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This is pdfTeX, Version 3.14159265-2.6-1.40.15 (TeX Live 2015/dev/Debian) (preloaded format=latex)
entering extended mode
(./latex_ea332f494edd1d5b8c26114131d47768a1b51a5b_p.tex
LaTeX2e <2014/05/01>
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l.7 \documentclass
                  [12pt]{article}

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l.13 \usepackage
                {sagetex}

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l.14 \usepackage
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l.20 \begin{document}
                     
[1]

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l.31 \begin{sageverbatim}
                         

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l.33 \end{sageverbatim}
                       
(/usr/share/texlive/texmf-dist/tex/latex/base/omscmr.fd) [2]

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l.63 \begin{sageverbatim}
                         

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l.67 \begin{sageverbatim}
                         

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l.69 \end{sageverbatim}
                       

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l.71 \begin{sageverbatim}
                         

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l.73 \end{sageverbatim}
                       

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l.75 \begin{sageverbatim}
                         
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                $
l.76 harary.num_
                verts(), harary.num_edges()

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l.77 \end{sageverbatim}
                       
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l.77 \end{sageverbatim}
                       

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l.79 \begin{sageverbatim}
                         
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l.80 harary.is_
               planar()

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l.83 \begin{sageverbatim}
                         
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l.84 H=harary.hamiltonian_
                          cycle()

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l.88 \begin{sageverbatim}
                         
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l.89 harary.degree_
                   sequence()

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l.92 \begin{sageverbatim}
                         
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l.93 sorted(harary.degree_
                          sequence())

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\OT1/cmr/m/n/12 (1,3)])   harary   harary.plot()   harary.num$[]\OML/cmm/m/it/1
2 erts\OT1/cmr/m/n/12 ()\OML/cmm/m/it/12 ; harary:num[]dges\OT1/cmr/m/n/12 ()$ 
 harary.is$[]\OML/cmm/m/it/12 lanar\OT1/cmr/m/n/12 ()$

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\OT1/cmr/m/n/12 H=harary.hamiltonian$[]\OML/cmm/m/it/12 ycle\OT1/cmr/m/n/12 ()\
OML/cmm/m/it/12 H:plot\OT1/cmr/m/n/12 ()$  harary.degree$[]\OML/cmm/m/it/12 equ
ence\OT1/cmr/m/n/12 ()$  sorted(harary.degree$[]\OML/cmm/m/it/12 equence\OT1/cm
r/m/n/12 ())$ 

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l.100 \begin{sageverbatim}
                          

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l.102 \end{sageverbatim}
                        

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l.104 \begin{sageverbatim}
                          
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l.105 trees_
            iterator = graphs.trees(8)

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l.112 \begin{sageverbatim}
                          

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l.114 \end{sageverbatim}
                        

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l.118 \begin{sageverbatim}
                          
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l.119 graphs_
             list.show_graphs(T8)

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\OML/cmm/m/it/12 graphs:trees\OT1/cmr/m/n/12 (8)\OML/cmm/m/it/12 T\OT1/cmr/m/n/
12 8 = \OML/cmm/m/it/12 list\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 trees[]terator\OT
1/cmr/m/n/12 )\OML/cmm/m/it/12 T\OT1/cmr/m/n/12 8$ From a path to a star:  [tre
e.diameter()
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l.125 \includegraphics
                      {4peghanoi.jpg}\par

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l.135 \begin{sageverbatim}
                          

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l.142 \begin{sageverbatim}
                          
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l.143 solution=T.shortest_
                          path((0,0,0,0), (1,1,1,1))

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l.149 \begin{sageverbatim}
                          

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l.153 \begin{sageverbatim}
                          

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l.159 \begin{sageverbatim}
                          

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l.165 \begin{sageverbatim}
                          

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l.168 \end{sageverbatim}
                        

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l.172 \begin{sageverbatim}
                          
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l.174 T.num_
            verts()

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l.178 \begin{sageverbatim}
                          
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l.179 solution = T.shortest_
                            path(0, 4^8-1)

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l.183 \begin{sageverbatim}
                          

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l.185 \end{sageverbatim}
                        

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l.189 \begin{sageverbatim}
                          
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l.191 A = T.automorphism_
                         group()

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l.195 \begin{sageverbatim}
                          
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l.197 S4.is_
            isomorphic(A)

