From 26daad033ca3aebfc65e0b4ddfaea72888e2f38a Mon Sep 17 00:00:00 2001 From: =?utf8?q?Bj=C3=B8rn=20Rustad?= Date: Wed, 16 Nov 2011 10:37:33 +0100 Subject: [PATCH] Initial commit --- Makefile | 5 + egellip.m | 51 + elerr.kopi.m | 8 + elerr.m | 8 + elint.kopi.m | 5 + elint.m | 5 + freewR.m | 149 +++ main.kopi.m | 1 + main.m | 1 + newtfree.m | 9 + newton.m | 17 + newton_error.m | 12 + octave-core | Bin 0 -> 584 bytes rapport.aux | 37 + rapport.log | 2685 ++++++++++++++++++++++++++++++++++++++++++ rapport.tex | 356 ++++++ rigidbodysimulator.m | 33 + romberg.m | 30 + romberg.py | 26 + rombergold.m | 24 + 20 files changed, 3462 insertions(+) create mode 100644 Makefile create mode 100644 egellip.m create mode 100644 elerr.kopi.m create mode 100644 elerr.m create mode 100644 elint.kopi.m create mode 100644 elint.m create mode 100644 freewR.m create mode 100644 main.kopi.m create mode 100644 main.m create mode 100644 newtfree.m create mode 100644 newton.m create mode 100644 newton_error.m create mode 100644 octave-core create mode 100644 rapport.aux create mode 100644 rapport.log create mode 100644 rapport.tex create mode 100644 rigidbodysimulator.m create mode 100644 romberg.m create mode 100644 romberg.py create mode 100644 rombergold.m diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..13d90dd --- /dev/null +++ b/Makefile @@ -0,0 +1,5 @@ +all: + latex rapport.tex + latex rapport.tex + dvips rapport.dvi + ps2pdf rapport.ps diff --git a/egellip.m b/egellip.m new file mode 100644 index 0000000..fccadb1 --- /dev/null +++ b/egellip.m @@ -0,0 +1,51 @@ +function [sn,cn,dn]=egellip(h,phiin,m,ny)%,tol) +%Solve the elliptic integral from 0 to phi + +%if nargin<3, tol = eps; end +%if nargin<2, error('Not enough input arguments.'); end + +a(1) = 1; +c(1) = sqrt(m); +b(1) = sqrt(1-m); + +i = 1; +while abs(c(i)) > eps + i = i + 1; + a(i) = 0.5 * (a(i-1) + b(i-1)); + b(i) = sqrt(a(i-1)* b(i-1)); + c(i) = 0.5 * (a(i-1) - b(i-1)); +end +n=i-1; +phiit(1)=phiin; +for j=1:n + phijf=mod(phiit(j),pi); + nte=(phiit(j)-phijf)/pi; + tempf=atan((b(j)/a(j))*tan(phijf)); + if tempf<0 + tempf=tempf+pi; + end + phiit(j+1)=tempf+nte*pi+phiit(j); +end +%lamtau=phiit(i)/(a(i)*2^(i-1)); +%un= +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +phin(:,i)=[(2.^(n-1)).*a(i)*h*ny+phiit(i);(2.^n)*a(i)*h*ny+phiit(i)]; +while i > 1 + i = i - 1; + phin(:,i) = phin(:,i+1); + %if ~isempty(in) + phin(:,i) = 0.5*(asin(c(i+1).*sin(rem(phin(:,i+1),2*pi))./a(i+1)) + phin(:,i+1)); + %end +end +sn = sin(rem(phin(:,1),2*pi)); +cn = cos(rem(phin(:,1),2*pi)); +dn = sqrt(1 - m .* sn.^2); + +% special case m = 1 +m1 = find(m==1); +sn(m1) = tanh([h*ny/2+phiit(m1)/((2.^(n)).*a(i));h*ny+phiit(i)/((2.^(n)).*a(i))]); +cn(m1) = sech([h*ny/2+phiit(m1)/((2.^(n)).*a(i));h*ny+phiit(i)/((2.^(n)).*a(i))]); +dn(m1) = sech([h*ny/2+phiit(m1)/((2.^(n)).*a(i));h*ny+phiit(i)/((2.^(n)).*a(i))]); + + diff --git a/elerr.kopi.m b/elerr.kopi.m new file mode 100644 index 0000000..81f0da4 --- /dev/null +++ b/elerr.kopi.m @@ -0,0 +1,8 @@ +function [el, e1] = elerr(k, L) + +[il, i1] = elint(k, pi/2, L) + +el = abs(ellipke(k^2) - il) +e1 = abs(ellipke(k^2) - i1) + +end diff --git a/elerr.m b/elerr.m new file mode 100644 index 0000000..98b02f9 --- /dev/null +++ b/elerr.m @@ -0,0 +1,8 @@ +function [el, e1] = elerr(k, L) + +[il, i1] = elint(k, pi/2, L); + +el = abs(ellipke(k^2) - il) +e1 = abs(ellipke(k^2) - i1) + +end diff --git a/elint.kopi.m b/elint.kopi.m new file mode 100644 index 0000000..6487784 --- /dev/null +++ b/elint.kopi.m @@ -0,0 +1,5 @@ +function [il, i1] = elint(k, phi, L) + +f = @(x) 1.0 / sqrt(1 - k^2 * sin(x)^2); + +[il, i1] = romberg(f, 0, phi, L); diff --git a/elint.m b/elint.m new file mode 100644 index 0000000..5af223f --- /dev/null +++ b/elint.m @@ -0,0 +1,5 @@ +function [il, i1] = elint(k, phi, L) + +f = @(x) 1.0 / sqrt(1 - k^2 * sin(x)^2); + +[il, i1] = rombergold(f, 0, phi, L); diff --git a/freewR.m b/freewR.m new file mode 100644 index 0000000..3b30de3 --- /dev/null +++ b/freewR.m @@ -0,0 +1,149 @@ +function momentum=freewR(h,a,b,c,m01,m02,m03) +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% Solve ( I=diag(A,B,C), Omega = angular velocity, R(t) \in SO(3) ) +% +% m'= m x (inv(I)*m) +% +% Return exact solution for the angular momentum m=m(t_0+h) in one step h, +% with initial condition m(t_0) = m_0 = (m01,m02,m03). +% +% +% Subfunctions: egellip +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +Inert=diag([a,b,c],0); % Inertia tensor +Inert_inv=diag([1/a,1/b,1/c],0); + +OmeganU(:,1)=[m01/a;m02/b;m03/c]; % Variables +omega0=[m01/a;m02/b;m03/c]; % For temporary use + +b1=sqrt(b*(c-b)); +b3=sqrt(b*(b-a)); + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%% BEGIN +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +T=(a*omega0(1)^2+b*omega0(2)^2+c*omega0(3)^2)/2; +GG=a^2*omega0(1)^2+b^2*omega0(2)^2+c^2*omega0(3)^2; + +a1=sqrt(2*T*c-GG); +a3=sqrt(GG-2*T*a); + +k=b3*a1/(b1*a3); + %***************************************************** + % First case: (b1/a1 >= b3/a3) + %***************************************************** + if k<=1 + ni=b1*a3/(b*sqrt(a*c)); + %************************************************** + % Adjusting the initial value (first case) + % Calculate "phi_0" (phinoll) + %************************************************** + if omega0(1)>=0 + if omega0(2)>=0 % (First quarter) + phinoll=asin(omega0(2)*b1/a1); + if omega0(3)<0 + ni=-ni; + a3=-a3; + end + else %omega0(2)<0 (Fourth quarter) + phinoll=asin(omega0(2)*b1/a1)+2*pi; + if omega0(3)<0 + ni=-ni; + a3=-a3; + end + end + else %omega0(1)<0 + if omega0(2)>=0 % (Second quarter) + phinoll=pi-asin(omega0(2)*b1/a1); + if omega0(3)<0 + ni=-ni; + a3=-a3; + end + else %omega0(2)<0 (Third quarter) + phinoll=2*pi-acos(omega0(1)*sqrt(a*(c-a))/a1); + if omega0(3)<0 + ni=-ni; + a3=-a3; + end + end + end + %************************************************************* + % Integrating omega by means of Jacobi elliptic functions: + % (first case) + %************************************************************* + [Sn,Cn,Dn]=egellip(h,phinoll,k^2,ni); + v=a1/sqrt(a*(c-a))*Cn'; + midt1=v(1,1); + OmeganU(1,1)=v(1,2); + v=a1/b1*Sn'; + midt2=v(1,1); + OmeganU(2,1)=v(1,2); + v=a3/sqrt(c*(c-a))*Dn'; + midt3=v(1,1); + OmeganU(3,1)=v(1,2); + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + else + %***************************************************** + % Second