \tl_if_eq:VxT on line 265 -Defining \tl_if_eq:VxF on line 265 -Defining \tl_if_eq_p:xn on line 266 -Defining \tl_if_eq:xnTF on line 266 -Defining \tl_if_eq:xnT on line 266 -Defining \tl_if_eq:xnF on line 266 -Defining \tl_if_eq_p:nn on line 266 -Defining \tl_if_eq:nnTF on line 266 -Defining \tl_if_eq:nnT on line 266 -Defining \tl_if_eq:nnF on line 266 -Defining \tl_if_eq_p:on on line 266 -Defining \tl_if_eq:onTF on line 266 -Defining \tl_if_eq:onT on line 266 -Defining \tl_if_eq:onF on line 266 -Defining \tl_if_eq_p:Vn on line 266 -Defining \tl_if_eq:VnTF on line 266 -Defining \tl_if_eq:VnT on line 266 -Defining \tl_if_eq:VnF on line 266 -Defining \tl_if_eq_p:xo on line 267 -Defining \tl_if_eq:xoTF on line 267 -Defining \tl_if_eq:xoT on line 267 -Defining \tl_if_eq:xoF on line 267 -Defining \tl_if_eq_p:no on line 267 -Defining \tl_if_eq:noTF on line 267 -Defining \tl_if_eq:noT on line 267 -Defining \tl_if_eq:noF on line 267 -Defining \tl_if_eq_p:oo on line 267 -Defining \tl_if_eq:ooTF on line 267 -Defining \tl_if_eq:ooT on line 267 -Defining \tl_if_eq:ooF on line 267 -Defining \tl_if_eq_p:xV on line 268 -Defining \tl_if_eq:xVTF on line 268 -Defining \tl_if_eq:xVT on line 268 -Defining \tl_if_eq:xVF on line 268 -Defining \tl_if_eq_p:nV on line 268 -Defining \tl_if_eq:nVTF on line 268 -Defining \tl_if_eq:nVT on line 268 -Defining \tl_if_eq:nVF on line 268 -Defining \tl_if_eq_p:VV on line 268 -Defining \tl_if_eq:VVTF on line 268 -Defining \tl_if_eq:VVT on line 268 -Defining \tl_if_eq:VVF on line 268 -Defining \tl_to_lowercase:n on line 369 -Defining \tl_to_uppercase:n on line 370 -Defining \tl_to_str:n on line 371 -Defining \tl_to_str:N on line 372 -Defining \tl_to_str_aux:w on line 374 -Defining \tl_to_str:c on line 375 -Defining \tl_map_function:nN on line 376 -Defining \tl_map_function:NN on line 379 -Defining \tl_map_function_aux:Nn on line 383 -Defining \tl_map_function:cN on line 387 -Defining \exp_args:NcN on line 387 -Defining \tl_map_inline:nn on line 388 -Defining \tl_map_inline:Nn on line 397 -Defining \tl_map_inline:cn on line 406 -Defining \g_tl_inline_level_num on line 407 -Defining \tl_map_variable:nNn on line 408 -Defining \tl_map_variable:NNn on line 411 -Defining \tl_map_variable:cNn on line 412 -Defining \tl_map_variable_aux:Nnn on line 413 -Defining \tl_map_break: on line 418 -Defining \tl_reverse:n on line 419 -Defining \tl_reverse_aux:nN on line 422 -Defining \tl_reverse:V on line 426 -Defining \tl_reverse:o on line 426 -Defining \tl_reverse:N on line 427 -Defining \tl_elt_count:n on line 430 -Defining \tl_elt_count:V on line 435 -Defining \tl_elt_count:o on line 435 -Defining \tl_elt_count:N on line 436 -Defining \tl_set_rescan:Nnn on line 441 -Defining \tl_gset_rescan:Nnn on line 442 -Defining \c_two_ats_with_two_catcodes_tl on line 451 -Defining \tl_set_rescan_aux:NNnn on line 452 -Defining \tl_set_rescan:Nnx on line 468 -Defining \tl_gset_rescan:Nnx on line 478 -Defining \tl_rescan:nn on line 486 -Defining \tl_if_in:NnTF on line 500 -Defining \tl_if_in:NnT on line 500 -Defining \tl_if_in:NnF on line 500 -Defining \tl_if_in:cnTF on line 501 -Defining \tl_if_in:cnT on line 502 -Defining \tl_if_in:cnF on line 503 -Defining \tl_if_in:nnTF on line 509 -Defining \tl_if_in:nnT on line 509 -Defining \tl_if_in:nnF on line 509 -Defining \tl_if_in:VnTF on line 510 -Defining \tl_if_in:VnT on line 511 -Defining \tl_if_in:VnF on line 512 -Defining \tl_if_in:onTF on line 513 -Defining \tl_if_in:onT on line 514 -Defining \tl_if_in:onF on line 515 -Defining \tl_replace_in_aux:NNnn on line 517 -Defining \tl_replace_in:Nnn on line 532 -Defining \tl_replace_in:cnn on line 533 -Defining \exp_args:Ncnn on line 533 -Defining \tl_greplace_in:Nnn on line 534 -Defining \tl_greplace_in:cnn on line 535 -Defining \tl_replace_all_in:Nnn on line 552 -Defining \tl_replace_all_in:cnn on line 554 -Defining \tl_greplace_all_in:Nnn on line 555 -Defining \tl_greplace_all_in:cnn on line 557 -Defining \tl_remove_in:Nn on line 558 -Defining \tl_gremove_in:Nn on line 559 -Defining \tl_remove_in:cn on line 560 -Defining \tl_gremove_in:cn on line 561 -Defining \tl_remove_all_in:Nn on line 562 -Defining \tl_gremove_all_in:Nn on line 565 -Defining \tl_remove_all_in:cn on line 568 -Defining \tl_gremove_all_in:cn on line 569 -Defining \tl_head:n on line 570 -Defining \tl_head_i:n on line 571 -Defining \tl_tail:n on line 572 -Defining \tl_tail:f on line 573 -Defining \tl_head_iii:n on line 574 -Defining \tl_head_iii:f on line 575 -Defining \tl_head:w on line 576 -Defining \tl_head_i:w on line 577 -Defining \tl_tail:w on line 578 -Defining \tl_head_iii:w on line 579 -Defining \tl_head:V on line 580 -Defining \tl_tail:V on line 581 -Defining \tl_if_head_eq_meaning_p:nN on line 585 -Defining \tl_if_head_eq_meaning:nNTF on line 585 -Defining \tl_if_head_eq_meaning:nNT on line 585 -Defining \tl_if_head_eq_meaning:nNF on line 585 -Defining \tl_if_head_eq_charcode_p:nN on line 590 -Defining \tl_if_head_eq_charcode:nNTF on line 590 -Defining \tl_if_head_eq_charcode:nNT on line 590 -Defining \tl_if_head_eq_charcode:nNF on line 590 -Defining \tl_if_head_eq_charcode_p:fN on line 600 -Defining \tl_if_head_eq_charcode:fNTF on line 601 -Defining \tl_if_head_eq_charcode:fNT on line 602 -Defining \tl_if_head_eq_charcode:fNF on line 603 -Defining \tl_if_head_eq_catcode_p:nN on line 608 -Defining \tl_if_head_eq_catcode:nNTF on line 608 -Defining \tl_if_head_eq_catcode:nNT on line 608 -Defining \tl_if_head_eq_catcode:nNF on line 608 -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3num.sty -Package: l3num 2009/08/08 v1451 L3 Experimental token numbers -Defining \if_num:w on line 56 -Defining \if_case:w on line 57 -Defining \num_incr:c on line 62 -Defining \num_decr:c on line 63 -Defining \num_gincr:c on line 64 -Defining \num_gdecr:c on line 65 -Defining \num_zero:N on line 66 -Defining \num_gzero:N on line 67 -Defining \num_zero:c on line 68 -Defining \num_gzero:c on line 69 -Defining \num_new:N on line 70 -Defining \num_new:c on line 71 -Defining \num_set:Nn on line 72 -Defining \num_set:cn on line 75 -Defining \num_gset:Nn on line 76 -Defining \num_gset:cn on line 77 -Defining \num_set_eq:NN on line 78 -Defining \num_set_eq:cN on line 79 -Defining \num_set_eq:Nc on line 79 -Defining \num_set_eq:cc on line 79 -Defining \num_gset_eq:NN on line 80 -Defining \num_gset_eq:cN on line 81 -Defining \num_gset_eq:Nc on line 81 -Defining \num_gset_eq:cc on line 81 -Defining \num_add:Nn on line 82 -Defining \num_add:cn on line 83 -Defining \num_gadd:Nn on line 84 -Defining \num_gadd:cn on line 85 -Defining \num_use:N on line 86 -Defining \num_use:c on line 87 -Defining \num_show:N on line 88 -Defining \num_show:c on line 89 -Defining \num_elt_count:n on line 90 -Defining \num_elt_count_prop:Nn on line 91 -Defining \l_tmpa_num on line 92 -Defining \l_tmpb_num on line 93 -Defining \l_tmpc_num on line 94 -Defining \g_tmpa_num on line 95 -Defining \g_tmpb_num on line 96 -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3intexpr.sty -Package: l3intexpr 2009/03/20 v1086 L3 Integer Expressions -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3quark.sty -Package: l3quark 2009/05/31 v1365 L3 Experimental Quark Commands -Defining \quark_new:N on line 56 -Defining \q_stop on line 57 -Defining \q_no_value on line 58 -Defining \q_nil on line 59 -Defining \q_error on line 60 -Defining \q_mark on line 61 -Defining \q_recursion_tail on line 62 -Defining \q_recursion_stop on line 63 -Defining \quark_if_recursion_tail_stop:n on line 64 -Defining \quark_if_recursion_tail_stop:N on line 70 -Defining \quark_if_recursion_tail_stop:o on line 75 -Defining \quark_if_recursion_tail_stop_do:nn on line 76 -Defining \quark_if_recursion_tail_stop_do:Nn on line 85 -Defining \quark_if_recursion_tail_stop_do:on on line 93 -Defining \exp_args:Non on line 93 -Defining \quark_if_recursion_tail_aux:w on line 94 -Defining \quark_if_no_value_p:N on line 98 -Defining \quark_if_no_value:NTF on line 98 -Defining \quark_if_no_value:NT on line 98 -Defining \quark_if_no_value:NF on line 98 -Defining \quark_if_no_value_p:n on line 118 -Defining \quark_if_no_value:nTF on line 118 -Defining \quark_if_no_value:nT on line 118 -Defining \quark_if_no_value:nF on line 118 -Defining \quark_if_nil_p:N on line 121 -Defining \quark_if_nil:NTF on line 121 -Defining \quark_if_nil:NT on line 121 -Defining \quark_if_nil:NF on line 121 -Defining \quark_if_nil_p:n on line 