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l.198 \end{sageverbatim}
                        

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\OT1/cmr/m/n/12 graphs.HanoiTowerGraph(4, 4, la-bels=False, po-si-tions=True) T
.show(figsize=12)

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\OT1/cmr/m/n/12 For-get about graph-ics, work with graph it-self.  T = graphs.H
anoiTowerGraph(4,

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\OT1/cmr/m/n/12 graphs.HanoiTowerGraph(4, 6, la-bels=False, po-si-tions=False) 
A = T.automorphism$[]\OML/cmm/m/it/12 roup\OT1/cmr/m/n/12 ()\OML/cmm/m/it/12 A:
order\OT1/cmr/m/n/12 ()$
[3]

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l.210 \begin{sageverbatim}
                          
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l.211 G.degree_
               seq

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l.218 \begin{sageverbatim}
                          
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l.220 A = P.automorphism_
                         group()

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l.226 \end{sageverbatim}
                        

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l.228 \begin{sageverbatim}
                          
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l.229 A.is_
           transitive()

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l.236 \begin{sageverbatim}
                          

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l.240 \begin{sageverbatim}
                          

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l.244 \begin{sageverbatim}
                          
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l.245 H.is_
           isomorphic(DihedralGroup(6))

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l.248 \begin{sageverbatim}
                          
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l.249 ds = A.derived_
                     series()

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l.256 \begin{sageverbatim}
                          
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l.258 B.is_
           isomorphic(AlternatingGroup(5))

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l.263 \begin{sageverbatim}
                          
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l.264 A = random_
                 matrix(ZZ, 1000, 1000)

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l.266 \end{sageverbatim}
                        
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                $
l.266 \end{sageverbatim}
                        

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l.268 \begin{sageverbatim}
                          

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l.270 \end{sageverbatim}
                        

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l.272 \begin{sageverbatim}
                          
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l.273 adj = K.adjacency_
                        matrix()

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l.275 \end{sageverbatim}
                        
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                $
l.275 \end{sageverbatim}
                        

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l.277 \begin{sageverbatim}
                          

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l.279 \end{sageverbatim}
                        

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l.283 \begin{sageverbatim}
                          
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l.285 S.add_
            vertices([4, 5, 6])

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l.289 \end{sageverbatim}
                        
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l.289 \end{sageverbatim}
                        

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l.291 \begin{sageverbatim}
                          
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l.292 graph_
            editor(S)

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l.293 \end{sageverbatim}
                        
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l.293 \end{sageverbatim}
                        

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l.295 \begin{sageverbatim}
                          
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l.296 adj = S.adjacency_
                        matrix()

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l.299 \end{sageverbatim}
                        
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l.299 \end{sageverbatim}
                        

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l.303 \begin{sageverbatim}
                          
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l.304 adjQ = adj.change_
                        ring(QQ)

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l.312 \begin{sageverbatim}
                          

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l.314 \end{sageverbatim}
                        

Overfull \hbox (29.13197pt too wide) in paragraph at lines 216--316
\OT1/cmr/m/n/12 sg = S.subgroups(); sg   [H.order() for H in sg]   H.is$[]\OML/
cmm/m/it/12 somorphic\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 DihedralGroup\OT1/cmr/m/
n/12 (6))$

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\OT1/cmr/m/n/12 ds = A.derived$[]\OML/cmm/m/it/12 eries\OT1/cmr/m/n/12 ()$  [K.
order() for K in ds]   B = ds[1] B.is$[]\OML/cmm/m/it/12 somorphic\OT1/cmr/m/n/
12 (\OML/cmm/m/it/12 AlternatingGroup\OT1/cmr/m/n/12 (5))$

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\OT1/cmr/m/n/12 Com-pre-hen-sive sup-port for lin-ear al-ge-bra.  A = random$[]
\OML/cmm/m/it/12 atrix\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 ZZ; \OT1/cmr/m/n/12 100
0\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 1000)\OML/cmm/m/it/12 timeA:determinant\OT1
/cmr/m/n/12 ()$