case: (b1/a1 < b3/a3) + %***************************************************** + k=b1*a3/(a1*b3); + ni=a1*b3/(b*sqrt(a*c)); + %***************************************************** + % Adjusting the initial value (second case) + % Calculate "phi_0" (phinoll) + %***************************************************** + if omega0(3)>=0 + if omega0(2)>=0 % (First quarter) + phinoll=asin(omega0(2)*b3/a3); + if omega0(1)<0 + ni=-ni; + a1=-a1; + end + else %omega0(2)<0 (Fourth quarter) + phinoll=asin(omega0(2)*b3/a3)+2*pi; + if omega0(1)<0 + ni=-ni; + a1=-a1; + end + end + else %omega0(3)<0 + if omega0(2)>=0 % (Second quarter) + phinoll=acos(omega0(3)*sqrt(c*(c-a))/a3); + if omega0(1)<0 + ni=-ni; + a1=-a1; + end + else %omega0(2)<0 (Third quarter) + phinoll=2*pi-acos(omega0(3)*sqrt(c*(c-a))/a3); + if omega0(1)<0 + ni=-ni; + a1=-a1; + end + end + end + %************************************************************* + % Integrating omega by means of Jacobi elliptic functions: + % (first case) + %************************************************************* + [Sn,Cn,Dn]=egellip(h,phinoll,k^2,ni); + v=a1/sqrt(a*(c-a))*Dn'; + midt1=v(1,1); + OmeganU(1,1)=v(1,2); + v=a3/b3*Sn'; + midt2=v(1,1); + OmeganU(2,1)=v(1,2); + v=a3/sqrt(c*(c-a))*Cn'; + midt3=v(1,1); + OmeganU(3,1)=v(1,2); + end +%************************************************************* +% Approximation of rotation matrix +%************************************************************* +%midtt=[midt1;midt2;midt3]; +%Rmat=expso3(h*midtt); +momentum=Inert*OmeganU; + diff --git a/main.kopi.m b/main.kopi.m new file mode 100644 index 0000000..0682cb3 --- /dev/null +++ b/main.kopi.m @@ -0,0 +1 @@ +i = elint(0.5, 2, 15) diff --git a/main.m b/main.m new file mode 100644 index 0000000..0682cb3 --- /dev/null +++ b/main.m @@ -0,0 +1 @@ +i = elint(0.5, 2, 15) diff --git a/newtfree.m b/newtfree.m new file mode 100644 index 0000000..6c3c2d5 --- /dev/null +++ b/newtfree.m @@ -0,0 +1,9 @@ +function estimate = newtfree(previous, h, T) + estimate = previous; + F = @(x) x - previous - .25*h*cross(x+previous,T\(x + previous)); + + J = @(x) [1, .25*h*(1/T(2,2)-1/T(3,3))*(previous(3)+x(3)),.25*h*(1/T(2,2)-1/T(3,3))*(previous(2)+x(2));.25*h*(1/T(3,3)-1/T(1,1))*(previous(3)+x(3)), 1,.25*h*(1/T(3,3)-1/T(1,1))*(previous(1)+x(1));.25*h*(1/T(1,1)-1/T(2,2))*(previous(2)+x(2)),.25*h*(1/T(1,1)-1/T(2,2))*(previous(1)+x(1)),1]; + while norm(F(estimate)) > 10*eps + estimate = estimate - J(estimate)\F(estimate); + end +end diff --git a/newton.m b/newton.m new file mode 100644 index 0000000..29eafee --- /dev/null +++ b/newton.m @@ -0,0 +1,17 @@ +function null = newton(u, k, x0, tol) + +x = x0; + +f = @(x) 1/sqrt(1 - k^2 * sin(x)^2); + +G = romberg(k, 0, x, tol/10) - u; +while (abs(G) > tol) + G = romberg(k, 0, x, eps) - u; + Gder = f(x); + xtemp = x - G/Gder; + x = xtemp; +end + +null = x; + +end diff --git a/newton_error.m b/newton_error.m new file mode 100644 index 0000000..e857fc5 --- /dev/null +++ b/newton_error.m @@ -0,0 +1,12 @@ +start = 0; +k = 0.5; + +C = []; +tol = 100000*eps; +for u = linspace(0,100,10) + am = newton(u, k, start, tol); + err = abs(sin(am) - ellipj(u, k^2)); + C = [C; (err / tol)]; +end + +max(C) diff --git a/octave-core b/octave-core new file mode 100644 index 0000000000000000000000000000000000000000..88618ba84e8f469630bc258c1951da0eff061fdb GIT binary patch literal 584 zcmeZIE=ep))iu=hVc=k3V9?7;EK1MJ(*rUY82+;XiQ?qMoWvq_umF%?1Y&nE=RZG? zN-NDvF3HT#Q^-inOUX&)0}46VB}@^h0?i_#S|(sUFI zbQCIpq@Dp77-}l$0y(Bc*#E(v6KEdTk@=-1xLo~FYo+g#unFw(wQdnzjxqHNMl8OT}P$n_27(@P( Y`}LWdH_zEasxNtAzJ&O&f|@=70C2O0R{#J2 literal 0 HcmV?d00001 diff --git a/rapport.aux b/rapport.aux new file mode 100644 index 0000000..cb63d8d --- /dev/null +++ b/rapport.aux @@ -0,0 +1,37 @@ +\relax +\@writefile{toc}{\contentsline {section}{Part 1}{1}} +\@writefile{toc}{\contentsline {subsection}{Problem 1}{1}} +\@writefile{toc}{\contentsline {subsubsection}{a)}{1}} +\newlabel{eq:sdiv_linear}{{1}{1}} +\newlabel{eq:sdiv_integrated}{{2}{1}} +\newlabel{eq:sdiv_evaluated}{{3}{1}} +\newlabel{eq:s_difference}{{4}{1}} +\newlabel{eq:sder_sum}{{5}{1}} +\newlabel{eq:s_matrix}{{6}{1}} +\@writefile{lot}{\contentsline {table}{\numberline {1}{\ignorespaces \sf Data determining our spline polynomials.}}{2}} +\newlabel{tab:data}{{1}{2}} +\newlabel{eq:poly}{{7}{2}} +\@writefile{toc}{\contentsline {subsubsection}{b)}{2}} +\newlabel{eq:g_def}{{8}{2}} +\newlabel{eq:g_der_zero}{{9}{2}} +\newlabel{eq:xbar_error}{{10}{2}} +\newlabel{eq:2s_bound}{{11}{2}} +\newlabel{eq:si_bound}{{12}{2}} +\newlabel{eq:error_bound}{{13}{2}} +\@writefile{toc}{\contentsline {subsection}{Problem 2}{2}} +\@writefile{toc}{\contentsline {subsubsection}{a)}{2}} +\newlabel{eq:integral}{{14}{2}} +\@writefile{lot}{\contentsline {table}{\numberline {2}{\ignorespaces \sf Showing the convergence for the Romberg method over the interval $[0, 5]$ with $k = 0.5$ as $L$ increases.}}{3}} +\newlabel{tab:romberg_conv}{{2}{3}} +\newlabel{eq:euler_maclaurin}{{15}{3}} +\@writefile{toc}{\contentsline {subsubsection}{b)}{3}} +\@writefile{lot}{\contentsline {table}{\numberline {3}{\ignorespaces \sf Estimated integral for decreasing values of tolerance limit.}}{3}} +\newlabel{tab:tol_test}{{3}{3}} +\@writefile{toc}{\contentsline {subsubsection}{c)}{3}} +\@writefile{toc}{\contentsline {subsection}{Problem 3}{4}} +\@writefile{toc}{\contentsline {subsubsection}{a)}{4}} +\newlabel{eq:runge_kutta}{{16}{4}} +\newlabel{eq:runge_kutta_newton}{{17}{4}} +\newlabel{eq:jacobian}{{18}{4}} +\@writefile{toc}{\contentsline {subsubsection}{b)}{4}} +\@writefile{toc}{\contentsline {subsubsection}{c)}{4}} diff --git a/rapport.log b/rapport.log new file mode 100644 index 0000000..3217080 --- /dev/null +++ b/rapport.log @@ -0,0 +1,2685 @@ +This is pdfTeX, Version 3.1415926-1.40.10 (TeX Live 2009/Debian) (format=latex 2011.9.28) 16 NOV 2011 10:33 +entering extended mode + %&-line parsing enabled. +**rapport.tex +(./rapport.tex +LaTeX2e <2009/09/24> +Babel and hyphenation patterns for english, usenglishmax, dumylang, noh +yphenation, loaded. 