140 -Defining \quark_if_nil:nTF on line 140 -Defining \quark_if_nil:nT on line 140 -Defining \quark_if_nil:nF on line 140 -Defining \quark_if_nil_p:V on line 141 -Defining \quark_if_nil:VTF on line 142 -Defining \quark_if_nil:VT on line 143 -Defining \quark_if_nil:VF on line 144 -Defining \quark_if_nil_p:o on line 145 -Defining \quark_if_nil:oTF on line 146 -Defining \quark_if_nil:oT on line 147 -Defining \quark_if_nil:oF on line 148 -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3seq.sty -Package: l3seq 2009/06/17 v1415 L3 Experimental sequences and stacks -Defining \seq_elt:w on line 56 -Defining \seq_elt_end: on line 57 -Defining \seq_new:N on line 58 -Defining \seq_new:c on line 59 -Defining \seq_clear:N on line 60 -Defining \seq_clear:c on line 61 -Defining \seq_gclear:N on line 62 -Defining \seq_gclear:c on line 63 -Defining \seq_clear_new:N on line 64 -Defining \seq_clear_new:c on line 65 -Defining \seq_gclear_new:N on line 66 -Defining \seq_gclear_new:c on line 67 -Defining \seq_set_eq:NN on line 68 -Defining \seq_set_eq:cN on line 69 -Defining \seq_set_eq:Nc on line 70 -Defining \seq_set_eq:cc on line 71 -Defining \seq_gset_eq:NN on line 72 -Defining \seq_gset_eq:cN on line 73 -Defining \seq_gset_eq:Nc on line 74 -Defining \seq_gset_eq:cc on line 75 -Defining \seq_gconcat:NNN on line 76 -Defining \seq_gconcat:ccc on line 79 -Defining \seq_if_empty_p:N on line 80 -Defining \seq_if_empty:NTF on line 80 -Defining \seq_if_empty:NT on line 80 -Defining \seq_if_empty:NF on line 80 -Defining \seq_if_empty_p:c on line 81 -Defining \seq_if_empty:cTF on line 81 -Defining \seq_if_empty:cT on line 81 -Defining \seq_if_empty:cF on line 81 -Defining \seq_if_empty_err:N on line 82 -Defining \seq_if_in:NnTF on line 94 -Defining \seq_if_in:NnT on line 94 -Defining \seq_if_in:NnF on line 94 -Defining \seq_if_in:cVTF on line 95 -Defining \seq_if_in:coTF on line 95 -Defining \seq_if_in:cnTF on line 95 -Defining \seq_if_in:cxTF on line 95 -Defining \seq_if_in:cVT on line 96 -Defining \seq_if_in:coT on line 96 -Defining \seq_if_in:cnT on line 96 -Defining \seq_if_in:cxT on line 96 -Defining \seq_if_in:cVF on line 97 -Defining \seq_if_in:coF on line 97 -Defining \seq_if_in:cnF on line 97 -Defining \seq_if_in:cxF on line 97 -Defining \seq_get:NN on line 98 -Defining \seq_get_aux:w on line 102 -Defining \seq_get:cN on line 105 -Defining \seq_pop_aux:nnNN on line 106 -Defining \seq_pop_aux:w on line 110 -Defining \seq_show:N on line 115 -Defining \seq_show:c on line 116 -Defining \seq_display:N on line 117 -Defining \seq_display:c on line 131 -Defining \seq_put_aux:Nnn on line 132 -Defining \seq_put_aux:w on line 135 -Defining \seq_put_left:Nn on line 136 -Defining \seq_put_left:NV on line 139 -Defining \seq_put_left:No on line 139 -Defining \seq_put_left:Nx on line 139 -Defining \seq_put_left:cn on line 139 -Defining \seq_put_left:cV on line 139 -Defining \seq_put_left:co on line 139 -Defining \seq_put_right:Nn on line 140 -Defining \seq_put_right:NV on line 142 -Defining \seq_put_right:No on line 142 -Defining \seq_put_right:Nx on line 142 -Defining \seq_put_right:cn on line 142 -Defining \seq_put_right:cV on line 142 -Defining \seq_put_right:co on line 142 -Defining \seq_gput_left:Nn on line 143 -Defining \seq_gput_right:Nn on line 147 -Defining \seq_gput_left:NV on line 151 -Defining \seq_gput_left:No on line 151 -Defining \seq_gput_left:Nx on line 151 -Defining \seq_gput_left:cn on line 151 -Defining \seq_gput_left:cV on line 151 -Defining \seq_gput_left:co on line 151 -Defining \seq_gput_right:NV on line 152 -Defining \seq_gput_right:No on line 152 -Defining \seq_gput_right:Nx on line 152 -Defining \seq_gput_right:cn on line 152 -Defining \seq_gput_right:cV on line 152 -Defining \seq_gput_right:co on line 152 -Defining \seq_gput_right:Nc on line 153 -Defining \seq_map_variable_aux:Nnw on line 154 -Defining \seq_map_variable:NNn on line 160 -Defining \seq_map_variable:cNn on line 164 -Defining \seq_map_break: on line 166 -Defining \seq_map_break:n on line 167 -Defining \seq_map_function:NN on line 168 -Defining \seq_map_function:cN on line 173 -Defining \seq_map_inline:Nn on line 174 -Defining \seq_map_inline:cn on line 179 -Defining \l_seq_remove_seq on line 180 -Defining \seq_remove_duplicates_aux:NN on line 185 -Defining \seq_remove_duplicates_aux:n on line 190 -Defining \seq_remove_duplicates:N on line 191 -Defining \seq_gremove_duplicates:N on line 194 -Defining \seq_push:Nn on line 197 -Defining \seq_push:NV on line 198 -Defining \seq_push:No on line 199 -Defining \seq_push:cn on line 200 -Defining \seq_pop:NN on line 201 -Defining \seq_pop:cN on line 202 -Defining \seq_gpush:Nn on line 203 -Defining \seq_gpop:NN on line 204 -Defining \seq_gpush:NV on line 205 -Defining \seq_gpush:No on line 205 -Defining \seq_gpush:cn on line 205 -Defining \seq_gpush:Nv on line 205 -Defining \seq_gpop:cN on line 206 -Defining \seq_top:NN on line 207 -Defining \seq_top:cN on line 208 -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3toks.sty -Package: l3toks 2009/06/14 v1412 L3 Experimental Token Registers -Defining \toks_new:c on line 57 -Defining \toks_use:N on line 58 -Defining \toks_use:c on line 59 -Defining \toks_set:Nn on line 60 -Defining \toks_set:NV on line 61 -Defining \toks_set:Nv on line 64 -Defining \toks_set:No on line 67 -Defining \toks_set:Nf on line 68 -Defining \toks_set:Nx on line 71 -Defining \toks_set:cn on line 71 -Defining \toks_set:cV on line 71 -Defining \toks_set:cv on line 71 -Defining \exp_args:Ncv on line 71 -Defining \toks_set:co on line 71 -Defining \toks_set:cx on line 71 -Defining \toks_set:cf on line 71 -Defining \toks_gset:Nn on line 72 -Defining \toks_gset:NV on line 73 -Defining \toks_gset:No on line 73 -Defining \toks_gset:Nx on line 73 -Defining \toks_gset:cn on line 73 -Defining 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-Defining \toks_if_empty_p:N on line 138 -Defining \toks_if_empty:NTF on line 138 -Defining \toks_if_empty:NT on line 138 -Defining \toks_if_empty:NF on line 138 -Defining \toks_if_empty_p:c on line 139 -Defining \toks_if_empty:cTF on line 140 -Defining \toks_if_empty:cT on line 141 -Defining \toks_if_empty:cF on line 142 -Defining \toks_if_eq_p:NN on line 146 -Defining \toks_if_eq:NNTF on line 146 -Defining \toks_if_eq:NNT on line 146 -Defining \toks_if_eq:NNF on line 146 -Defining \toks_if_eq_p:Nc on line 147 -Defining \toks_if_eq_p:cN on line 147 -Defining \toks_if_eq_p:cc on line 147 -Defining \toks_if_eq:NcTF on line 148 -Defining \toks_if_eq:cNTF on line 148 -Defining \toks_if_eq:ccTF on line 148 -Defining \toks_if_eq:NcT on line 149 -Defining \toks_if_eq:cNT on line 149 -Defining \toks_if_eq:ccT on line 149 -Defining \toks_if_eq:NcF on line 150 -Defining \toks_if_eq:cNF on line 150 -Defining \toks_if_eq:ccF on line 150 -\l_tmpb_toks=\toks18 -\l_tmpc_toks=\toks19 -\g_tmpa_toks=\toks20 -\g_tmpb_toks=\toks21 -\g_tmpc_toks=\toks22 -\c_empty_toks=\toks23 -\l_tl_replace_toks=\toks24 -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3int.sty -Package: l3int 2009/05/28 v1362 L3 Experimental Integer module -Defining \int_to_roman:w on line 56 -Defining \int_to_number:w on line 57 -Defining \int_advance:w on line 58 -Defining \int_new:N on line 59 -Defining \int_new:c on line 63 -Defining \int_set:Nn on line 64 -Defining \int_gset:Nn on line 66 -Defining \int_set:cn on line 69 -Defining \int_gset:cn on line 70 -Defining \int_incr:N on line 71 -Defining \int_decr:N on line 73 -Defining \int_gincr:N on line 75 -Defining \int_gdecr:N on line 78 -Defining \int_incr:c on line 85 -Defining \int_decr:c on line 86 -Defining \int_gincr:c on line 87 -Defining \int_gdecr:c on line 88 -Defining \int_zero:N on line 89 -Defining \int_zero:c on line 90 -Defining \int_gzero:N on line 91 -Defining \int_gzero:c on line 92 -Defining \int_add:Nn on line 93 -Defining \int_sub:Nn on line 96 -Defining \int_gadd:Nn on line 99 -Defining \int_gsub:Nn on line 102 -Defining \int_add:cn on line 105 -Defining \int_gadd:cn on line 106 -Defining \int_sub:cn on line 107 -Defining \int_gsub:cn on line 108 -Defining \int_use:N on line 109 -Defining \int_use:c on line 110 -Defining \int_show:N on line 111 -Defining \int_show:c on line 112 -Defining \int_to_arabic:n on line 113 -Defining \int_roman_lcuc_mapping:Nnn on line 114 -Defining \int_to_roman:n on line 126 -Defining \int_to_Roman:n on line 130 -Defining \int_to_roman_lcuc:NN on line 134 -Defining \int_alph_default_conversion_rule:n on line 148 -Defining \int_Alph_default_conversion_rule:n on line 157 -Defining \int_to_alph:n on line 166 -Defining \int_to_Alph:n on line 170 -Defining \int_to_symbol:n on line 174 -Defining \int_symbol_math_conversion_rule:n on line 185 -Defining \int_symbol_text_conversion_rule:n on line 198 -Defining \l_tmpa_int on line 211 -\l_tmpa_int=\count95 -Defining \l_tmpb_int on 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\c_ten_thousand_two on line 257 -Defining \c_ten_thousand_three on line 258 -Defining \c_ten_thousand_four on line 259 -Defining \c_twenty_thousand on line 260 -Defining \c_max_int on line 261 -\c_max_int=\count100 -Defining \int_get_sign_and_digits:n on line 262 -Defining \int_get_sign:n on line 265 -Defining \int_get_digits:n on line 268 -Defining \int_get_sign_and_digits_aux:nNNN on line 271 -Defining \int_get_sign_and_digits_aux:oNNN on line 287 -Defining \exp_args:NoNNN on line 287 -Defining \int_convert_from_base_ten_aux:nnn on line 300 -Defining \int_convert_from_base_ten_aux:nfn on line 313 -Defining \exp_args:Nnfn on line 313 -Defining \int_convert_from_base_ten_aux:ffn on line 314 -Defining \exp_args:Nffn on line 314 -Defining \int_convert_to_base_ten_aux:nn on line 333 -Defining \int_convert_to_base_ten_auxi:nnN on line 336 -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3prg.sty -Package: l3prg 2009/09/20 v1545 L3 Experimental control structures -Defining \group_align_safe_begin: on line 72 -Defining \group_align_safe_end: on line 74 -Defining \scan_align_safe_stop: on line 75 -Defining \prg_replicate:nn on line 85 -Defining \prg_replicate_aux:N on line 91 -Defining \prg_replicate_first_aux:N on line 94 -Defining \prg_replicate_ on line 97 -Defining \prg_replicate_0:n on line 98 -Defining \prg_replicate_1:n on line 99 -Defining \prg_replicate_2:n on line 100 -Defining \prg_replicate_3:n on line 101 -Defining \prg_replicate_4:n on line 103 -Defining \prg_replicate_5:n on line 105 -Defining \prg_replicate_6:n on line 107 -Defining \prg_replicate_7:n on line 109 -Defining \prg_replicate_8:n on line 111 -Defining \prg_replicate_9:n on line 113 -Defining \prg_replicate_first_0:n on line 115 -Defining \prg_replicate_first_1:n on line 116 -Defining \prg_replicate_first_2:n on line 117 -Defining \prg_replicate_first_3:n on line 118 -Defining \prg_replicate_first_4:n on line 119 -Defining \prg_replicate_first_5:n on line 120 -Defining \prg_replicate_first_6:n on line 121 -Defining \prg_replicate_first_7:n on line 122 -Defining \prg_replicate_first_8:n on line 123 -Defining \prg_replicate_first_9:n on line 124 -Defining \prg_stepwise_function:nnnN on line 125 -Defining \prg_stepwise_function_incr:nnnN on line 131 -Defining \prg_stepwise_function_decr:nnnN on line 140 -Defining \g_prg_inline_level_int on line 149 -\g_prg_inline_level_int=\count101 -Defining \prg_stepwise_inline:nnnn on line 150 -Defining \prg_stepwise_inline_incr:Nnnn on line 160 -Defining \prg_stepwise_inline_decr:Nnnn on line 168 -Defining \prg_stepwise_variable:nnnNn on line 176 -Defining \prg_stepwise_variable_incr:nnnNn on line 182 -Defining \prg_stepwise_variable_decr:nnnNn on line 190 -Defining \bool_new:N on line 198 -Defining \bool_new:c on line 199 -Defining \bool_set_true:N on line 200 -Defining \bool_set_true:c on line 201 -Defining \bool_set_false:N on line 202 -Defining \bool_set_false:c on line 203 -Defining \bool_gset_true:N on line 204 -Defining \bool_gset_true:c on line 205 -Defining \bool_gset_false:N on line 206 -Defining \bool_gset_false:c on line 207 -Defining \bool_set_eq:NN on line 208 -Defining \bool_set_eq:Nc on line 209 -Defining \bool_set_eq:cN on line 210 -Defining \bool_set_eq:cc on line 211 -Defining \bool_gset_eq:NN on line 212 -Defining \bool_gset_eq:Nc on line 213 -Defining \bool_gset_eq:cN on line 214 -Defining \bool_gset_eq:cc on line 215 -Defining \l_tmpa_bool on line 216 -Defining \g_tmpa_bool on line 217 -Defining \bool_if_p:c on line 221 -Defining \bool_if:cTF on line 222 -Defining \bool_if:cT on line 223 -Defining \bool_if:cF on line 224 -Defining \bool_while_do:Nn on line 225 -Defining \bool_while_do:cn on line 228 -Defining \bool_until_do:Nn on line 229 -Defining \bool_until_do:cn on line 232 -Defining \bool_do_while:Nn on line 233 -Defining \bool_do_while:cn on line 236 -Defining \bool_do_until:Nn on line 237 -Defining \bool_do_until:cn on line 240 -Defining \bool_cleanup:N on line 259 -Defining \bool_choose:NN on line 263 -Defining \bool_&_1:w on line 264 -Defining \bool_|_0:w on line 265 -Defining \bool_)_0:w on line 266 -Defining \bool_)_1:w on line 267 -Defining \bool_S_0:w on line 268 -Defining \bool_S_1:w on line 269 -Defining \bool_set:Nn on line 283 -Defining \bool_gset:Nn on line 284 -Defining \bool_set:cn on line 287 -Defining \bool_gset:cn on line 288 -Defining \bool_not_p:n on line 289 -Defining \bool_xor_p:nn on line 290 -Defining \bool_while_do:nn on line 298 -Defining \bool_until_do:nn on line 301 -Defining \bool_do_while:nn on line 304 -Defining \bool_do_until:nn on line 307 -Defining \prg_case_int:nnn on line 310 -Defining \prg_case_int_aux:nnn on line 314 -Defining \prg_case_dim:nnn on line 320 -Defining \prg_case_dim_aux:nnn on line 324 -Defining \prg_case_str:nnn on line 330 -Defining \prg_case_str_aux:nnn on line 334 -Defining \prg_case_tl:Nnn on line 340 -Defining \prg_case_tl_aux:NNn on line 344 -Defining \prg_end_case:nw on line 350 -Defining \prg_define_quicksort:nnn on line 352 -Defining \prg_variable_get_scope:N on line 442 -Defining \prg_variable_get_scope_aux:w on line 442 -Defining \prg_variable_get_type:N on line 459 -Defining \prg_variable_get_type_aux:w on line 459 -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3clist.sty -Package: l3clist 2009/08/05 v1441 L3 Experimental comma separated lists -Defining \clist_new:N on line 56 -Defining \clist_new:c on line 57 -Defining \clist_clear:N on line 58 -Defining \clist_clear:c on line 59 -Defining \clist_gclear:N on line 60 -Defining \clist_gclear:c on line 61 -Defining \clist_clear_new:N on line 62 -Defining \clist_clear_new:c on line 63 -Defining \clist_gclear_new:N on line 64 -Defining \clist_gclear_new:c on line 65 -Defining \clist_set_eq:NN on line 66 -Defining \clist_set_eq:cN on line 67 -Defining \clist_set_eq:Nc on line 68 -Defining \clist_set_eq:cc on line 69 -Defining \clist_gset_eq:NN on line 70 -Defining \clist_gset_eq:cN on line 71 -Defining \clist_gset_eq:Nc on line 72 -Defining \clist_gset_eq:cc on line 73 -Defining \clist_set_from_seq_aux:NNN on line 74 -Defining \clist_set_from_seq:NN on line 81 -Defining \clist_gset_from_seq:NN on line 82 -Defining \clist_if_empty_p:N on line 83 -Defining \clist_if_empty:NTF on line 83 -Defining \clist_if_empty:NT on line 83 -Defining \clist_if_empty:NF on line 83 -Defining \clist_if_empty_p:c on line 84 -Defining \clist_if_empty:cTF on line 84 -Defining \clist_if_empty:cT on line 84 -Defining \clist_if_empty:cF on line 84 -Defining \clist_if_empty_err:N on line 85 -Defining \clist_if_eq_p:NN on line 91 -Defining \clist_if_eq:NNTF on line 91 -Defining \clist_if_eq:NNT on line 91 -Defining \clist_if_eq:NNF on line 91 -Defining \clist_if_eq_p:cN on line 92 -Defining \clist_if_eq:cNTF on line 92 -Defining \clist_if_eq:cNT on line 92 -Defining \clist_if_eq:cNF on line 92 -Defining \clist_if_eq_p:Nc on line 93 -Defining \clist_if_eq:NcTF on line 93 -Defining \clist_if_eq:NcT on line 93 -Defining 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on line 160 -Defining \clist_put_right:NV on line 163 -Defining \clist_put_right:No on line 163 -Defining \clist_put_right:Nx on line 163 -Defining \clist_put_right:cn on line 163 -Defining \clist_put_right:cV on line 163 -Defining \clist_put_right:co on line 163 -Defining \clist_gput_right:Nn on line 164 -Defining \clist_gput_right:NV on line 167 -Defining \clist_gput_right:No on line 167 -Defining \clist_gput_right:Nx on line 167 -Defining \clist_gput_right:cn on line 167 -Defining \clist_gput_right:cV on line 167 -Defining \clist_gput_right:co on line 167 -Defining \clist_map_function:NN on line 168 -Defining \clist_map_function:cN on line 174 -Defining \clist_map_function:nN on line 175 -Defining \clist_map_function_aux:Nw on line 180 -Defining \clist_map_break: on line 185 -Defining \g_clist_inline_level_int on line 186 -\g_clist_inline_level_int=\count102 -Defining \clist_map_inline:Nn on line 187 -Defining \clist_map_inline:cn on line 198 -Defining \clist_map_inline:nn on line 199 -Defining \clist_map_variable:nNn on line 210 -Defining \clist_map_variable:NNn on line 216 -Defining \clist_map_variable:cNn on line 217 -Defining \exp_args:NcNn on line 217 -Defining \clist_map_variable_aux:Nnw on line 218 -Defining \clist_concat_aux:NNNN on line 223 -Defining \clist_concat:NNN on line 232 -Defining \clist_gconcat:NNN on line 233 -Defining \clist_concat:ccc on line 234 -Defining \clist_gconcat:ccc on line 235 -Defining \l_clist_remove_clist on line 236 -Defining \clist_remove_duplicates_aux:NN on line 241 -Defining \clist_remove_duplicates_aux:n on line 246 -Defining \clist_remove_duplicates:N on line 247 -Defining \clist_gremove_duplicates:N on line 250 -Defining \clist_remove_element:Nn on line 253 -Defining \clist_gremove_element:Nn on line 256 -Defining \clist_remove_element_aux:NNn on line 268 -Defining \clist_remove_element_aux:n on line 269 -Defining \clist_push:Nn on line 270 -Defining \clist_push:NV on line 271 -Defining \clist_push:No on line 272 -Defining \clist_push:cn on line 273 -Defining \clist_pop:NN on line 274 -Defining \clist_pop:cN on line 275 -Defining \clist_gpush:Nn on line 276 -Defining \clist_gpush:NV on line 277 -Defining \clist_gpush:No on line 278 -Defining \clist_gpush:cn on line 279 -Defining \clist_gpop:NN on line 280 -Defining \clist_gpop:cN on line 281 -Defining \clist_top:NN on line 282 -Defining \clist_top:cN on line 283 -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3token.sty -Package: l3token 2009/09/22 v1550 L3 Experimental token investigation and manip -ulation -Defining \char_set_catcode:w on line 56 -Defining \char_set_catcode:nn on line 57 -Defining \char_value_catcode:w on line 60 -Defining \char_value_catcode:n on line 61 -Defining \char_show_value_catcode:w on line 64 -Defining \char_show_value_catcode:n on line 67 -Defining \char_make_escape:N on line 70 -Defining \char_make_begin_group:N on line 71 -Defining \char_make_end_group:N on line 72 -Defining \char_make_math_shift:N on line 73 -Defining \char_make_alignment:N on line 74 -Defining \char_make_end_line:N on line 75 -Defining \char_make_parameter:N on line 76 -Defining \char_make_math_superscript:N on line 77 -Defining \char_make_math_subscript:N on line 78 -Defining \char_make_ignore:N on line 79 -Defining \char_make_space:N on line 80 -Defining \char_make_letter:N on line 81 -Defining \char_make_other:N on line 82 -Defining \char_make_active:N on line 83 -Defining \char_make_comment:N on line 84 -Defining \char_make_invalid:N on line 85 -Defining \char_make_escape:n on line 86 -Defining \char_make_begin_group:n on line 87 -Defining \char_make_end_group:n on line 88 -Defining \char_make_math_shift:n on line 89 -Defining \char_make_alignment:n on line 90 -Defining \char_make_end_line:n on line 91 -Defining \char_make_parameter:n on line 92 -Defining \char_make_math_superscript:n on line 93 -Defining \char_make_math_subscript:n on line 94 -Defining \char_make_ignore:n on line 95 -Defining \char_make_space:n on line 96 -Defining \char_make_letter:n on line 97 -Defining \char_make_other:n on line 98 -Defining \char_make_active:n on line 99 -Defining \char_make_comment:n on line 100 -Defining \char_make_invalid:n on line 101 -Defining \char_set_mathcode:w on line 102 -Defining \char_set_mathcode:nn on line 103 -Defining \char_gset_mathcode:w on line 106 -Defining \char_gset_mathcode:nn on line 107 -Defining \char_value_mathcode:w on line 110 -Defining \char_value_mathcode:n on line 111 -Defining \char_show_value_mathcode:w on line 114 -Defining \char_show_value_mathcode:n on line 115 -Defining \char_set_lccode:w on line 118 -Defining \char_set_lccode:nn on line 119 -Defining \char_value_lccode:w on line 122 -Defining \char_value_lccode:n on line 123 -Defining \char_show_value_lccode:w on line 125 -Defining \char_show_value_lccode:n on line 126 -Defining \char_set_uccode:w on line 128 -Defining \char_set_uccode:nn on line 129 -Defining \char_value_uccode:w on line 132 -Defining \char_value_uccode:n on line 133 -Defining \char_show_value_uccode:w on line 135 -Defining \char_show_value_uccode:n on line 136 -Defining \char_set_sfcode:w on line 138 -Defining \char_set_sfcode:nn on line 139 -Defining \char_value_sfcode:w on line 142 -Defining \char_value_sfcode:n on line 143 -Defining \char_show_value_sfcode:w on line 146 -Defining \char_show_value_sfcode:n on line 147 -Defining \token_new:Nn on line 150 -Defining \c_group_begin_token on line 151 -Defining \c_group_end_token on line 152 -Defining \c_math_shift_token on line 155 -Defining \c_alignment_tab_token on line 157 -Defining \c_parameter_token on line 158 -Defining \c_math_superscript_token on line 159 -Defining \c_math_subscript_token on line 161 -Defining \c_space_token on line 162 -Defining \c_letter_token on line 163 -Defining \c_other_char_token on line 164 -Defining \token_if_group_begin_p:N on line 171 -Defining \token_if_group_begin:NTF on line 171 -Defining \token_if_group_begin:NT on line 171 -Defining \token_if_group_begin:NF on line 171 -Defining \token_if_group_end_p:N on line 175 -Defining \token_if_group_end:NTF on line 175 -Defining \token_if_group_end:NT on line 175 -Defining \token_if_group_end:NF on line 175 -Defining \token_if_math_shift_p:N on line 179 -Defining \token_if_math_shift:NTF on line 179 -Defining \token_if_math_shift:NT on line 179 -Defining \token_if_math_shift:NF on line 179 -Defining \token_if_alignment_tab_p:N on line 183 -Defining \token_if_alignment_tab:NTF on line 183 -Defining \token_if_alignment_tab:NT on line 183 -Defining \token_if_alignment_tab:NF on line 183 -Defining \token_if_parameter_p:N on line 187 -Defining \token_if_parameter:NTF on line 187 -Defining \token_if_parameter:NT on line 187 -Defining \token_if_parameter:NF on line 187 -Defining \token_if_math_superscript_p:N on line 191 -Defining \token_if_math_superscript:NTF on line 191 -Defining \token_if_math_superscript:NT on line 191 -Defining \token_if_math_superscript:NF on line 191 -Defining \token_if_math_subscript_p:N on line 195 -Defining \token_if_math_subscript:NTF on line 195 -Defining \token_if_math_subscript:NT on line 195 -Defining \token_if_math_subscript:NF on line 195 -Defining \token_if_space_p:N on line 199 -Defining \token_if_space:NTF on line 199 -Defining \token_if_space:NT on line 199 -Defining \token_if_space:NF on line 199 -Defining \token_if_letter_p:N on line 203 -Defining \token_if_letter:NTF on line 203 -Defining \token_if_letter:NT on line 203 -Defining \token_if_letter:NF on line 203 -Defining \token_if_other_char_p:N on line 207 -Defining \token_if_other_char:NTF on line 207 -Defining \token_if_other_char:NT on line 207 -Defining \token_if_other_char:NF on line 207 -Defining \token_if_active_char_p:N on line 211 -Defining \token_if_active_char:NTF on line 211 -Defining \token_if_active_char:NT on line 211 -Defining \token_if_active_char:NF on line 211 -Defining \token_if_eq_meaning_p:NN on line 215 -Defining \token_if_eq_meaning:NNTF on line 215 -Defining \token_if_eq_meaning:NNT on line 215 -Defining \token_if_eq_meaning:NNF on line 215 -Defining \token_if_eq_catcode_p:NN on line 219 -Defining \token_if_eq_catcode:NNTF on line 219 -Defining \token_if_eq_catcode:NNT on line 219 -Defining \token_if_eq_catcode:NNF on line 219 -Defining \token_if_eq_charcode_p:NN on line 223 -Defining \token_if_eq_charcode:NNTF on line 223 -Defining \token_if_eq_charcode:NNT on line 223 -Defining \token_if_eq_charcode:NNF on line 223 -Defining \token_if_macro_p:N on line 226 -Defining \token_if_macro:NTF on line 226 -Defining \token_if_macro:NT on line 226 -Defining \token_if_macro:NF on line 226 -Defining \token_if_macro_p_aux:w on line 227 -Defining \token_if_cs_p:N on line 233 -Defining \token_if_cs:NTF on line 233 -Defining \token_if_cs:NT on line 233 -Defining \token_if_cs:NF on line 233 -Defining \token_if_expandable_p:N on line 241 -Defining \token_if_expandable:NTF on line 241 -Defining \token_if_expandable:NT on line 241 -Defining \token_if_expandable:NF on line 241 -Defining \token_if_chardef_p:N on line 333 -Defining \token_if_chardef:NTF on line 333 -Defining \token_if_chardef:NT on line 333 -Defining \token_if_chardef:NF on line 333 -Defining \token_if_chardef_aux:w on line 333 -Defining \token_if_mathchardef_p:N on line 333 -Defining \token_if_mathchardef:NTF on line 333 -Defining \token_if_mathchardef:NT