This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Debian) (preloaded format=latex 2025.1.13) 13 OCT 2025 07:36 entering extended mode restricted \write18 enabled. %&-line parsing enabled. **SandBoxSageAxiomInterface.tex (./SandBoxSageAxiomInterface.tex LaTeX2e <2022-11-01> patch level 1 L3 programming layer <2023-01-16> (/usr/share/texlive/texmf-dist/tex/latex/base/article.cls Document Class: article 2022/07/02 v1.4n Standard LaTeX document class (/usr/share/texlive/texmf-dist/tex/latex/base/size10.clo File: size10.clo 2022/07/02 v1.4n Standard LaTeX file (size option) ) \c@part=\count185 \c@section=\count186 \c@subsection=\count187 \c@subsubsection=\count188 \c@paragraph=\count189 \c@subparagraph=\count190 \c@figure=\count191 \c@table=\count192 \abovecaptionskip=\skip48 \belowcaptionskip=\skip49 \bibindent=\dimen140 ) (/usr/share/texmf/tex/latex/axiom.sty \nwmarginglue=\dimen141 \codehsize=\dimen142 \codemargin=\dimen143 \nwdefspace=\dimen144 \equivbox=\box51 LaTeX Font Info: External font `cmex10' loaded for size (Font) <7> on input line 77. LaTeX Font Info: External font `cmex10' loaded for size (Font) <5> on input line 77. \plusequivbox=\box52 \nwcodetopsep=\skip50 \nwcodepenalty=\count193 \@original@textwidth=\dimen145 \nwcodecommentsep=\skip51 \@nwlopage=\count194 \@nwhipage=\count195 \@nwlosub=\count196 \@nwhisub=\count197 \@nwpagetemp=\count198 \@nwpagecount=\count199 \sub@page=\count266 \@nwalph@n=\count267 \nw@chunkcount=\count268 \@commacount=\count269 \nwix@counter=\count270 ) (/usr/share/texlive/texmf-dist/tex/latex/l3backend/l3backend-dvips.def File: l3backend-dvips.def 2023-01-16 L3 backend support: dvips \l__pdf_internal_box=\box53 \g__pdf_backend_object_int=\count271 \l__pdf_backend_content_box=\box54 \l__pdf_backend_model_box=\box55 \g__pdf_backend_annotation_int=\count272 \g__pdf_backend_link_int=\count273 \g__pdf_backend_link_sf_int=\count274 ) (./SandBoxSageAxiomInterface.aux) \openout1 = `SandBoxSageAxiomInterface.aux'. LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 8. LaTeX Font Info: ... okay on input line 8. LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 8. LaTeX Font Info: ... okay on input line 8. LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 8. LaTeX Font Info: ... okay on input line 8. LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 8. LaTeX Font Info: ... okay on input line 8. LaTeX Font Info: Checking defaults for TS1/cmr/m/n on input line 8. LaTeX Font Info: ... okay on input line 8. LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 8. LaTeX Font Info: ... okay on input line 8. LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 8. LaTeX Font Info: ... okay on input line 8. LaTeX Font Info: External font `cmex10' loaded for size (Font) <9> on input line 25. LaTeX Font Info: External font `cmex10' loaded for size (Font) <6> on input line 25. Overfull \hbox (3.42267pt too wide) in paragraph at lines 44--46 \OT1/cmr/m/n/9 a nor-mal lin-ear rep-re-sen-ta-tion of any Ax-iom ob-ject x, us e \OT1/cmtt/m/n/9 str(x). no emph [] Overfull \hbox (11.82156pt too wide) in paragraph at lines 54--54 []\OT1/cmtt/m/n/9 You can always use x.str() to obtain the linear representatio n [] Overfull \hbox (25.9964pt too wide) in paragraph at lines 55--55 []\OT1/cmtt/m/n/9 of an object, even without changing the display2d flag. This can [] Overfull \hbox (1.2963pt too wide) in paragraph at lines 81--81 []\OT1/cmtt/m/n/9 the factor method on it. Notice that the notation \code{f.f actor()}[] [] [1 ] Overfull \hbox (16.54651pt too wide) in paragraph at lines 83--83 []\OT1/cmtt/m/n/9 because of the excellent implementation of axiom. For exampl e, [] Overfull \hbox (180.84421pt too wide) in paragraph at lines 141--141 [] \OT1/cmtt/m/n/9 8.201219330881975641524897300208124427852048438593149412 21237124017312418754011041266612384955016056b1[] [] Overfull \hbox (445.44113pt too wide) in paragraph at lines 141--141 [] \OT1/cmtt/m/n/9 93326215443944152681699238856266700490715968264381621468 5929638952175999932299156089414639761565182862536979208272237582511852109168640 00000000000000000000000[] [] Overfull \hbox (185.56915pt too wide) in paragraph at lines 141--141 [] \OT1/cmtt/m/n/9 x^6*y^3 + 9*x^4*y^3 + 27*x^2*y^3 + 27*y^3 + 3*x^5*y^2 + 18*x^3*y^2 + 27*x*y^2 + 3*x^4*y + 9*x^2*y + x^3[] [] Overfull \hbox (161.94443pt too wide) in paragraph at lines 141--141 [] \OT1/cmtt/m/n/9 (27*y^3*z^6 + 135*y^2*z^5 + (675*y^3 + 225*y)*z^4 + (225 0*y^2 + 125)*z^3 + (5625*y^3 + 1875*y)*z^2[] [] Overfull \hbox (313.14267pt too wide) in paragraph at lines 141--141 [] \OT1/cmtt/m/n/9 {\Tt{}a\ =\ (25*sqrt(79)*{\%}i\ +\ 25)/(6*sqrt(79)*{\%}i \ -\ 34),b\ =\ (5*sqrt(79)*{\%}i\ +\ 5)/(sqrt(79)*{\%}i\ +\ 11),\nwnewline[] [] Overfull \hbox (317.86761pt too wide) in paragraph at lines 141--141 []\OT1/cmtt/m/n/9 \ \ \ \ \ [a\ =\ (25*sqrt(79)*{\%}i\ -\ 25)/(6*sqrt(79)*{\%} i\ +\ 34),b\ =\ (5*sqrt(79)*{\%}i\ -\ 5)/(sqrt(79)*{\%}i\ -\ 11),\nwnewline[] [] [2] Overfull \hbox (6.02124pt too wide) in paragraph at lines 141--141 [] \OT1/cmtt/m/n/9 sage: axiom('x^2 + y^2 = (x^2 - y^2)/sqrt(x^2 + y^2)').s olve('y')[] [] Overfull \hbox (161.94443pt too wide) in paragraph at lines 141--141 [] \OT1/cmtt/m/n/9 [y = - sqrt(( - y^2 - x^2)*sqrt(y^2 + x^2) + x^2),y = s qrt(( - y^2 - x^2)*sqrt(y^2 + x^2) + x^2)][] [] Overfull \hbox (1073.85883pt too wide) in paragraph at lines 147--147 [] \OT1/cmtt/m/n/9 \left[ \left[ a=\frac{25 \sqrt{79} i+25}{6 \sqrt{79} i-3 4} , b= \frac{5 \sqrt{79} i+5}{\sqrt{79} i+11} , c=\frac{\sqrt{79} i+1}{10} \right] , \left[ a=\frac{25 \sqrt{79} i-25}{6 \sqrt{79} i+34} , b= \frac{5 \s qrt{79} i-5}{\sqrt{79} i-11} , c=-\frac{\sqrt{79} i-1}{10} \right] \right][] [] Overfull \hbox (30.72134pt too wide) in paragraph at lines 149--149 []\OT1/cmtt/m/n/9 (TODO: For OS X should create pdf output and use preview inst ead?) [] Overfull \hbox (53.27069pt too wide) in paragraph at lines 178--178 [] \OT1/cmtt/m/n/9 k*x^3*%e^(k*x)*sin(w*x) + 3*x^2*%e^(k*x)*sin(w*x) + w*x^ 3*%e^(k*x)*cos(w*x)[] [] Overfull \hbox (1536.90344pt too wide) in paragraph at lines 178--178 [] \OT1/cmtt/m/n/9 (((k*w^6 + 3*k^3*w^4 + 3*k^5*w^2 + k^7)*x^3 + (3*w^6 + 3 *k^2*w^4 - 3*k^4*w^2 - 3*k^6)*x^2 + ( - 18*k*w^4 - 12*k^3*w^2 + 6*k^5)*x - 6*w^ 4 + 36*k^2*w^2 - 6*k^4)*%e^(k*x)*sin(w*x) + (( - w^7 - 3*k^2*w^5 - 3*k^4*w^3 - k^6*w)*x^3 + (6*k*w^5 + 12*k^3*w^3 + 6*k^5*w)*x^2 + (6*w^5 - 12*k^2*w^3 - 18*k^ 4*w)*x - 24*k*w^3 + 24*k^3*w)*%e^(k*x)*cos(w*x))/(w^8 + 4*k^2*w^6 + 6*k^4*w^4 + 4*k^6*w^2 + k^8)[] [] [3] Overfull \hbox (76.89542pt too wide) in paragraph at lines 194--194 [] \OT1/cmtt/m/n/9 {\Tt{}[0,4],[3,1\nwendquote},[1,0,0, - 4],[0,1,0, - 2],[ 0,0,1, - 4/3],[1,2,3,4]][] [] Overfull \hbox (185.56915pt too wide) in paragraph at lines 243--243 [] \OT1/cmtt/m/n/9 360*(2*s - 2)/(s^2 - 2*s + 2)^4 - 480*(2*s - 2)^3/(s^2 - 2*s + 2)^5 + 120*(2*s - 2)^5/(s^2 - 2*s + 2)^6[] [] [4] Overfull \hbox (30.72134pt too wide) in paragraph at lines 244--244 []\OT1/cmtt/m/n/9 Even better, use view(axiom("laplace(diff(x(t),t,2),t,s)")) t o see [] ! Missing $ inserted. $ l.249 ...tinued fraction $a + 1/(b + 1/(c + \cdots ))$ is I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing $ inserted. $ l.249 ... fraction $a + 1/(b + 1/(c + \cdots))$ is I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing } inserted. } l.249 ... fraction $a + 1/(b + 1/(c + \cdots))$ is I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Extra }, or forgotten \endgroup. \@par ... \@noitemerr {\@@par }\fi \else {\@@par } \fi l.249 ... fraction $a + 1/(b + 1/(c + \cdots))$ is I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. Overfull \hbox (6.02124pt too wide) in paragraph at lines 275--275 [] \OT1/cmtt/m/n/9 sage.: axiom('plot3d(x^2-y^2, [x,-2,2], [y,-2,2], [grid, 12,12])')[] [] Overfull \hbox (1.2963pt too wide) in paragraph at lines 285--285 [] \OT1/cmtt/m/n/9 ----------------------- - --------------- --------[] [] Overfull \hbox (1.2963pt too wide) in paragraph at lines 285--285 [] \OT1/cmtt/m/n/9 (%e - 1) (%e + 1) (%e - 1) (%e + 1)[] [] ! Missing $ inserted. $ l.286 We formally compute the limit as $n\to \infty$ of $2S/n$ as follows: I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing $ inserted. $ l.286 ...mit as $n\to\infty$ of $2S/n$ as follows: I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing } inserted. } l.286 ...mit as $n\to\infty$ of $2S/n$ as follows: I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Extra }, or forgotten \endgroup. \@par ... \@noitemerr {\@@par }\fi \else {\@@par } \fi l.286 ...mit as $n\to\infty$ of $2S/n$ as follows: I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. ! Missing $ inserted. $ l.293 Obtaining digits of $\pi $: I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing $ inserted. $ l.293 Obtaining digits of $\pi$: I've inserted a begin-math/end-math symbol since I think you left one out. Proceed, with fingers crossed. ! Missing } inserted. } l.293 Obtaining digits of $\pi$: I've inserted something that you may have forgotten. (See the above.) With luck, this will get me unwedged. But if you really didn't forget anything, try typing `2' now; then my insertion and my current dilemma will both disappear. ! Extra }, or forgotten \endgroup. \@par ... \@noitemerr {\@@par }\fi \else {\@@par } \fi l.293 Obtaining digits of $\pi$: I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. [5] Overfull \hbox (185.56915pt too wide) in paragraph at lines 299--299 [] \OT1/cmtt/m/n/9 3.141592653589793238462643383279502884197169399375105820 974944592307816406286208998628034825342117068b0[] [] ! Extra }, or forgotten \endgroup. l.343 } I've deleted a group-closing symbol because it seems to be spurious, as in `$x}$'. But perhaps the } is legitimate and you forgot something else, as in `\hbox{$x}'. In such cases the way to recover is to insert both the forgotten and the deleted material, e.g., by typing `I$}'. [6] LaTeX Font Info: External font `cmex10' loaded for size (Font) <12> on input line 345. LaTeX Font Info: External font `cmex10' loaded for size (Font) <8> on input line 345. Overfull \hbox (475.92542pt too wide) in paragraph at lines 345--345 [][] [] [7] [8] Overfull \hbox (82.74953pt too wide) in paragraph at lines 439--439 []\OT1/cmtt/m/n/10 8.201219330881975641524897300208124427852048438593149412212 37124017312418754011041266612384955016056b1[] [] Overfull \hbox (376.74696pt too wide) in paragraph at lines 442--442 []\OT1/cmtt/m/n/10 93326215443944152681699238856266700490715968264381621468592 9638952175999932299156089414639761565182862536979208272237582511852109168640000 00000000000000000000[] [] Overfull \hbox (4.00021pt too wide) in paragraph at lines 446--446 []\OT1/cmtt/m/n/10 x^6*y^3 + 9*x^4*y^3 + 27*x^2*y^3 + 27*y^3 + 3*x^5*y^2 + 18* x^3*y^2 + 27*x*y^2 + 3*x^4*y [] Overfull \hbox (61.74971pt too wide) in paragraph at lines 451--451 []\OT1/cmtt/m/n/10 (27*y^3*z^6 + 135*y^2*z^5 + (675*y^3 + 225*y)*z^4 + (2250*y ^2 + 125)*z^3 + (5625*y^3 + 1875*y)*z^2 [] Overfull \hbox (4.00021pt too wide) in paragraph at lines 457--457 []\OT1/cmtt/m/n/10 [[a = (25*sqrt(79)*%i + 25)/(6*sqrt(79)*%i - 34),b = (5*sqr t(79)*%i + 5)/(sqrt(79)*%i + [] Overfull \hbox (51.2498pt too wide) in paragraph at lines 457--457 \OT1/cmtt/m/n/10 11),c = (sqrt(79)*%i + 1)/10],[a = (25*sqrt(79)*%i - 25)/(6*s qrt(79)*%i + 34),b = (5*sqrt(79)*%i [] Overfull \hbox (19.75008pt too wide) in paragraph at lines 463--463 []\OT1/cmtt/m/n/10 [y = - sqrt(( - y^2 - x^2)*sqrt(y^2 + x^2) + x^2),y = sqrt (( - y^2 - x^2)*sqrt(y^2 + x^2) [] Overfull \hbox (56.49976pt too wide) in paragraph at lines 467--467 []\OT1/cmtt/m/n/10 \left[ \left[ a=\frac{25 \sqrt{79} i+25}{6 \sqrt{79} i-34} , b= \frac{5 \sqrt{79} i+5}{\sqrt{79} [] Overfull \hbox (35.49994pt too wide) in paragraph at lines 467--467 \OT1/cmtt/m/n/10 i+11} , c=\frac{\sqrt{79} i+1}{10} \right] , \left[ a=\fra c{25 \sqrt{79} i-25}{6 \sqrt{79} [] Overfull \hbox (19.75008pt too wide) in paragraph at lines 467--467 \OT1/cmtt/m/n/10 i+34} , b= \frac{5 \sqrt{79} i-5}{\sqrt{79} i-11} , c=-\frac {\sqrt{79} i-1}{10} \right] [] [9] Overfull \hbox (14.50012pt too wide) in paragraph at lines 488--488 []\OT1/cmtt/m/n/10 (((k*w^6 + 3*k^3*w^4 + 3*k^5*w^2 + k^7)*x^3 + (3*w^6 + 3*k^ 2*w^4 - 3*k^4*w^2 - 3*k^6)*x^2 [] Overfull \hbox (9.25017pt too wide) in paragraph at lines 488--488 \OT1/cmtt/m/n/10 + ( - 18*k*w^4 - 12*k^3*w^2 + 6*k^5)*x - 6*w^4 + 36*k^2*w^2 - 6*k^4)*%e^(k*x)*sin(w*x) + [] Overfull \hbox (35.49994pt too wide) in paragraph at lines 488--488 \OT1/cmtt/m/n/10 (( - w^7 - 3*k^2*w^5 - 3*k^4*w^3 - k^6*w)*x^3 + (6*k*w^5 + 12 *k^3*w^3 + 6*k^5*w)*x^2 + (6*w^5 [] Overfull \hbox (4.00021pt too wide) in paragraph at lines 488--488 \OT1/cmtt/m/n/10 - 12*k^2*w^3 - 18*k^4*w)*x - 24*k*w^3 + 24*k^3*w)*%e^(k*x)*co s(w*x))/(w^8 + 4*k^2*w^6 + [] [10] Overfull \hbox (19.75008pt too wide) in paragraph at lines 541--541 []\OT1/cmtt/m/n/10 360*(2*s - 2)/(s^2 - 2*s + 2)^4 - 480*(2*s - 2)^3/(s^2 - 2* s + 2)^5 + 120*(2*s - 2)^5/(s^2 [] [11] [12] Overfull \hbox (87.99948pt too wide) in paragraph at lines 615--615 []\OT1/cmtt/m/n/10 3.141592653589793238462643383279502884197169399375105820974 944592307816406286208998628034825342117068b0[] [] [13] [14] [15] [16] [17] [18] [19] Overfull \hbox (4.00021pt too wide) in paragraph at lines 946--946 []\OT1/cmtt/m/n/10 raise TypeError, "Error executing code in Axiom\nCODE:\n\t% s\nAxiom ERROR:\n\t%s"%(cmd, [] [20] Overfull \hbox (103.74934pt too wide) in paragraph at lines 1002--1002 []\OT1/cmtt/m/n/10 sage.: opts = '[gnuplot_preamble, "set nokey"], [gnuplot_te rm, ps], [gnuplot_out_file, "circle-plot.eps"]'[] [] [21] Overfull \hbox (4.00021pt too wide) in paragraph at lines 1057--1057 []\OT1/cmtt/m/n/10 sage.: axiom.plot3d_parametric(["v*sin(u)","v*cos(u)","v"], ["u","v"],[-3.2,3.2],[0,3])[] [] [22] Overfull \hbox (30.24998pt too wide) in paragraph at lines 1059--1059 []\OT1/cmtt/m/n/10 sage.: axiom.plot3d_parametric(["v*sin(u)","v*cos(u)","v"], ["u","v"],[-3.2,3.2],[0,3],opts)[] [] Overfull \hbox (40.7499pt too wide) in paragraph at lines 1065--1065 []\OT1/cmtt/m/n/10 sage.: _ = axiom.eval("expr_1: cos(y)*(10.0+6*cos(x)); expr _2: sin(y)*(10.0+6*cos(x)); expr_3: [] [23] Overfull \hbox (9.25017pt