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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 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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 \toks_gset:cV on line 73 +Defining \toks_gset:co on line 73 +Defining \toks_gset:cx on line 73 +Defining \toks_set_eq:NN on line 74 +Defining \toks_gset_eq:NN on line 75 +Defining \toks_set_eq:Nc on line 76 +Defining \toks_set_eq:cN on line 76 +Defining \toks_set_eq:cc on line 76 +Defining \toks_gset_eq:Nc on line 77 +Defining \toks_gset_eq:cN on line 77 +Defining \toks_gset_eq:cc on line 77 +Defining \toks_clear:N on line 78 +Defining \toks_gclear:N on line 81 +Defining \toks_clear:c on line 85 +Defining \toks_gclear:c on line 86 +Defining \toks_use_clear:N on line 87 +Defining \toks_use_gclear:N on line 90 +Defining \toks_use_clear:c on line 94 +Defining \toks_use_gclear:c on line 95 +Defining \toks_show:N on line 96 +Defining \toks_show:c on line 97 +Defining \toks_put_left:Nn on line 98 +Defining \toks_put_left:NV on line 102 +Defining \toks_put_left:No on line 102 +Defining \toks_put_left:Nx on line 102 +Defining \toks_put_left:cn on line 102 +Defining \toks_put_left:co on line 102 +Defining \toks_put_left:cV on line 102 +Defining \toks_gput_left:Nn on line 103 +Defining \toks_gput_left:NV on line 107 +Defining \toks_gput_left:No on line 107 +Defining \toks_gput_left:Nx on line 107 +Defining \toks_gput_left:cn on line 107 +Defining \toks_gput_left:cV on line 107 +Defining \toks_gput_left:co on line 107 +Defining \toks_put_left_aux:w on line 108 +Defining \toks_put_right:Nn on line 111 +Defining \toks_gput_right:Nn on line 114 +Defining \toks_put_right:NV on line 118 +Defining \toks_put_right:No on line 124 +Defining \toks_put_right:Nx on line 129 +Defining \toks_put_right:cn on line 129 +Defining \toks_put_right:cV on line 129 +Defining \toks_put_right:co on line 129 +Defining \toks_gput_right:NV on line 130 +Defining \toks_gput_right:No on line 130 +Defining \toks_gput_right:Nx on line 130 +Defining \toks_gput_right:cn on line 130 +Defining \toks_gput_right:cV on line 130 +Defining \toks_gput_right:co on line 130 +Defining \toks_put_right:Nf on line 131 +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=\toks25 +\l_tmpc_toks=\toks26 +\g_tmpa_toks=\toks27 +\g_tmpb_toks=\toks28 +\g_tmpc_toks=\toks29 +\c_empty_toks=\toks30 +\l_tl_replace_toks=\toks31 +) +(/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=\count110 +Defining \l_tmpb_int on line 212 +\l_tmpb_int=\count111 +Defining \l_tmpc_int on line 213 +\l_tmpc_int=\count112 +Defining \g_tmpa_int on line 214 +\g_tmpa_int=\count113 +Defining \g_tmpb_int on line 215 +\g_tmpb_int=\count114 +Defining \int_const:Nn on line 221 +Defining \c_one on line 234 +Defining \c_two on line 235 +Defining \c_three on line 236 +Defining \c_four on line 237 +Defining \c_five on line 238 +Defining \c_six on line 239 +Defining \c_seven on line 240 +Defining \c_eight on line 241 +Defining \c_nine on line 242 +Defining \c_ten on line 243 +Defining \c_eleven on line 244 +Defining \c_twelve on line 245 +Defining \c_thirteen on line 246 +Defining \c_fourteen on line 247 +Defining \c_fifteen on line 248 +Defining \c_thirty_two on line 250 +Defining \c_hundred_one on line 251 +Defining \c_twohundred_fifty_five on line 252 +Defining \c_twohundred_fifty_six on line 253 +Defining \c_thousand on line 254 +Defining \c_ten_thousand on line 255 +Defining \c_ten_thousand_one on line 256 +Defining \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=\count115 +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=\count116 +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 \clist_if_eq:NcF on line 93 +Defining \clist_if_eq_p:cc on line 94 +Defining \clist_if_eq:ccTF on line 94 +Defining \clist_if_eq:ccT on line 94 +Defining \clist_if_eq:ccF on line 94 +Defining \clist_if_in:NnTF on line 101 +Defining \clist_if_in:NnT on line 101 +Defining \clist_if_in:NnF on line 101 +Defining \clist_if_in:NVTF on line 102 +Defining \clist_if_in:NoTF on line 102 +Defining \clist_if_in:cnTF on line 102 +Defining \clist_if_in:cVTF on line 102 +Defining \clist_if_in:coTF on line 102 +Defining \clist_if_in:NVT on line 103 +Defining \clist_if_in:NoT on line 103 +Defining \clist_if_in:cnT on line 103 +Defining \clist_if_in:cVT on line 103 +Defining \clist_if_in:coT on line 103 +Defining \clist_if_in:NVF on line 104 +Defining \clist_if_in:NoF on line 104 +Defining \clist_if_in:cnF on line 104 +Defining \clist_if_in:cVF on line 104 +Defining \clist_if_in:coF on line 104 +Defining \clist_use:N on line 105 +Defining \clist_use:c on line 113 +Defining \clist_get:NN on line 114 +Defining \clist_get_aux:w on line 118 +Defining \clist_get:cN on line 119 +Defining \clist_pop_aux:nnNN on line 120 +Defining \clist_pop_aux:w on line 124 +Defining \clist_pop_auxi:w on line 129 +Defining \clist_show:N on line 130 +Defining \clist_show:c on line 131 +Defining \clist_display:N on line 132 +Defining \clist_display:c on line 146 +Defining \clist_put_aux:NNnnNn on line 147 +Defining \clist_put_left:Nn on line 152 +Defining \clist_put_left:NV on line 155 +Defining \clist_put_left:No on line 155 +Defining \clist_put_left:Nx on line 155 +Defining \clist_put_left:cn on line 155 +Defining \clist_put_left:cV on line 155 +Defining \clist_put_left:co on line 155 +Defining \clist_gput_left:Nn on line 156 +Defining \clist_gput_left:NV on line 159 +Defining \clist_gput_left:No on line 159 +Defining \clist_gput_left:Nx on line 159 +Defining \clist_gput_left:cn on line 159 +Defining \clist_gput_left:cV on line 159 +Defining \clist_gput_left:co on line 159 +Defining \clist_put_right:Nn 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=\count117 +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=\toks32 +\l_msg_redirect_names_prop=\toks33 +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=\toks34 +Defining \msg_error:nnxx on line 328 +\l_msg_redirect_error_prop=\toks35 +Defining \msg_warning:nnxx on line 349 +\l_msg_redirect_warning_prop=\toks36 +Defining \msg_info:nnxx on line 356 +\l_msg_redirect_info_prop=\toks37 +Defining \msg_log:nnxx on line 363 +\l_msg_redirect_log_prop=\toks38 +Defining \msg_trace:nnxx on line 369 +\l_msg_redirect_trace_prop=\toks39 +Defining \msg_none:nnxx on line 375 +\l_msg_redirect_none_prop=\toks40 +Defining \msg_redirect_class:nn on line 378 +Defining \msg_redirect_module:nnn on line 381 +Defining \msg_redirect_name:nnn on line 384 +Defining \msg_kernel_new:nnnn on line 385 +Defining \msg_kernel_new:nnn on line 388 +Defining \msg_kernel_new:nn on line 391 +Defining \msg_kernel_set:nnnn on line 394 +Defining \msg_kernel_set:nnn on line 397 +Defining \msg_kernel_set:nn on line 400 +Defining \msg_kernel_classes_new:n on line 410 +Defining \msg_kernel_fatal:nxx on line 421 +Defining \msg_kernel_fatal:nx on line 422 +Defining \msg_kernel_fatal:n on line 422 +Defining \msg_kernel_error:nxx on line 443 +Defining \msg_kernel_error:nx on line 444 +Defining \msg_kernel_error:n on line 444 +Defining \msg_kernel_warning:nxx on line 445 +Defining \msg_kernel_warning:nx on line 448 +Defining \msg_kernel_warning:n on line 448 +Defining \msg_kernel_info:nxx on line 449 +Defining \msg_kernel_info:nx on line 452 +Defining \msg_kernel_info:n on line 452 +Defining \msg_text > LaTeX/coding-bug:nn on line 453 +Defining \msg_text > LaTeX/message-unknown:nn on line 459 +Defining \msg_text > LaTeX/message-class-unknown:nn on line 467 +Defining \msg_text > LaTeX/message-loop:nn on line 474 +) +(/usr/share/texmf-texlive/tex/latex/expl3/l3skip.sty +Package: l3skip 2009/05/28 v1362 L3 Experimental skip registers +Defining \skip_new:N on line 56 +Defining \skip_new:c on line 60 +Defining \skip_set:Nn on line 61 +Defining \skip_gset:Nn on line 64 +Defining \skip_set:cn on line 68 +Defining \skip_gset:cn on line 69 +Defining \skip_zero:N on line 70 +Defining \skip_gzero:N on line 73 +Defining \skip_zero:c on line 77 +Defining \skip_gzero:c on line 78 +Defining \skip_add:Nn on line 79 +Defining \skip_add:cn on line 82 +Defining \skip_sub:Nn on line 83 +Defining \skip_gadd:Nn on line 86 +Defining \skip_gadd:cn on line 90 +Defining \skip_gsub:Nn on line 91 +Defining \skip_horizontal:N on line 95 +Defining \skip_horizontal:c on line 96 +Defining \skip_horizontal:n on line 97 +Defining \skip_vertical:N on line 98 +Defining \skip_vertical:c on line 99 +Defining \skip_vertical:n on line 100 +Defining \skip_use:N on line 101 +Defining \skip_use:c on line 102 +Defining \skip_show:N on line 103 +Defining \skip_show:c on line 104 +Defining \skip_eval:n on line 105 +Defining \l_tmpa_skip on line 108 +\l_tmpa_skip=\skip46 +Defining \l_tmpb_skip on line 109 +\l_tmpb_skip=\skip47 +Defining \l_tmpc_skip on line 110 +\l_tmpc_skip=\skip48 +Defining \g_tmpa_skip on line 111 +\g_tmpa_skip=\skip49 +Defining \g_tmpb_skip on line 112 +\g_tmpb_skip=\skip50 +Defining \skip_if_infinite_glue_p:n on line 120 +Defining \skip_if_infinite_glue:nTF on line 120 +Defining \skip_if_infinite_glue:nT on line 120 +Defining \skip_if_infinite_glue:nF on line 120 +Defining \skip_split_finite_else_action:nnNN on line 121 +Defining \dim_new:N on line 133 +Defining \dim_new:c on line 137 +Defining \dim_set:Nn on line 138 +Defining \dim_set:cn on line 139 +Defining \dim_set:Nc on line 139 +Defining \dim_gset:Nn on line 140 +Defining \dim_gset:cn on line 141 +Defining \dim_gset:Nc on line 141 +Defining \dim_gset:cc on line 141 +Defining \dim_zero:N on line 142 +Defining \dim_zero:c on line 143 +Defining \dim_gzero:N on line 144 +Defining \dim_gzero:c on line 145 +Defining \dim_add:Nn on line 146 +Defining \dim_add:cn on line 149 +Defining \dim_add:Nc on line 149 +Defining \dim_gadd:Nn on line 150 +Defining \dim_gadd:cn on line 151 +Defining \dim_sub:Nn on line 152 +Defining \dim_sub:cn on line 153 +Defining \dim_sub:Nc on line 153 +Defining \dim_gsub:Nn on line 154 +Defining \dim_gsub:cn on line 155 +Defining \dim_use:N on line 156 +Defining \dim_use:c on line 157 +Defining \dim_show:N on line 158 +Defining \dim_show:c on line 159 +Defining \l_tmpa_dim on line 160 +\l_tmpa_dim=\dimen122 +Defining \l_tmpb_dim on line 161 +\l_tmpb_dim=\dimen123 +Defining \l_tmpc_dim on line 162 +\l_tmpc_dim=\dimen124 +Defining \l_tmpd_dim on line 163 +\l_tmpd_dim=\dimen125 +Defining \g_tmpa_dim on line 164 +\g_tmpa_dim=\dimen126 +Defining \g_tmpb_dim on line 165 +\g_tmpb_dim=\dimen127 +Defining \c_zero_dim on line 166 +Defining \c_max_dim on line 167 +Defining \dim_eval:n on line 168 +Defining \if_dim:w on line 169 +Defining \dim_compare_p:nNn on line 173 +Defining \dim_compare:nNnTF on line 173 +Defining \dim_compare:nNnT on line 173 +Defining \dim_compare:nNnF on line 173 +Defining \dim_while_do:nNnn on line 174 +Defining \dim_until_do:nNnn on line 177 +Defining \dim_do_while:nNnn on line 180 +Defining \dim_do_until:nNnn on line 183 +Defining \muskip_new:N on line 186 +Defining \muskip_set:Nn on line 190 +Defining \muskip_gset:Nn on line 191 +Defining \muskip_add:Nn on line 192 +Defining \muskip_gadd:Nn on line 193 +Defining \muskip_sub:Nn on line 194 +Defining \muskip_gsub:Nn on line 195 +Defining \muskip_use:N on line 196 +)) +(/usr/share/texmf-texlive/tex/latex/expl3/l3box.sty +Package: l3box 2009/06/01 v1375 L3 Experimental Box module +Defining \box_new:N on line 56 +Defining \box_new:c on line 60 +Defining \if_hbox:N on line 61 +Defining \if_vbox:N on line 62 +Defining \if_box_empty:N on line 63 +Defining \box_if_horizontal_p:N on line 66 +Defining \box_if_horizontal:NTF on line 66 +Defining \box_if_horizontal:NT on line 66 +Defining \box_if_horizontal:NF on line 66 +Defining \box_if_vertical_p:N on line 69 +Defining \box_if_vertical:NTF on line 69 +Defining \box_if_vertical:NT on line 69 +Defining \box_if_vertical:NF on line 69 +Defining \box_if_horizontal_p:c on line 70 +Defining \box_if_horizontal:cTF on line 71 +Defining \box_if_horizontal:cT on line 72 +Defining \box_if_horizontal:cF on line 73 +Defining \box_if_vertical_p:c on line 74 +Defining \box_if_vertical:cTF on line 75 +Defining \box_if_vertical:cT on line 76 +Defining \box_if_vertical:cF on line 77 +Defining \box_if_empty_p:N on line 80 +Defining \box_if_empty:NTF on line 80 +Defining \box_if_empty:NT on line 80 +Defining \box_if_empty:NF on line 80 +Defining \box_if_empty_p:c on line 81 +Defining \box_if_empty:cTF on line 82 +Defining \box_if_empty:cT on line 83 +Defining \box_if_empty:cF on line 84 +Defining \box_set_eq:NN on line 85 +Defining \box_set_eq:cN on line 86 +Defining \box_set_eq:Nc on line 86 +Defining \box_set_eq:cc on line 86 +Defining \box_gset_eq:NN on line 87 +Defining \box_gset_eq:cN on line 88 +Defining \box_gset_eq:Nc on line 88 +Defining \box_gset_eq:cc on line 88 +Defining \l_last_box on line 89 +Defining \box_set_to_last:N on line 90 +Defining \box_set_to_last:c on line 91 +Defining \box_gset_to_last:N on line 92 +Defining \box_gset_to_last:c on line 93 +Defining \box_move_left:nn on line 94 +Defining \box_move_right:nn on line 95 +Defining \box_move_up:nn on line 96 +Defining \box_move_down:nn on line 97 +Defining \box_clear:N on line 98 +Defining \box_clear:c on line 99 +Defining \box_gclear:N on line 100 +Defining \box_gclear:c on line 101 +Defining \box_ht:N on line 102 +Defining \box_dp:N on line 103 +Defining \box_wd:N on line 104 +Defining \box_ht:c on line 105 +Defining \box_dp:c on line 106 +Defining \box_wd:c on line 107 +Defining \box_use_clear:N on line 108 +Defining \box_use_clear:c on line 109 +Defining \box_use:N on line 110 +Defining \box_use:c on line 111 +Defining \box_show:c on line 113 +Defining \l_tmpa_box on line 115 +Defining \l_tmpb_box on line 116 +\l_tmpb_box=\box30 +Defining \vbox:n on line 117 +Defining \vbox_set:Nn on line 118 +Defining \vbox_set:cn on line 119 +Defining \vbox_gset:Nn on line 120 +Defining \vbox_gset:cn on line 121 +Defining \vbox_set_to_ht:Nnn on line 122 +Defining \vbox_set_to_ht:cnn on line 125 +Defining \vbox_gset_to_ht:Nnn on line 126 +Defining \vbox_gset_to_ht:cnn on line 127 +Defining \vbox_gset_to_ht:ccn on line 127 +Defining \exp_args:Nccn on line 127 +Defining \vbox_set_inline_begin:N on line 128 +Defining \vbox_set_inline_end: on line 130 +Defining \vbox_gset_inline_begin:N on line 131 +Defining \vbox_gset_inline_end: on line 133 +Defining \vbox_to_ht:nn on line 134 +Defining \vbox_to_zero:n on line 135 +Defining \vbox_set_split_to_ht:NNn on line 136 +Defining \vbox_unpack:N on line 139 +Defining \vbox_unpack:c on line 140 +Defining \vbox_unpack_clear:N on line 141 +Defining \vbox_unpack_clear:c on line 142 +Defining \hbox:n on line 143 +Defining \hbox_set:Nn on line 144 +Defining \hbox_set:cn on line 145 +Defining \hbox_gset:Nn on line 146 +Defining \hbox_gset:cn on line 147 +Defining \hbox_set_to_wd:Nnn on line 148 +Defining \hbox_set_to_wd:cnn on line 151 +Defining \hbox_gset_to_wd:Nnn on line 152 +Defining \hbox_gset_to_wd:cnn on line 153 +Defining \hbox_set_inline_begin:N on line 154 +Defining \hbox_set_inline_begin:c on line 157 +Defining \hbox_set_inline_end: on line 158 +Defining \hbox_gset_inline_begin:N on line 159 +Defining \hbox_gset_inline_begin:c on line 162 +Defining \hbox_gset_inline_end: on line 163 +Defining \hbox_to_wd:nn on line 164 +Defining \hbox_to_zero:n on line 165 +Defining \hbox_unpack:N on line 166 +Defining \hbox_unpack:c on line 167 +Defining \hbox_unpack_clear:N on line 168 +Defining \hbox_unpack_clear:c on line 169 +) +(/usr/share/texmf-texlive/tex/latex/expl3/l3keyval.sty +Package: l3keyval 2009/07/13 v1424 L3 Experimental keyval processing +Defining \l_KV_tmpa_tl on line 56 +Defining \l_KV_tmpb_tl on line 57 +Defining \c_KV_single_equal_sign_tl on line 58 +\l_KV_parse_toks=\toks41 +\l_KV_currkey_toks=\toks42 +\l_KV_currval_toks=\toks43 +Defining \l_KV_remove_one_level_of_braces_bool on line 62 +Defining \KV_sanitize_outerlevel_active_equals:N on line 76 +Defining \KV_sanitize_outerlevel_active_commas:N on line 76 +Defining \KV_remove_surrounding_spaces:nw on line 79 +Defining \KV_remove_surrounding_spaces_auxi:w on line 82 +Defining \KV_remove_surrounding_spaces_auxii:w on line 85 +Defining \KV_add_value_element:w on line 86 +Defining \KV_set_key_element:w on line 94 +Defining \KV_add_element_aux:w on line 109 +Defining \KV_parse_sanitize_aux:n on line 110 +Defining \KV_parse_no_sanitize_aux:n on line 121 +Defining \KV_split_key_value_current:w on line 139 +Defining \KV_split_key_value_space_removal:w on line 140 +Defining \KV_split_key_value_space_removal_detect_error:wTF on line 157 +Defining \KV_val_preserve_braces:NnN on line 160 +Defining \KV_split_key_value_space_removal_aux:w on line 161 +Defining \KV_split_key_value_no_space_removal:w on line 187 +Defining \KV_key_no_value_elt:n on line 201 +Defining \KV_key_value_elt:nn on line 202 +Defining \KV_parse_no_space_removal_no_sanitize:n on line 203 +Defining \KV_parse_space_removal_sanitize:n on line 207 +Defining \KV_parse_space_removal_no_sanitize:n on line 211 +) +(/usr/share/texmf-texlive/tex/latex/expl3/l3keys.sty +Package: l3keys 2009/09/17 v1542 L3 Experimental key-value support +Defining \c_keys_root_tl on line 56 +Defining \c_keys_properties_root_tl on line 57 +Defining \c_keys_value_forbidden_tl on line 58 +Defining \c_keys_value_required_tl on line 59 +Defining \l_keys_choice_int on line 60 +\l_keys_choice_int=\count118 +Defining \l_keys_choice_tl on line 61 +Defining \l_keys_choice_code_tl on line 62 +Defining \l_keys_key_tl on line 63 +Defining \l_keys_path_tl on line 64 +Defining \l_keys_property_tl on line 65 +Defining \l_keys_module_tl on line 66 +Defining \l_keys_nesting_seq on line 67 +Defining \l_keys_nesting_tl on line 68 +Defining \l_keys_no_value_bool on line 69 +\l_keys_value_toks=\toks44 +Defining \keys_bool_set:NN on line 86 +Defining \keys_choice_code_store:x on line 89 +Defining \keys_choice_find:n on line 94 +Defining \keys_choice_make: on line 103 +Defining \keys_choices_generate:n on line 117 +Defining \keys_choices_generate_aux:n on line 126 +Defining \keys_cmd_set:nn on line 131 +Defining \keys_cmd_set:nx on line 136 +Defining \keys_cmd_set_aux:n on line 140 +Defining \keys_default_set:n on line 143 +Defining \keys_default_set:V on line 144 +Defining \keys_define:nn on line 157 +Defining \keys_define_elt:n on line 161 +Defining \keys_define_elt:nn on line 165 +Defining \keys_define_elt_aux:nn on line 176 +Defining \keys_define_key:n on line 191 +Defining \keys_execute: on line 196 +Defining \keys_execute_unknown: on line 201 +Defining \keys_execute_aux:nn on line 209 +Defining \keys_if_value_requirement:nTF on line 217 +Defining \keys_meta_make:n on line 226 +Defining \keys_meta_make:x on line 227 +Defining \keys_property_find:n on line 235 +Defining \keys_property_find_aux:n on line 238 +Defining \keys_property_find_aux:w on line 239 +Defining \keys_property_new:nn on line 252 +Defining \keys_property_undefine:n on line 255 +Defining \keys_set:nn on line 268 +Defining \keys_set:nV on line 269 +Defining \keys_set:nv on line 269 +Defining \exp_args:Nnv on line 269 +Defining \keys_set_elt:n on line 273 +Defining \keys_set_elt:nn on line 277 +Defining \keys_set_elt_aux:nn on line 291 +Defining \keys_set_elt_aux: on line 303 +Defining \keys_show:nn on line 306 +Defining \keys_tmp:w on line 307 +Defining \keys_value_or_default:n on line 317 +Defining \keys_value_requirement:n on line 321 +Defining \keys_variable_set:NnNN on line 329 +Defining \keys_properties.bool_set:N on line 332 +Defining \keys_properties.bool_gset:N on line 335 +Defining \keys_properties.choice: on line 338 +Defining \keys_properties.choice_code:n on line 341 +Defining \keys_properties.choice_code:x on line 344 +Defining \keys_properties.code:n on line 347 +Defining \keys_properties.code:x on line 350 +Defining \keys_properties.default:n on line 353 +Defining \keys_properties.default:V on line 356 +Defining \keys_properties.dim_set:N on line 359 +Defining \keys_properties.dim_gset:N on line 362 +Defining \keys_properties.generate_choices:n on line 365 +Defining \keys_properties.int_set:N on line 368 +Defining \keys_properties.int_gset:N on line 371 +Defining \keys_properties.meta:n on line 374 +Defining \keys_properties.meta:x on line 377 +Defining \keys_properties.skip_set:N on line 380 +Defining \keys_properties.skip_gset:N on line 383 +Defining \keys_properties.tl_set:N on line 386 +Defining \keys_properties.tl_set_x:N on line 389 +Defining \keys_properties.tl_gset:N on line 392 +Defining \keys_properties.tl_gset_x:N on line 395 +Defining \keys_properties.value_forbidden: on line 398 +Defining \keys_properties.value_required: on line 401 +Defining \msg_text > LaTeX/key-choice-unknown:nn on line 402 +Defining \msg_text > LaTeX/key-initial-without-code:nn on line 406 +Defining \msg_text > LaTeX/key-unknown:nn on line 410 +Defining \msg_text > LaTeX/key-value-forbidden:nn on line 413 +Defining \msg_text > LaTeX/key-value-required:nn on line 417 +Defining \msg_text > LaTeX/key-no-property:nn on line 421 +Defining \msg_text > LaTeX/key-no-set-function:nn on line 424 +Defining \msg_text > LaTeX/key-property-unknown:nn on line 434 +Defining \msg_text > LaTeX/key-property-value-required:nn on line 437 +) +(/usr/share/texmf-texlive/tex/latex/expl3/l3precom.sty +Package: l3precom 2009/08/08 v1453 L3 Experimental precompilation module +\c_cs_dump_stream=\write3 +Defining \g_cs_dump_name_tl on line 60 +Defining \g_cs_dump_seq on line 61 +Defining \cs_record_name:N on line 62 +Defining \cs_record_name:c on line 67 +Defining \cs_dump: on line 68 +Defining \cs_load_dump:n on line 94 +Defining \g_gen_sym_num on line 103 +Defining \g_ggen_sym_num on line 104 +Defining \cs_gen_sym:N on line 105 +Defining \cs_ggen_sym:N 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on input line 241 +. + + +LaTeX Font Warning: Font shape `OT1/cmr/m/n' in size <3.83247> not available +(Font) size <5> substituted on input line 241. + + +LaTeX Font Warning: Font shape `OML/cmm/m/it' in size <3.83247> not available +(Font) size <5> substituted on input line 241. + + +LaTeX Font Warning: Font shape `OMS/cmsy/m/n' in size <3.83247> not available +(Font) size <5> substituted on input line 241. + +[3] + +LaTeX Warning: Reference `fig:ode_comparison' on page 4 undefined on input line + 350. + +[4] (./rapport.aux) + +LaTeX Font Warning: Size substitutions with differences +(Font) up to 2.90001pt have occurred. + + +LaTeX Warning: There were undefined references. + + ) +Here is how much of TeX's memory you used: + 7600 strings out of 495062 + 117931 string characters out of 1182644 + 195834 words of memory out of 3000000 + 10653 multiletter control sequences out of 15000+50000 + 21980 words of font info for 89 fonts, out of 3000000 for 9000 + 28 hyphenation exceptions out of 8191 + 37i,16n,40p,230b,280s stack positions out of 5000i,500n,10000p,200000b,50000s + +Output written on rapport.dvi (4 pages, 19104 bytes). diff --git a/rapport.tex b/rapport.tex new file mode 100644 index 0000000..daab39c --- /dev/null +++ b/rapport.tex @@ -0,0 +1,356 @@ +% Fag: Numerisk matematikk +% Project 1 +% Utført av: Bjørn, Mats og Edvard + +\documentclass[12pt, a4paper]{article} +\usepackage[latin1]{inputenc} +\usepackage{listings} +\usepackage{graphicx} +\usepackage{color} +\usepackage{amssymb, amsmath} +\setcounter{secnumdepth}{0} +\setlength{\textheight}{240mm} +\setlength{\textwidth}{150mm} +\usepackage[hmargin=1cm,vmargin=2cm]{geometry} +\usepackage{xfrac} + +\definecolor{orange}{rgb}{1,0.5,0} + +\lstset{ % + language=Matlab, % the language of the code + basicstyle=\footnotesize, % the size of the fonts that are used for the code + numbers=left, % where to put the line-numbers + numberstyle=\footnotesize, % the size of the fonts that are used for the line-numbers + stepnumber=1, % the step between two line-numbers. If it's 1, each line + % will be numbered + numbersep=5pt, % how far the line-numbers are from the code + backgroundcolor=\color{white}, % choose the background color. You must add \usepackage{color} + tabsize=4, % sets default tabsize to 2 spaces + captionpos=b, % sets the caption-position to bottom + breaklines=true, % sets automatic line breaking + keywordstyle=\color{orange}\bfseries, + commentstyle=\color[rgb]{0,0,0.9} +} + +\begin{document} + +\title{Semester Project 2 in TMA4215} +\author{ + Candidate numbers: 10012, 10023, 10056 +} + +\maketitle + +\abstract{ +In this project we look at quadratic splines for interpolating a set of data +points. We also use the Romberg method for numerical evaluation of an integral. +In the end we use a mid-point Runge-Kutta method for solving a differential +equation. +} + +\section{Part 1} +\subsection{Problem 1} +\subsubsection{a)} +Since we are going to make a quadratic spline, we know that the derivative of +ths spline will be a function consisting of interconnected line segments. If we +call the spline $s$ and write $s_i$ for the value of the spline in data point +$i$, we know that +\begin{equation} + \label{eq:sdiv_linear} + s'(x) = s_i' + \frac{s_{i+1}' - s_i'}{x_{i+1} - x_i} \left(x-x_i\right). +\end{equation} +Integrating gives +\begin{equation} + \label{eq:sdiv_integrated} + s(x) = s_i'x + \frac{s_{i+1}' - s_i'}{2\left( x_{i+1} - x_i \right)} \left(x-x_i\right)^2 + C_i, +\end{equation} +and evaluating in the point $x_i$ gives +\begin{equation} + \label{eq:sdiv_evaluated} + s(x_i) = s_i'x_i + C_i = f_i. +\end{equation} +The value of our spline in the data points, $s_i$ should be equal to the +function value in the data points, $f_i$. Using \eqref{eq:sdiv_integrated} and +\eqref{eq:sdiv_evaluated} to write the difference between two succeeding points +we get +\begin{equation} + \label{eq:s_difference} + s_{i+1} - s_i = \frac{1}{2} s_i' \left( x_{i+1} - x_i \right) + \frac{1}{2} + s_{i+1}' \left(x_{i+1} - x_i\right). +\end{equation} +Moving the derivatives to the left side and simplifying leads to the following +set of equations: +\begin{equation} + \label{eq:sder_sum} + s_i' + s_{i+1}' = \frac{2\left(f_{i+1} - f_i\right)}{x_{i+1} - x_i}. +\end{equation} +Together with the extra condition that $s'(x_0) = 0$, we can write this as the +matrix equation +\begin{equation} + \label{eq:s_matrix} + \begin{bmatrix} +1 & 0 & 0 & \hdots & 0 \\ +1 & 1 & 0 & & \\ +0 & 1 & 1 & & \\ +\vdots & & & \ddots & \\ +0 & & & 1 & 1 + \end{bmatrix} + \begin{bmatrix} +s_0' \\ +s_1' \\ +s_2' \\ +\vdots \\ +s_n' + \end{bmatrix} + = + \begin{bmatrix} +0 \\ +\frac{2\left(f_1 - f_0\right)}{x_1 - x_0} \\ +\frac{2\left(f_2 - f_1\right)}{x_2 - x_1} \\ +\frac{2\left(f_3 - f_2\right)}{x_3 - x_2} \\ +\vdots \\ +\frac{2\left(f_n - f_{n-1}\right)}{x_n - x_{n-1}} + \end{bmatrix} +\end{equation} +Inserting the interpolation data we obtain the derivatives of our spline, and +table \ref{tab:data} shows what our spline has to satisfy. +\begin{table}[h] + \caption{\sf Data determining our spline polynomials.} + \begin{center} + \begin{tabular}{c c c} + \hline + $x$ & $s(x)$ & $s'(x)$ \\ + \hline + 0 & 1 & 0 \\ + 0.5 & 2 & 4 \\ + 1 & 0.5 & -10 \\ + \hline + \end{tabular} + \end{center} + \label{tab:data} +\end{table} +From table \ref{tab:data}, we easily derive the two quadratic polynomials: +\begin{equation} + \label{eq:poly} + \begin{split} + p_1 &= 4x^2 + 1 \\ + p_2 &= -14x^2 + 18x - \frac{7}{2} + \end{split} +\end{equation} + +\subsubsection{b)} +To find an error bound we define +\begin{equation} + \label{eq:g_def} + g(x) = f(x) - s(x) - \frac{x-x_{j-1}}{\bar{x} - x_{j-1}}\left( f(\bar{x}) - + s(\bar{x}) \right) +\end{equation} +on the interval $I_j = [x_{j-1}, x_j]$ where $\bar{x} \in I_j$. Since this +function is $0$ in both $x_{j-1}$ and $\bar{x}$, we know that $\exists \xi \in +\left( x_{j-1}, \bar{x} \right)$ such that +\begin{equation} + \label{eq:g_der_zero} + 0 = g'(\xi) = f'(\xi) - s'(\xi) - \left(f(\bar{x}) - s(\bar{x})\right) + \frac{1}{\bar{x} - x_{j-i}}, +\end{equation} +which gives +\begin{equation} + \label{eq:xbar_error} + \left|f(\bar{x}) - s(\bar{x})\right| = \left(\bar{x} - x_{j-1}\right) + \left|f'(\xi) - s'(\xi)\right| \leq h\left(\|f'\|_{\infty} + + \max_i|s_i'|\right). +\end{equation} +If we choose $i$ such that $|s_i'| = \max_l|s_l'|$, we derive an upper bound for +$|s_i'|$ using equation \eqref{eq:s_difference} by looking at +\begin{equation} + \label{eq:2s_bound} + \begin{split} + 2s_{i+1}' \leq s_i' + s_{i+1}' &= \frac{2(f_{i+1} - f_i)}{h} \\ + &= 2f'(\eta) \\ + &\leq 2\|f'\|_{\infty} + \end{split} +\end{equation} +which simplifies to +\begin{equation} + \label{eq:si_bound} + \begin{split} + |s_i'| &= |2f'(\eta) - s_{i+1}'| \\ + &\leq 2|f'(\eta)| + |s_{i+1}'| \\ + &\leq 3|f'(\eta)| \leq 3\|f'\|_{\infty} + \end{split} +\end{equation} +Inserting into equation \eqref{eq:xbar_error} gives an upper bound for the error +\begin{equation} + \label{eq:error_bound} + \left|f(x) - s(x)\right| \leq 4h \|f'\|_{\infty}, \forall x \in + [a,b]. +\end{equation} + +\subsection{Problem 2} +\subsubsection{a)} +In this problem we are looking at how to use the Romberg method to evaluate the +following integral: +\begin{equation} + \label{eq:integral} + \varphi = \int{0}{\varphi} \frac{\mathrm{d}\theta}{\sqrt{1 - k^2 + \sin{\theta}^2}}. +\end{equation} + +Our code for integrating functions using the Romberg method is shown in the file +\emph{romberg.m}. Table \ref{tab:romberg_conv} shows the convergence of the +Romberg method applied to the elliptic integral when $L$ increases. +\begin{table}[h!] + \caption{\sf Showing the convergence for the Romberg method over the interval +$[0, 5]$ with $k = 0.5$ as $L$ increases.} + \begin{center} + \begin{tabular}{c l c} + \hline + $L$ & Romberg \\ + \hline + 1 & 5.34 \\ + 2 & 5.27 \\ + 3 & 5.40 \\ + 5 & 5.3879 \\ + 7 & 5.3878724 \\ + 10 & 5.38787242753557 \\ + \hline + quad() & 5.38787242753557 \\ + \hline + \end{tabular} + \end{center} + \label{tab:romberg_conv} +\end{table} + +For the complete elliptic integral of the first kind, we compare the error in +the Romberg method with the error in the trapezoid method. We observe that as +$L$ increases, the error in the trapezoid method decreases much faster than the +error in the Romberg method. For example with $k = 0.5$ and $L = 4$ the error in +the trapezoid method is $2.2e-16$ while the error in the Romberg method is +$1.5e-06$. + +The small error in the trapezoid method can be explained using the +Euler-Maclaurin formula which gives the error in terms of the derivatives of the +function in the end points: +\begin{equation} + \label{eq:euler_maclaurin} + S - I = \sum_{k=2}^p \frac{B_k}{k!} \left( f^{(k-1)}(n) - f^{(k-1)}(0) \right) + + R. +\end{equation} +One can easily derive that the all the odd derivatives of the function we are +integrating, \eqref{eq:integral}, are periodic and equal to zero in +$n \sfrac{\pi}{2}$. This, combined with the fact that all the odd Bernoulli +numbers are zero except for $B_1$, makes the error in \eqref{eq:euler_maclaurin} +disappear Q=EQE=WQR=)WQR)=. + +\subsubsection{b)} +The file \emph{romberg.m} shows the use of the given estimate for the error. +Although the accuracy increases when we decrease the given tolerance value, it +does not match the number of correct decimals. This is shown in table +\ref{tab:tol_test} where we have integrated with $k = 0.5$ from $0$ to $5$. +\begin{table}[h!] + \caption{\sf Estimated integral for decreasing values of tolerance limit.