on line 333 -Defining \token_if_mathchardef:NF on line 333 -Defining \token_if_mathchardef_aux:w on line 333 -Defining \token_if_int_register_p:N on line 333 -Defining \token_if_int_register:NTF on line 333 -Defining \token_if_int_register:NT on line 333 -Defining \token_if_int_register:NF on line 333 -Defining \token_if_int_register_aux:w on line 333 -Defining \token_if_skip_register_p:N on line 333 -Defining \token_if_skip_register:NTF on line 333 -Defining \token_if_skip_register:NT on line 333 -Defining \token_if_skip_register:NF on line 333 -Defining \token_if_skip_register_aux:w on line 333 -Defining \token_if_dim_register_p:N on line 333 -Defining \token_if_dim_register:NTF on line 333 -Defining \token_if_dim_register:NT on line 333 -Defining \token_if_dim_register:NF on line 333 -Defining \token_if_dim_register_aux:w on line 333 -Defining \token_if_toks_register_p:N on line 333 -Defining \token_if_toks_register:NTF on line 333 -Defining \token_if_toks_register:NT on line 333 -Defining \token_if_toks_register:NF on line 333 -Defining \token_if_toks_register_aux:w on line 333 -Defining \token_if_protected_macro_p:N on line 333 -Defining \token_if_protected_macro:NTF on line 333 -Defining \token_if_protected_macro:NT on line 333 -Defining \token_if_protected_macro:NF on line 333 -Defining \token_if_protected_macro_aux:w on line 333 -Defining \token_if_long_macro_p:N on line 333 -Defining \token_if_long_macro:NTF on line 333 -Defining \token_if_long_macro:NT on line 333 -Defining \token_if_long_macro:NF on line 333 -Defining \token_if_long_macro_aux:w on line 333 -Defining \token_if_protected_long_macro_p:N on line 333 -Defining \token_if_protected_long_macro:NTF on line 333 -Defining \token_if_protected_long_macro:NT on line 333 -Defining \token_if_protected_long_macro:NF on line 333 -Defining \token_if_protected_long_macro_aux:w on line 333 -Defining \token_get_prefix_arg_replacement_aux:w on line 364 -Defining \token_get_prefix_spec:N on line 364 -Defining \token_get_arg_spec:N on line 364 -Defining \token_get_replacement_spec:N on line 364 -Defining \token_if_primitive_p:N on line 383 -Defining \token_if_primitive:NTF on line 383 -Defining \token_if_primitive:NT on line 383 -Defining \token_if_primitive:NF on line 383 -Defining \token_if_primitive_p_aux:N on line 384 -Defining \l_peek_token on line 405 -Defining \g_peek_token on line 406 -Defining \l_peek_search_token on line 407 -Defining \peek_after:NN on line 408 -Defining \peek_gafter:NN on line 409 -Defining \l_peek_true_tl on line 412 -Defining \l_peek_false_tl on line 413 -Defining \peek_tmp:w on line 414 -Defining \l_peek_search_tl on line 415 -Defining \peek_token_generic:NNTF on line 416 -Defining \peek_token_generic:NNT on line 424 -Defining \peek_token_generic:NNF on line 427 -Defining \peek_token_remove_generic:NNTF on line 430 -Defining \peek_token_remove_generic:NNT on line 439 -Defining \peek_token_remove_generic:NNF on line 442 -Defining \l_peek_true_aux_tl on line 445 -Defining \c_peek_true_remove_next_tl on line 448 -Defining \peek_execute_branches_meaning: on line 449 -Defining \peek_execute_branches_catcode: on line 456 -Defining \peek_execute_branches_charcode: on line 463 -Defining \peek_execute_branches_charcode_aux:NN on line 472 -Defining \peek_def_aux:nnnn on line 480 -Defining \peek_def_aux_ii:nnnnn on line 485 -Defining \peek_meaning:NTF on line 498 -Defining \peek_meaning:NT on line 498 -Defining \peek_meaning:NF on line 498 -Defining \peek_meaning_ignore_spaces:NTF on line 503 -Defining \peek_meaning_ignore_spaces:NT on line 503 -Defining \peek_meaning_ignore_spaces:NF on line 503 -Defining \peek_meaning_remove:NTF on line 508 -Defining \peek_meaning_remove:NT on line 508 -Defining \peek_meaning_remove:NF on line 508 -Defining \peek_meaning_remove_ignore_spaces:NTF on line 513 -Defining \peek_meaning_remove_ignore_spaces:NT on line 513 -Defining \peek_meaning_remove_ignore_spaces:NF on line 513 -Defining \peek_catcode:NTF on line 518 -Defining \peek_catcode:NT on line 518 -Defining \peek_catcode:NF on line 518 -Defining \peek_catcode_ignore_spaces:NTF on line 523 -Defining \peek_catcode_ignore_spaces:NT on line 523 -Defining \peek_catcode_ignore_spaces:NF on line 523 -Defining \peek_catcode_remove:NTF on line 528 -Defining \peek_catcode_remove:NT on line 528 -Defining \peek_catcode_remove:NF on line 528 -Defining \peek_catcode_remove_ignore_spaces:NTF on line 533 -Defining \peek_catcode_remove_ignore_spaces:NT on line 533 -Defining \peek_catcode_remove_ignore_spaces:NF on line 533 -Defining \peek_charcode:NTF on line 538 -Defining \peek_charcode:NT on line 538 -Defining \peek_charcode:NF on line 538 -Defining \peek_charcode_ignore_spaces:NTF on line 543 -Defining \peek_charcode_ignore_spaces:NT on line 543 -Defining \peek_charcode_ignore_spaces:NF on line 543 -Defining \peek_charcode_remove:NTF on line 548 -Defining \peek_charcode_remove:NT on line 548 -Defining \peek_charcode_remove:NF on line 548 -Defining \peek_charcode_remove_ignore_spaces:NTF on line 553 -Defining \peek_charcode_remove_ignore_spaces:NT on line 553 -Defining \peek_charcode_remove_ignore_spaces:NF on line 553 -Defining \peek_ignore_spaces_aux: on line 554 -Defining \peek_ignore_spaces_execute_branches: on line 557 -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3io.sty -Package: l3io 2009/05/31 v1369 L3 Experimental i/o module -Defining \iow_new:c on line 57 -Defining \iow_open:Nn on line 58 -Defining \iow_open:cn on line 62 -Defining \iow_close:N on line 63 -Defining \c_iow_term_stream on line 64 -Defining \c_ior_term_stream on line 65 -Defining \c_iow_log_stream on line 66 -Defining \c_ior_log_stream on line 67 -Defining \iow_now:Nx on line 68 -Defining \iow_now:Nn on line 69 -Defining \iow_log:n on line 73 -Defining \iow_term:n on line 75 -Defining \iow_now_when_avail:Nn on line 76 -Defining \iow_now_when_avail:cn on line 79 -Defining \iow_now_buffer_safe_aux:w on line 80 -Defining \iow_now_buffer_safe:Nx on line 83 -Defining \iow_now_buffer_safe:Nn on line 86 -Defining \iow_shipout_x:Nx on line 90 -Defining \iow_shipout:Nn on line 91 -Defining \iow_shipout:Nx on line 94 -Defining \iow_newline: on line 95 -Defining \iow_space: on line 96 -Defining \iow_char:N on line 97 -Defining \c_iow_comment_char on line 98 -Defining \c_iow_lbrace_char on line 99 -Defining \c_iow_rbrace_char on line 100 -Defining \ior_open:Nn on line 103 -Defining \if_eof:w on line 107 -Defining \ior_if_eof_p:N on line 110 -Defining \ior_if_eof:NTF on line 110 -Defining \ior_if_eof:NT on line 110 -Defining \ior_if_eof:NF on line 110 -Defining \ior_to:NN on line 111 -Defining \ior_gto:NN on line 114 -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3prop.sty -Package: l3prop 2009/09/16 v1536 L3 Experimental Property Lists -Defining \q_prop on line 56 -Defining \prop_new:N on line 57 -Defining \prop_new:c on line 58 -Defining \prop_clear:N on line 59 -Defining \prop_clear:c on line 60 -Defining \prop_gclear:N on line 61 -Defining \prop_gclear:c on line 62 -Defining \prop_set_eq:NN on line 63 -Defining \prop_set_eq:Nc on line 64 -Defining \prop_set_eq:cN on line 65 -Defining \prop_set_eq:cc on line 66 -Defining \prop_gset_eq:NN on line 67 -Defining \prop_gset_eq:Nc on line 68 -Defining \prop_gset_eq:cN on line 69 -Defining \prop_gset_eq:cc on line 70 -Defining \prop_show:N on line 71 -Defining \prop_show:c on line 72 -Defining \prop_display:N on line 73 -Defining \prop_display:c on line 89 -Defining \prop_split_aux:Nnn on line 90 -Defining \prop_get:NnN on line 96 -Defining \prop_get_aux:w on line 99 -Defining \prop_get:NVN on line 100 -Defining \exp_args:NNVN on line 100 -Defining \prop_get:cnN on line 100 -Defining \exp_args:NcnN on line 100 -Defining \prop_get:cVN on line 100 -Defining \exp_args:NcVN on line 100 -Defining \prop_gget:NnN on line 101 -Defining \prop_gget_aux:w on line 103 -Defining \prop_gget:NVN on line 104 -Defining \prop_gget:cnN on line 104 -Defining \prop_gget:cVN on line 104 -Defining \prop_get_gdel:NnN on line 105 -Defining \prop_get_del_aux:w on line 107 -Defining \prop_put:Nnn on line 113 -Defining \prop_gput:Nnn on line 119 -Defining \prop_put_aux:w on line 125 -Defining \prop_put:NnV on line 133 -Defining \exp_args:NNnV on line 133 -Defining \prop_put:NVn on line 133 -Defining \exp_args:NNVn on line 133 -Defining \prop_put:NVV on line 133 -Defining \exp_args:NNVV on line 133 -Defining \prop_put:cnn on