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\OT1/cmr/m/n/12 S.add$[]\OML/cmm/m/it/12 ertices\OT1/cmr/m/n/12 ([4\OML/cmm/m/i
t/12 ; \OT1/cmr/m/n/12 5\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 6])\OML/cmm/m/it/12 
S:add[]dges\OT1/cmr/m/n/12 ([(2\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 4)\OML/cmm/m/
it/12 ; \OT1/cmr/m/n/12 (2\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 5)\OML/cmm/m/it/12
 ; \OT1/cmr/m/n/12 (2\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 6)])\OML/cmm/m/it/12 S:
add[]dges\OT1/cmr/m/n/12 ([(3\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 4)\OML/cmm/m/it
/12 ; \OT1/cmr/m/n/12 (3\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 5)\OML/cmm/m/it/12 ;
 \OT1/cmr/m/n/12 (3\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 6)])\OML/cmm/m/it/12 S:pl
ot\OT1/cmr/m/n/12 ()$

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l.323 \begin{sageverbatim}
                          
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l.324 stirling_
               number2(500,30)

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l.328 number_
             of_derangements(["a", 'b', 'c', 'd', 'e'])

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l.333 \begin{sageverbatim}
                          

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l.337 \begin{sageverbatim}
                          

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l.341 \begin{sageverbatim}
                          

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l.349 \begin{sageverbatim}
                          

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l.351 \end{sageverbatim}
                        

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l.353 \begin{sageverbatim}
                          

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l.357 \begin{sageverbatim}
                          

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l.359 \end{sageverbatim}
                        

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l.365 \begin{sageverbatim}
                          
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l.367 p = bernoulli_
                    polynomial(t, 5); p

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l.370 \begin{sageverbatim}
                          

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l.372 \end{sageverbatim}
                        

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l.374 \begin{sageverbatim}
                          

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l.380 \begin{sageverbatim}
                          
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l.382 q(t) = bernoulli_
                       polynomial(t, 5); q

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l.383 \end{sageverbatim}
                        

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l.385 \begin{sageverbatim}
                          

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l.387 \end{sageverbatim}
                        

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l.389 \begin{sageverbatim}
                          

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l.391 \end{sageverbatim}
                        

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l.395 \begin{sageverbatim}
                          
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l.397 r = bernoulli_
                    polynomial(t, 5); r

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l.398 \end{sageverbatim}
                        

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l.400 \begin{sageverbatim}
                          
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l.401 r.is_
           irreducible()

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l.402 \end{sageverbatim}
                        

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l.404 \begin{sageverbatim}
                          

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l.406 \end{sageverbatim}
                        

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l.408 \begin{sageverbatim}
                          

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l.410 \end{sageverbatim}
                        

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l.414 \begin{sageverbatim}
                          

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l.417 \end{sageverbatim}
                        

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l.419 \begin{sageverbatim}
                          

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l.421 \end{sageverbatim}
                        

Overfull \hbox (72.02396pt too wide) in paragraph at lines 321--425
[]\OT1/cmr/m/n/12 The usual func-tions:  stirling$[]\OML/cmm/m/it/12 umber\OT1/
cmr/m/n/12 2(500\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 30)$  number$[]\OML/cmm/m/it
/12 f[]erangements\OT1/cmr/m/n/12 (["\OML/cmm/m/it/12 a\OT1/cmr/m/n/12 "\OML/cm
m/m/it/12 ;[] b[];[] c[];[] d[];[] e[]\OT1/cmr/m/n/12 ])$
[4]

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l.429 \begin{sageverbatim}
                          

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l.431 \end{sageverbatim}
                        

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l.433 \begin{sageverbatim}
                          
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                $
l.434 A = random_
                 matrix(QQ, 4, num_bound=9, den_bound=9)

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l.436 \end{sageverbatim}
                        
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l.436 \end{sageverbatim}
                        

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l.440 \begin{sageverbatim}
                          
! Missing $ inserted.
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                $
l.442 P.set_
            latex_options(vertex_shape='diamond', vertex_color='red', vertex...