} + \begin{center} + \begin{tabular}{c l c} + \hline + Tolerance & Romberg \\ + \hline + $10^{-1}$ & 5.28 \\ + $10^{-3}$ & 5.39 \\ + $10^{-5}$ & 5.38786 \\ + $10^{-7}$ & 5.38786 \\ + $10^{-9}$ & 5.38787243 \\ + $10^{-11}$ & 5.38787242753 \\ + \hline + quad() & 5.38787242753557 \\ + \hline + \end{tabular} + \end{center} + \label{tab:tol_test} +\end{table} + +\subsubsection{c)} +The Octave file \emph{newton.m} shows an implementation of Newton's method to +solve $\varphi = am(u,k)$ which is the inverse of the elliptic integral. As the +Newton method is used to find the zero, we stop when the function is no further +away from zero than the given tolerance. + +We ran this method on 100 values between -1 and 1 and compared it with the +Octave function \emph{ellipj}. This gave an error of $C\cdot TOL$ where $C$ had +a maximum value of 5. + +When choosing larger values for $|u|$ our code does not work as well. We have to +increase our tolerance to get it to return something at all, and the error in +the results varies a lot. + +\subsection{Problem 3} +\subsubsection{a)} +The mid-point Runge-Kutta method is implemented in the Octave file +\emph{PENISPENIS.m}. This gives the relation between two succeeding function +values on the following form: +\begin{equation} + \label{eq:runge_kutta} + \mathbf{m}_{n+1} - \mathbf{m}_n = hf \left(t + \frac{1}{2} h, \frac{1}{2} +(\mathbf{m}_{n+1} + \mathbf{m}_n) \right). +\end{equation} +Since this is an implicit method we use Newtons method to estimate $y_{n+1}$ for +each step of Runge-Kutta. Rearranging so that we have something that can be +solved by Newton gives +\begin{equation} + \label{eq:runge_kutta_newton} + F(\mathbf{m}_{n+1}) = \mathbf{m}_{n+1} - \mathbf{m}_n - h +\mathbf{\bar{m}}_{n+1} + \times \left(T^{-1} \mathbf{\bar{m}}_{n+1}\right) = 0, +\end{equation} +where $\mathbf{\bar{m}}_{n+1} = \frac{1}{2} \left(\mathbf{m}_{n} + +\mathbf{m}_{n+1}\right)$. + +While $\mathbf{m}_n$ is a known constant calculated earlier, the +$\mathbf{m}_{n+1}$ is a three-dimensional vector of unknowns. We need the +Jacobian to use the Newton method: +\begin{equation} + \label{eq:jacobian} + J(\mathbf{x}) = + \begin{bmatrix} +1 & +\frac{h}{2} \left(\frac{1}{I_2} - \frac{1}{I_3}\right) x_3 & +\frac{h}{2} \left(\frac{1}{I_2} - \frac{1}{I_3}\right) x_2 \\ +\frac{h}{2} \left(\frac{1}{I_3} - \frac{1}{I_1}\right) x_3 & +1 & +\frac{h}{2} \left(\frac{1}{I_3} - \frac{1}{I_1}\right) x_1 \\ +\frac{h}{2} \left(\frac{1}{I_1} - \frac{1}{I_2}\right) x_2 & +\frac{h}{2} \left(\frac{1}{I_1} - \frac{1}{I_2}\right) x_1 & +1 \\ + \end{bmatrix}. +\end{equation} +The Newton iteration is now given by +\begin{equation} + \mathbf{m}_{n+1}^{k+1} = \mathbf{m}_{n+1}^k - + \frac{F(\mathbf{m}_{n+1}^k)}{J(\mathbf{\bar{m}}_{n+1}^k)}, +\end{equation} +where we iterate over $k$ until we are pleased with our new approximation for +$\mathbf{m}_{n+1}$. + +To find the order of our method we consider our means of solving the ODE with +step sizes $\frac{1}{2^k}$ where $k = 1, 2, ..., 5$. For each $k$ we compute the +values of our Runge-Kutta method and the provided elliptic method in the +interval zero to one. The values of the Runge-Kutta method is subtracted from +the elliptic method, and the norms of these give a sequence of errors. ***. The +elements in the sequence are now on the form $C (\frac{1}{2^k})^p$ where $p$ is +the order of the method. We now divide the first element by the second, the +second by the third and so on. Taking the base-two-logarithm of this gives us +$p$. This is found numerically to be $2$ in the Octave function +\emph{freerigid.m}. + +HER MÅ VI SETTE INN EN TABELL SOM SAMMENLIGNER LØSNINGENE + +\subsubsection{b)} +We chose to use the Octave-forge function \emph{ode45} as a comparison against +the other methods. With the time interval $[0, 50]$, the Octave script +\emph{rigidbodysimulator.m} produced the plot showed in figure +\ref{fig:ode_comparison}. PLX INSERT IGUURE. EXPLAIN ANALYZE. We observe that +the \emph{ode45}-method, which is a Runge-Kutta-method of order (4, 5), has an +error that often grows faster than the others. + +\subsubsection{c)} + +\end{document} diff --git a/rigidbodysimulator.m b/rigidbodysimulator.m new file mode 100644 index 0000000..4885802 --- /dev/null +++ b/rigidbodysimulator.m @@ -0,0 +1,33 @@ +start = [1;1;1]; +interval = [0, 30]; +h = 1; +tspan = [0:h:30]; +T = diag([3, 4, 5]); +f = @(t,x) cross(x,T\x); + +midpoint = []; +midpoint(1,:) = start; +elliptic = []; +elliptic(1,:) = start; +ode = []; +ode(1,:) = start; +t = 0; +i = 2; +while t < interval(2) + midpoint(i,:) = newtfree(midpoint(i-1,:)', h, T); + elliptic(i,:) = freewR(h, T(1,1), T(2,2), T(3,3), elliptic(i-1,1), elliptic(i-1,2), elliptic(i-1,3)); + t = t + h; + i = i + 1; +end +ode = ode45(f, interval, start'); + +clf; +hold off; +figure(1); +hold on; +plot3(midpoint(:,1), midpoint(:,2), midpoint(:,3), 'r-'); +hold on; +plot3(elliptic(:,1), elliptic(:,2), elliptic(:,3), 'b-'); +hold on; +plot3(ode.y(:,1), ode.y(:,2), ode.y(:,3), 'g-'); + diff --git a/romberg.m b/romberg.m new file mode 100644 index 0000000..3d903d2 --- /dev/null +++ b/romberg.m @@ -0,0 +1,30 @@ +function integral = romberg(k, a, b, tol) + +f = @(x) 1/sqrt(1 - k^2 * sin(x)^2); + +R(1,1) = 0.5 * (b - a) * (f(a) + f(b)); +E(1,1) = 0; + +row = 2; +while 1 + hn = (b - a)/(2.0^(row-1)); + R(row,1) = 0.5 * R(row-1,1); + s = 0; + for k = [1:2^(row-2)] + s += f(a + (2*k-1)*hn); + end + R(row,1) += hn * s; + E(row,1) = 0; + + for col = [2:row] + R(row,col) = ((4^(col-1))*R(row,col-1) - R(row-1,col-1)) / (4**(col-1) - 1); + %est = R(row,col) - R(row,col-1); + est = (1.0/(4.0^col - 1)) * (R(row,col-1) - R(row-1,col-1)); + E(row,col) = abs(est); + if abs(est) < tol + integral = R(row,col); + return + end + end + row++; +end diff --git a/romberg.py b/romberg.py new file mode 100644 index 0000000..51e3d97 --- /dev/null +++ b/romberg.py @@ -0,0 +1,26 @@ +import numpy as np + +def romberg(f, a, b, tol): + + R = np.zeros((tol, tol)) + + R[0][0] = 0.5 * (b - a) * (f(a) + f(b)) + for i in xrange(1, tol): + hn = float(b - a)/float(2**i) + R[i][0] = 0.5 * R[i-1][0] + R[i][0] += hn * sum([f(a + (2*k-1)*hn) for k in xrange(1, 2**(i-1)+1)]) + print hn + print sum([f(a + (2*k-1)*hn) for k in xrange(1, 2**(i-1)+1)]) + + for i in xrange(1, tol): + for row in xrange(0, tol - i): + R[row][i] = ((4**i)*R[row+1][i-1] - R[row][i-1]) / (4**i - 1) + + return R + +def main(): + + print romberg(lambda x: np.sqrt(x), 0, 5, 6) + +if __name__ == '__main__': + main() diff --git a/rombergold.m b/rombergold.m new file mode 100644 index 0000000..4b3a26d --- /dev/null +++ b/rombergold.m @@ -0,0 +1,24 @@ +function [rll, rl0] = rombergold(f, a, b, L) + +R(1,1) = 0.5 * (b - a) * (f(a) + f(b)); + +for i = [2:L] + hn = (b - a)/(2.0^(i-1)); + R(i,1) = 0.5 * R(i-1,1); + s = 0; + for k = [1:2^(i-2)] + s += f(a + (2*k-1)*hn); + end + R(i,1) += hn * s; +end + +for i = [2:L] + for row = [i:L] + R(row,i) = ((4^(i-1))*R(row,i-1) - R(row-1,i-1)) / (4**(i-1) - 1); + end +end + +rll = R(L,L); +rl0 = R(L,1); + +end -- 2.47.3