line 133 -Defining \prop_gput:NnV on line 134 -Defining \prop_gput:Nno on line 134 -Defining \prop_gput:Nnx on line 134 -Defining \prop_gput:Nox on line 134 -Defining \prop_gput:cnn on line 134 -Defining \prop_gput:ccx on line 134 -Defining \prop_del:Nn on line 135 -Defining \prop_gdel:Nn on line 137 -Defining \prop_del_aux:w on line 139 -Defining \prop_del:NV on line 146 -Defining \prop_gdel:NV on line 147 -Defining \prop_gput_if_new:Nnn on line 148 -Defining \prop_put_if_new_aux:w on line 150 -Defining \prop_if_empty_p:N on line 152 -Defining \prop_if_empty:NTF on line 152 -Defining \prop_if_empty:NT on line 152 -Defining \prop_if_empty:NF on line 152 -Defining \prop_if_empty_p:c on line 153 -Defining \prop_if_empty:cTF on line 153 -Defining \prop_if_empty:cT on line 153 -Defining \prop_if_empty:cF on line 153 -Defining \prop_if_eq_p:NN on line 154 -Defining \prop_if_eq:NNTF on line 154 -Defining \prop_if_eq:NNT on line 154 -Defining \prop_if_eq:NNF on line 154 -Defining \prop_if_eq_p:cN on line 155 -Defining \prop_if_eq:cNTF on line 155 -Defining \prop_if_eq:cNT on line 155 -Defining \prop_if_eq:cNF on line 155 -Defining \prop_if_eq_p:Nc on line 156 -Defining \prop_if_eq:NcTF on line 156 -Defining \prop_if_eq:NcT on line 156 -Defining \prop_if_eq:NcF on line 156 -Defining \prop_if_eq_p:cc on line 157 -Defining \prop_if_eq:ccTF on line 157 -Defining \prop_if_eq:ccT on line 157 -Defining \prop_if_eq:ccF on line 157 -Defining \prop_if_in:NnTF on line 160 -Defining \prop_if_in:NnT on line 160 -Defining \prop_if_in:NnF on line 160 -Defining \prop_if_in_aux:w on line 161 -Defining \prop_if_in:NVTF on line 164 -Defining \prop_if_in:NoTF on line 164 -Defining \prop_if_in:cnTF on line 164 -Defining \prop_if_in:ccTF on line 164 -Defining \prop_if_in:NVT on line 165 -Defining \prop_if_in:NoT on line 165 -Defining \prop_if_in:cnT on line 165 -Defining \prop_if_in:ccT on line 165 -Defining \prop_if_in:NVF on line 166 -Defining \prop_if_in:NoF on line 166 -Defining \prop_if_in:cnF on line 166 -Defining \prop_if_in:ccF on line 166 -Defining \prop_map_function:cN on line 178 -Defining \prop_map_function:Nc on line 178 -Defining \prop_map_function:cc on line 178 -Defining \g_prop_inline_level_num on line 179 -Defining \prop_map_inline:Nn on line 180 -Defining \prop_map_inline:cn on line 188 -Defining \prop_map_break: on line 189 -) -(/usr/share/texmf-texlive/tex/latex/expl3/l3msg.sty -Package: l3msg 2009/09/01 v1502 L3 Experimental LaTeX Messages module -Defining \c_msg_fatal_tl on line 58 -Defining \c_msg_error_tl on line 59 -Defining \c_msg_warning_tl on line 60 -Defining \c_msg_info_tl on line 61 -Defining \c_msg_fatal_text_tl on line 64 -Defining \c_msg_help_text_tl on line 67 -Defining \c_msg_kernel_bug_text_tl on line 70 -Defining \c_msg_kernel_bug_more_text_tl on line 76 -Defining \c_msg_no_info_text_tl on line 80 -Defining \c_msg_return_text_tl on line 86 -Defining \c_msg_hide_tl - on line 94 -Defining \c_msg_on_line_tl on line 95 -Defining \c_msg_text_prefix_tl on line 96 -Defining \c_msg_more_text_prefix_tl on line 97 -Defining \c_msg_code_prefix_tl on line 98 -Defining \l_msg_class_tl on line 99 -Defining \l_msg_current_class_tl on line 100 -Defining \l_msg_names_clist on line 101 -\l_msg_redirect_classes_prop=\toks25 -\l_msg_redirect_names_prop=\toks26 -Defining \l_msg_redirect_classes_clist on line 104 -Defining \msg_line_number: on line 107 -Defining \msg_line_context: on line 113 -Defining \msg_newline: on line 114 -Defining \msg_two_newlines: on line 115 -Defining \msg_space: on line 116 -Defining \msg_two_spaces: on line 117 -Defining \msg_four_spaces: on line 118 -Defining \msg_generic_new:nnnn on line 119 -Defining \msg_generic_new:nnn on line 123 -Defining \msg_generic_new:nn on line 127 -Defining \msg_generic_set:nnnn on line 131 -Defining \msg_generic_set:nnn on line 136 -Defining \msg_generic_set:nn on line 141 -Defining \msg_generic_set_clist:n on line 146 -Defining \msg_generic_set_text:nn on line 154 -Defining \msg_generic_set_more_text:nnn on line 163 -Defining \msg_generic_set_code:nnnn on line 164 -Defining \msg_generic_set_code:nn on line 180 -Defining \msg_direct_interrupt:xxxxn on line 207 -Defining \msg_direct_interrupt_aux:n on line 214 -Defining \msg_direct_log:xx on line 221 -Defining \msg_direct_term:xx on line 228 -Defining \msg_new:nnnnn on line 229 -Defining \msg_new:nnnn on line 232 -Defining \msg_new:nnn on line 235 -Defining \msg_set:nnnnn on line 238 -Defining \msg_set:nnnn on line 241 -Defining \msg_set:nnn on line 244 -Defining \msg_class_new:nn on line 247 -Defining \msg_class_set:nn on line 263 -Defining \msg_use:nnnnxx on line 286 -Defining \msg_use_code: on line 287 -Defining \msg_use_loop:n on line 288 -Defining \msg_use_aux:nnn on line 297 -Defining \msg_use_aux:nn on line 308 -Defining \msg_use_loop_check:nn on line 316 -Defining \msg_fatal:nnxx on line 317 -\l_msg_redirect_fatal_prop=\toks27 -Defining \msg_error:nnxx on line 328 -\l_msg_redirect_error_prop=\toks28 -Defining \msg_warning:nnxx on line 349 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LaTeX Font Info: Try loading font information for OMS+cmr on input line 35. -(/usr/share/texmf-texlive/tex/latex/base/omscmr.fd +(/usr/lib/texlive/texmf-dist/tex/latex/base/omscmr.fd File: omscmr.fd 1999/05/25 v2.5h Standard LaTeX font definitions ) LaTeX Font Info: Font shape `OMS/cmr/m/n' in size <8> not available (Font) Font shape `OMS/cmsy/m/n' tried instead on input line 35. - [4]) [5] [6] + [4]) +File: figur.eps Graphic file (type eps) + +[5] [6] -LaTeX Font Warning: Font shape `OT1/cmr/bx/n' in size <3.83247> not available -(Font) size <5> substituted on input line 437. +LaTeX Font Warning: Font shape `OT1/cmr/bx/n' in size <4.19998> not available +(Font) size <5> substituted on input line 444. -[7] (./mostimportant.py [8]) [9] (./rapport.aux) +[7] [8] (./mostimportant.py) [9] (./rapport.aux) LaTeX Font Warning: Size substitutions with differences (Font) up to 2.90001pt have occurred. ) Here is how much of TeX's memory you used: - 8256 strings out of 495062 - 123525 string characters out of 1182643 - 255580 words of memory out of 3000000 - 11282 multiletter control sequences out of 15000+50000 - 22978 words of font info for 92 fonts, out of 3000000 for 9000 - 28 hyphenation exceptions out of 8191 - 37i,20n,43p,236b,1678s stack positions out of 5000i,500n,10000p,200000b,50000s - -Output written on rapport.dvi (9 pages, 52916 bytes). + 9520 strings out of 493630 + 149872 string characters out of 3146293 + 300141 words of memory out of 3000000 + 12665 multiletter control sequences out of 15000+200000 + 20467 words of font info for 82 fonts, out of 3000000 for 9000 + 831 hyphenation exceptions out of 8191 + 46i,20n,43p,458b,1668s stack positions out of 5000i,500n,10000p,200000b,50000s + +Output written on rapport.dvi (9 pages, 54488 bytes). diff --git a/rapport.pdf b/rapport.pdf index df60801..f5b69aa 100644 Binary files a/rapport.pdf and b/rapport.pdf differ diff --git a/rapport.ps b/rapport.ps index b2ddf50..3036984 100644 --- a/rapport.ps +++ b/rapport.ps 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M}B/d{-3 M}B/e{-2 M}B/f{-1 M} +B/g{0 M}B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p +-3 w}B/n{p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{ +0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end + +%%EndProcSet +%%BeginProcSet: cm-super-ts1.enc 0 0 +% This file is generated from `TS1uni.map' and `glyphlist.txt', `gl-other.txt' +/TS1Encoding [ +% 0x00 +/Grave +/Acute +/Circumflex % ? +/Tilde % ? +/Dieresis +/Hungarumlaut +/Ring % ? +/Caron +/Breve % ? +/Macron +/Dotaccent % ? +/cedilla +/ogonek +/quotesinglbase.ts1 +/.notdef +/.notdef +% 0x10 +/.notdef +/.notdef +/quotedblbase.ts1 +/.notdef +/.notdef +/twelveudash % ? +/threequartersemdash +/afii61664.cap % ? +/arrowleft +/arrowright +/tieaccentlowercase % ? +/tieaccentcapital % ? +/tieaccentlowercase.new % ? +/tieaccentcapital.new % ? +/.notdef +/afii61664.asc % ? +% 0x20 +/uni2422 +/.notdef +/.notdef +/.notdef +/dollar +/.notdef +/.notdef +/quotesingle +/.notdef +/.notdef 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0x80 +/breve.ts1 +/caron.ts1 +/hungarumlaut.ts1 +/dblgrave.ts1 +/dagger +/daggerdbl +/uni2016 +/perthousand +/bullet +/uni2103 +/dollaroldstyle +/centoldstyle +/florin +/colonmonetary +/uni20A9 +/uni20A6 +% 0x90 +/guarani % ? +/peso % ? +/lira +/recipe % ? +/uni203D +/gnaborretni % ? +/dong +/trademark +/uni2031 +/paragraph.alt % ? +/uni0E3F +/afii61352 +/discount % ? +/estimated +/openbullet +/uni2120 +% 0xA0 +/uni2045 +/uni2046 +/cent +/sterling +/currency +/yen +/brokenbar +/section +/dieresis.ts1 +/copyright +/ordfeminine +/copyleft % ? +/logicalnot +/uni2117 +/registered +/macron.ts1 +% 0xB0 +/degree +/plusminus +/twosuperior +/threesuperior +/acute.ts1 +/mu +/paragraph +/periodcentered +/uni203B +/onesuperior +/ordmasculine +/radical +/onequarter +/onehalf +/threequarters +/Euro % or /Euro.alt +% 0xC0 +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +% 0xD0 +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/multiply +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +% 0xE0 +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +% 0xF0 +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/divide +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +/.notdef +] def %%EndProcSet %%BeginProcSet: texps.pro 0 0 @@ -185,34 +464,34 @@ setcmykcolor}DC/Gray{0 0 0 0.50 setcmykcolor}DC/Black{0 0 0 1 setcmykcolor}DC/White{0 0 0 0 setcmykcolor}DC end %%EndProcSet -%%BeginFont: CMBX12 -%!PS-AdobeFont-1.0: CMBX12 003.002 -%%Title: CMBX12 +%%BeginFont: CMSS12 +%!PS-AdobeFont-1.0: CMSS12 003.002 +%%Title: CMSS12 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMBX12. +%Copyright: (), with Reserved Font Name CMSS12. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments -FontDirectory/CMBX12 known{/CMBX12 findfont dup/UniqueID known{dup -/UniqueID get 5000769 eq exch/FontType get 1 eq and}{pop false}ifelse +FontDirectory/CMSS12 known{/CMSS12 findfont dup/UniqueID known{dup +/UniqueID get 5000804 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /CMBX12 def -/FontBBox {-53 -251 1139 750 }readonly def -/UniqueID 5000769 def +/FontName /CMSS12 def +/FontBBox {-62 -251 978 758 }readonly def +/UniqueID 5000804 def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMBX12.) readonly def -/FullName (CMBX12) readonly def +/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMSS12.) readonly def +/FullName (CMSS12) readonly def /FamilyName (Computer Modern) readonly def -/Weight (Bold) readonly def +/Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def @@ -220,660 +499,36 @@ FontDirectory/CMBX12 known{/CMBX12 findfont dup/UniqueID known{dup end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 12 /fi put -dup 41 /parenright put -dup 49 /one put +dup 44 /comma put +dup 46 /period put +dup 48 /zero put dup 50 /two put -dup 67 /C put -dup 80 /P put +dup 53 /five put +dup 55 /seven put +dup 65 /A put +dup 82 /R put +dup 83 /S put dup 97 /a put dup 98 /b put -dup 99 /c put dup 100 /d put dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put dup 105 /i put +dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put +dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put +dup 117 /u put dup 118 /v put -readonly def -currentdict end -currentfile eexec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Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMTI10. +%Copyright: (), with Reserved Font Name CMTI12. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments -FontDirectory/CMTI10 known{/CMTI10 findfont dup/UniqueID known{dup -/UniqueID get 5000828 eq exch/FontType get 1 eq and}{pop false}ifelse +FontDirectory/CMTI12 known{/CMTI12 findfont dup/UniqueID known{dup +/UniqueID get 5000829 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /CMTI10 def -/FontBBox {-35 -250 1124 750 }readonly def -/UniqueID 5000828 def +/FontName /CMTI12 def +/FontBBox {-36 -251 1103 750 }readonly def +/UniqueID 5000829 def /PaintType 0 def /FontInfo 9 dict dup begin 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 @@ -3382,36 +2864,36 @@ A8259430C6D67F1A57AA6AE45ABCEF8E42CCE1243CBC567F367749718C81679A 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark -{restore}if -%%EndFont -%%BeginFont: CMR12 -%!PS-AdobeFont-1.0: CMR12 003.002 -%%Title: CMR12 +{restore}if +%%EndFont +%%BeginFont: CMBX12 +%!PS-AdobeFont-1.0: CMBX12 003.002 +%%Title: CMBX12 %Version: 003.002 %%CreationDate: Mon Jul 13 16:17:00 2009 %%Creator: David M. Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMR12. +%Copyright: (), with Reserved Font Name CMBX12. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments -FontDirectory/CMR12 known{/CMR12 findfont dup/UniqueID known{dup -/UniqueID get 5000794 eq exch/FontType get 1 eq and}{pop false}ifelse +FontDirectory/CMBX12 known{/CMBX12 findfont dup/UniqueID known{dup +/UniqueID get 5000769 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /CMR12 def -/FontBBox {-34 -251 988 750 }readonly def -/UniqueID 5000794 def +/FontName /CMBX12 def +/FontBBox {-53 -251 1139 750 }readonly def +/UniqueID 5000769 def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR12.) readonly def -/FullName (CMR12) readonly def +/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMBX12.) readonly def +/FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def +/Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def @@ -3419,46 +2901,26 @@ FontDirectory/CMR12 known{/CMR12 findfont dup/UniqueID known{dup end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for -dup 40 /parenleft put +dup 12 /fi put dup 41 /parenright put -dup 44 /comma put -dup 46 /period put -dup 48 /zero put dup 49 /one put dup 50 /two put -dup 51 /three put -dup 52 /four put -dup 53 /five put -dup 54 /six put -dup 55 /seven put -dup 56 /eight put -dup 57 /nine put -dup 58 /colon put -dup 65 /A put dup 67 /C put -dup 79 /O put -dup 82 /R put -dup 83 /S put -dup 84 /T put -dup 88 /X put +dup 76 /L put +dup 80 /P put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put -dup 102 /f put -dup 103 /g put dup 105 /i put -dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put -dup 112 /p put dup 114 /r put dup 115 /s put dup 116 /t put -dup 117 /u put dup 118 /v put readonly def currentdict end @@ -3469,402 +2931,285 @@ D9D66F633B846AB284BCF8B0411B772DE5CE3DD325E55798292D7BD972BD75FA 7C56816B03B901BF4A25A07175380E50A213F877C44778B3C5AADBCC86D6E551 E6AF364B0BFCAAD22D8D558C5C81A7D425A1629DD5182206742D1D082A12F078 0FD4F5F6D3129FCFFF1F4A912B0A7DEC8D33A57B5AE0328EF9D57ADDAC543273 -C01924195A181D03F5054A93B71E5065F8D92FE23794D2DB9C535A5E57376651 -F6823308463DC4E0339C78699AC82C769542FD3B410E236AF8AF68CF124D9224 -FD6EE92A38075CAAF82447C7AF41EF96F3ADF62F76FB425BEDE4C4124E7B1E0B -8BF254D91912D3A99557F5427907A56514C5A3EB961B94112077FE9417B70DA0 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Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMR10. +%Copyright: (), with Reserved Font Name CMMI12. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments -FontDirectory/CMR10 known{/CMR10 findfont dup/UniqueID known{dup -/UniqueID get 5000793 eq exch/FontType get 1 eq and}{pop false}ifelse +FontDirectory/CMMI12 known{/CMMI12 findfont dup/UniqueID known{dup +/UniqueID get 5087386 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /CMR10 def -/FontBBox {-40 -250 1009 750 }readonly def -/UniqueID 5000793 def -/PaintType 0 def -/FontInfo 9 dict dup begin -/version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR10.) readonly def -/FullName (CMR10) readonly def -/FamilyName (Computer Modern) readonly def -/Weight (Medium) readonly def -/ItalicAngle 0 def -/isFixedPitch false def -/UnderlinePosition -100 def -/UnderlineThickness 50 def -end readonly def -/Encoding 256 array -0 1 255 {1 index exch /.notdef put} for -dup 11 /ff put -dup 12 /fi put -dup 22 /macron put -dup 37 /percent put -dup 39 /quoteright put -dup 40 /parenleft put -dup 41 /parenright put -dup 43 /plus put -dup 44 /comma put -dup 45 /hyphen put -dup 46 /period put -dup 48 /zero put -dup 49 /one put -dup 50 /two put -dup 51 /three put -dup 52 /four put -dup 53 /five put -dup 54 /six put -dup 55 /seven put -dup 56 /eight put -dup 57 /nine put -dup 58 /colon put -dup 61 /equal put -dup 65 /A put -dup 66 /B put +/FontName /CMMI12 def +/FontBBox {-31 -250 1026 750 }readonly def +/UniqueID 5087386 def +/PaintType 0 def +/FontInfo 10 dict dup begin +/version (003.002) readonly 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Jones %Copyright: Copyright (c) 1997, 2009 American Mathematical Society -%Copyright: (), with Reserved Font Name CMBX10. +%Copyright: (), with Reserved Font Name CMR12. % This Font Software is licensed under the SIL Open Font License, Version 1.1. % This license is in the accompanying file OFL.txt, and