too wide) in paragraph at lines 1116--1116 []\OT1/cmtt/m/n/10 cmd = "ic2("+a+",%s=%s,%s=%s,diff(%s,%s)=%s);"%(vars[0],ics [0], vars[1],ics[1], vars[1], [] Overfull \hbox (14.50012pt too wide) in paragraph at lines 1137--1137 []\OT1/cmtt/m/n/10 sage.: axiom.de_solve_laplace("diff(f(x),x,2) = 2*diff(f(x) ,x)-f(x)", ["x","f"], [0,1,2])[] [] [24] [25] Overfull \hbox (35.49994pt too wide) in paragraph at lines 1234--1234 []\OT1/cmtt/m/n/10 sage.: zeta_ptsx = [ (pari(1/2 + i*I/10).zeta().real()).pre cision(1) for i in range (70,150)][] [] Overfull \hbox (35.49994pt too wide) in paragraph at lines 1235--1235 []\OT1/cmtt/m/n/10 sage.: zeta_ptsy = [ (pari(1/2 + i*I/10).zeta().imag()).pre cision(1) for i in range (70,150)][] [] Overfull \hbox (56.49976pt too wide) in paragraph at lines 1237--1237 []\OT1/cmtt/m/n/10 sage.: opts='[gnuplot_preamble, "set nokey"], [gnuplot_term , ps], [gnuplot_out_file, "zeta.eps"]'[] [] [26] Overfull \hbox (9.25017pt too wide) in paragraph at lines 1259--1259 []\OT1/cmtt/m/n/10 sage.: zeta_ptsx1 = [ (pari(1/2+i*I/10).zeta().real()).prec ision(1) for i in range (10)][] [] Overfull \hbox (9.25017pt too wide) in paragraph at lines 1260--1260 []\OT1/cmtt/m/n/10 sage.: zeta_ptsy1 = [ (pari(1/2+i*I/10).zeta().imag()).prec ision(1) for i in range (10)][] [] Overfull \hbox (30.24998pt too wide) in paragraph at lines 1262--1262 []\OT1/cmtt/m/n/10 sage.: zeta_ptsx1 = [ (pari(1/2+i*I/10).zeta().real()).prec ision(1) for i in range (10,150)][] [] Overfull \hbox (30.24998pt too wide) in paragraph at lines 1263--1263 []\OT1/cmtt/m/n/10 sage.: zeta_ptsy1 = [ (pari(1/2+i*I/10).zeta().imag()).prec ision(1) for i in range (10,150)][] [] [27] [28] [29] [30] [31] [32] [33] [34] [35] (./SandBoxSageAxiomInterface.aux) ) (\end occurred inside a group at level 9) ### semi simple group (level 9) entered at line 338 (\begingroup) ### semi simple group (level 8) entered at line 276 (\begingroup) ### semi simple group (level 7) entered at line 244 (\begingroup) ### semi simple group (level 6) entered at line 148 (\begingroup) ### semi simple group (level 5) entered at line 148 (\begingroup) ### semi simple group (level 4) entered at line 66 (\begingroup) ### semi simple group (level 3) entered at line 54 (\begingroup) ### semi simple group (level 2) entered at line 46 (\begingroup) ### simple group (level 1) entered at line 16 ({) ### bottom level Here is how much of TeX's memory you used: 773 strings out of 478052 13024 string characters out of 5840969 1869327 words of memory out of 5000000 20963 multiletter control sequences out of 15000+600000 517914 words of font info for 52 fonts, out of 8000000 for 9000 14 hyphenation exceptions out of 8191 34i,6n,38p,444b,835s stack positions out of 10000i,1000n,20000p,200000b,200000s Output written on SandBoxSageAxiomInterface.dvi (35 pages, 62772 bytes).