is also % available with a FAQ at: http://scripts.sil.org/OFL. %%EndComments -FontDirectory/CMBX10 known{/CMBX10 findfont dup/UniqueID known{dup -/UniqueID get 5000768 eq exch/FontType get 1 eq and}{pop false}ifelse +FontDirectory/CMR12 known{/CMR12 findfont dup/UniqueID known{dup +/UniqueID get 5000794 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def -/FontName /CMBX10 def -/FontBBox {-56 -250 1164 750 }readonly def -/UniqueID 5000768 def +/FontName /CMR12 def +/FontBBox {-34 -251 988 750 }readonly def +/UniqueID 5000794 def /PaintType 0 def /FontInfo 9 dict dup begin /version (003.002) readonly def -/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMBX10.) readonly def -/FullName (CMBX10) readonly def +/Notice (Copyright \050c\051 1997, 2009 American Mathematical Society \050\051, with Reserved Font Name CMR12.) readonly def +/FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def -/Weight (Bold) readonly def +/Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def @@ -6495,16 +5126,72 @@ FontDirectory/CMBX10 known{/CMBX10 findfont dup/UniqueID known{dup end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for +dup 11 /ff put +dup 12 /fi put +dup 22 /macron put +dup 37 /percent put +dup 39 /quoteright put +dup 40 /parenleft put +dup 41 /parenright put +dup 43 /plus put +dup 44 /comma put +dup 45 /hyphen put +dup 46 /period put +dup 48 /zero put +dup 49 /one put +dup 50 /two put +dup 51 /three put +dup 52 /four put +dup 53 /five put +dup 54 /six put +dup 55 /seven put +dup 56 /eight put +dup 57 /nine put +dup 58 /colon put +dup 61 /equal put dup 65 /A put +dup 66 /B put +dup 67 /C put +dup 70 /F put +dup 71 /G put +dup 73 /I put dup 76 /L put +dup 77 /M put +dup 78 /N put +dup 79 /O put dup 80 /P put +dup 82 /R put +dup 83 /S put +dup 84 /T put +dup 85 /U put +dup 87 /W put +dup 94 /circumflex put dup 97 /a put dup 98 /b put dup 99 /c put +dup 100 /d put +dup 101 /e put +dup 102 /f put +dup 103 /g put +dup 104 /h put +dup 105 /i put +dup 106 /j put +dup 107 /k put +dup 108 /l put +dup 109 /m put +dup 110 /n put dup 111 /o put +dup 112 /p put +dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put +dup 117 /u put +dup 118 /v put +dup 119 /w put +dup 120 /x put +dup 121 /y put +dup 122 /z put readonly def currentdict end currentfile eexec @@ -6514,280 +5201,544 @@ D9D66F633B846AB284BCF8B0411B772DE5CE3DD325E55798292D7BD972BD75FA 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b/rapport.tex @@ -9,7 +9,7 @@ \usepackage{color} \usepackage{xfrac} \usepackage{amssymb, amsmath} -\usepackage[margin=1in]{geometry} +\usepackage[margin=0.9in]{geometry} \setcounter{secnumdepth}{0} \lstset{ % @@ -44,14 +44,11 @@ \title{Semester Project 1 in TMA4265} \author{ - Candidate number: XXXXXX + Candidate number: 10037 } \maketitle -\abstract{ -} - %==============00 PROBLEM 1 00================% \section{Problem 1} %==========00 a 00============% @@ -80,8 +77,8 @@ are recurrent with period $d = 1$, while the class $\left\{1, ..., N-1\right\}$ transient with period $d = 2$. \item[$r_0 = 1, 0 < r < 1$] \hfill \\ -This case behaves like the previous case except that the period of the transient -class $\left\{1, ..., N-1\right\}$ has period $d = 1$. +This case behaves like the previous case except that the transient class +$\left\{1, ..., N-1\right\}$ has period $d = 1$. \end{description} @@ -144,7 +141,7 @@ and $\pi_N$ as \pi_N = \frac{p^N}{q^N}\pi_0. \end{equation} This concludes the derivation of the limiting probabilities for the ergodic -chains where $r_0 \neq 0$ +chains where $r_0 \neq 0$. %----------------------------------------------------------- When $r_0 = 1$ the Markov chain is equivalent to the Gamblers ruin problem. The @@ -276,16 +273,20 @@ respectively. \subsection{d)} The following Python code will simulate the Markov chain to verify the answers given in sub-problem \emph{b)} and \emph{c)}. -% KANSKJE GJØRE DENNE OM TIL ET VEDLEGG???????!!!! \lstinputlisting[language=Python]{simulate.py} +Figure \ref{fig:simulated_histories} shows a simulation of the chain when +starting in state 25, 50 and 75. We see that the simulation starting in state 50 +is the one using the most steps to get to state 100. + Table \ref{tab:jumps_to_100} and \ref{tab:ratio_to_100} shows the results of 5000 simulations of the given Markov chain. One simulation was run with $r_0 = 0.5$, where the average number of jumps before ending up in state 100 for the first time is shown in table \ref{tab:jumps_to_100}. The other simulation was run with $r_0 = 1$, making it possible to get stuck in state $0$ and $100$, and the estimated probability of ending up in state $100$ is shown in table -\ref{tab:ratio_to_100}. +\ref{tab:ratio_to_100}. The results coincide well with the calculated values +from sub-problem \emph{b)} an \emph{c)}. \begin{table}[h] \caption{\sf Avg. number of jumps before ending up in state $100$, over $5000$ runs} @@ -319,14 +320,20 @@ Start ($i$) & $P_{i,N}$ \\ \end{center} \end{table} +\begin{figure} + \includegraphics[width=\textwidth]{figur} + \caption{\sf Simulated time history when starting in state 25, 50 and 75} + \label{fig:simulated_histories} +\end{figure} + \subsubsection{Confidence intervals} We are asked to compute a 95\% confidence interval for the expected amount of -time the Markov chain takes to reach state 100 for the first time. In other word -we want a confidence interval for $E(N_{i,N})$ given by equation \eqref{eq:nin}. -When using results from our simulations we look at $\bar{T}$, the mean time it -takes to get to state $N$. Since we do not know the variance we use the sample -variance, which is unbiased and is therefore a good approximation for large $n$. -The sample variance is calculated as follows: +time the Markov chain takes to reach state 100 for the first time. In other +words we want a confidence interval for $E(N_{i,N})$ given by equation +\eqref{eq:nin}. When using results from our simulations we look at $\bar{T}$, +the mean time it takes to get to state $N$. Since we do not know the variance we +use the sample variance, which is unbiased and is therefore a good approximation +for large $n$. The sample variance is calculated as follows: \begin{equation} \label{eq:samplevariance} S^2 = \frac{1}{N-1} \sum_{k=1}^{N}(T_k - \bar{T})^2. @@ -334,7 +341,7 @@ The sample variance is calculated as follows: With this as the variance we can write a standardized normal random variable as \begin{equation} \label{eq:z} - Z = \frac{\bar{T} - \mu}{\frac{S}{\sqrt{N}}}. + Z \approx \frac{\bar{T} - \mu}{\frac{S}{\sqrt{N}}}. \end{equation} A 95\% confidence interval for $mu$ is then given by \begin{equation} @@ -357,11 +364,11 @@ that the Markov chain ever visits state 100. We denote a success, the travel from state $i$ to state $n$, as $p$. $X$ is the number of successes in $N$ trials. A point estimator for $p$ is given by $\hat{p} = \frac{X}{N}$. Since these trials have only to possible outcomes, success and failure, $X$ is -binomially distributed with parameter $Np$. For large $N$ we can find a +binomially distributed with parameter $Np$. For large $N$ we can approximate a standardized normally distributed random variable as show below. \begin{equation} \label{eq:z2} - Z = \frac{\hat{p} - p}{\sqrt{\frac{\hat{p}(1-\hat{p})}{N}}}. + Z \approx \frac{\hat{p} - p}{\sqrt{\frac{\hat{p}(1-\hat{p})}{N}}}. \end{equation} A 95\% confidence interval is then given by \begin{equation} diff --git a/simulate.py b/simulate.py index 7dfb8bb..01ad549 100644 --- a/simulate.py +++ b/simulate.py @@ -4,7 +4,7 @@ import random def run_chain(start, end, r0, p, q): current = start - r = random.SystemRandom() + r = random.random() steps = 0 while True: rand = r.random() @@ -54,9 +54,12 @@ def main(): S_steps = sum(abs(x - mean_steps)**2 for x in steps[start]) / (runs - 1) - print "Start in %d, r0 = 1, %.4f runs get to 100" % (start, ratio_to_100) - print "Start in %d, r0 = 0.5, %.4f steps to get to 100" % (start, np.mean(steps[start])) - print "Start in %d, r0 = 0.5, %.4f runs get to 100 in 1000 or more steps" % (start, float(runs_gte_1000)/float(runs)) + print "Start in %d, r0 = 1, %.4f runs get to 100" \ + % (start, ratio_to_100) + print "Start in %d, r0 = 0.5, %.4f steps to get to 100" \ + % (start, np.mean(steps[start])) + print "Start in %d, r0 = 0.5, %.4f runs get to 100 in 1000 or more steps" \ + % (start, float(runs_gte_1000)/float(runs)) if __name__ == '__main__': main()