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l.443 \end{sageverbatim}
                        
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l.443 \end{sageverbatim}
                        

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l.445 \begin{sageverbatim}
                          

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l.447 \end{sageverbatim}
                        

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l.449 \begin{sageverbatim}
                          
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                $
l.450 from sage.graphs.graph_
                             latex import setup_latex_preamble

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l.453 \end{sageverbatim}
                        
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                $
l.453 \end{sageverbatim}
                        

Overfull \hbox (83.80836pt too wide) in paragraph at lines 427--455
\OT1/cmr/m/n/12 Excellent L[]T[]Xsupport.  la-tex(integrate(sec(x), x))   A = r
andom$[]\OML/cmm/m/it/12 atrix\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 QQ; \OT1/cmr/m/
n/12 4\OML/cmm/m/it/12 ; num[]ound \OT1/cmr/m/n/12 =

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\OT1/cmr/m/n/12 9\OML/cmm/m/it/12 ; den[]ound \OT1/cmr/m/n/12 = 9)\OML/cmm/m/it
/12 latex\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 A\OT1/cmr/m/n/12 )$ L[]T[]X ver-sion
s of graphs:  P = graphs.PetersenGraph()

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\OT1/cmr/m/n/12 P.set$[]\OML/cmm/m/it/12 atex[]ptions\OT1/cmr/m/n/12 (\OML/cmm/
m/it/12 vertex[]hape \OT1/cmr/m/n/12 =[] \OML/cmm/m/it/12 diamond[]; vertex[]ol
or \OT1/cmr/m/n/12 =[] \OML/cmm/m/it/12 red[]; vertex[]abel[]olor \OT1/cmr/m/n/
12 =[]

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\OML/cmm/m/it/12 gold[]; edge[]olor \OT1/cmr/m/n/12 =[] \OML/cmm/m/it/12 blue[]
\OT1/cmr/m/n/12 )$  la-tex(P)   from sage.graphs.graph$[]\OML/cmm/m/it/12 atexi
mportsetup[]atex[]reamblesetup[]atex[]reamble\OT1/cmr/m/n/12 ()\OML/cmm/m/it/12
 latex:jsmath[]void[]ist\OT1/cmr/m/n/12 ([]\OML/cmm/m/it/12 tikzpicture[]\OT1/c
mr/m/n/12 )$ 
! Undefined control sequence.
l.456 \includegraphics
                      {petersen-uvic.png}

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l.461 \begin{sageverbatim}
                          

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l.463 \end{sageverbatim}
                        

Overfull \hbox (99.43594pt too wide) in paragraph at lines 469--471
[]$\OMS/cmsy/m/n/12 ^^O$ \OT1/cmr/m/n/12 In-put: []\OT1/cmtt/m/n/12 Today's dat
e \$2011-02-12=20110212\$ factors as \sage{factor(20110212)}. 

Underfull \hbox (badness 10000) in paragraph at lines 473--475


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l.483 \begin{sageverbatim}
                          
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                $
l.485 A_
        image = pylab.mean(pylab.imread(DATA + 'mystery.png'), 2)

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l.492 \end{sageverbatim}
                        
! Missing $ inserted.
<inserted text> 
                $
l.492 \end{sageverbatim}
                        

! LaTeX Error: Environment sageverbatim undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.496 \begin{sageverbatim}
                          
! Missing $ inserted.
<inserted text> 
                $
l.498 def animate_
                  contraction(g, e, frames = 12, **kwds):
! Missing $ inserted.
<inserted text> 
                $
l.511 
      

Overfull \hbox (4.7357pt too wide) in paragraph at lines 481--511
[]\OT1/cmr/m/n/12 Code adapted from a demon-stra-tion by William Stein  im-port
 py-lab A$[]\OML/cmm/m/it/12 mage \OT1/cmr/m/n/12 =

Overfull \hbox (22.7925pt too wide) in paragraph at lines 481--511
\OML/cmm/m/it/12 pylab:mean\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 pylab:imread\OT1/c
mr/m/n/12 (\OML/cmm/m/it/12 DATA \OT1/cmr/m/n/12 +[] \OML/cmm/m/it/12 mystery:p
ng[]\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 2)@\OML/cmm/m/it/12 int
eractdefsvd[]mage\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 i \OT1/cmr/m/n/12 =

Overfull \hbox (33.81068pt too wide) in paragraph at lines 481--511
\OML/cmm/m/it/12 sum\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 s\OT1/cmr/m/n/12 [\OML/cm
m/m/it/12 j\OT1/cmr/m/n/12 ] \OMS/cmsy/m/n/12 ^^C \OML/cmm/m/it/12 pylab:outer\
OT1/cmr/m/n/12 (\OML/cmm/m/it/12 u\OT1/cmr/m/n/12 [0 :\OML/cmm/m/it/12 ; j\OT1/
cmr/m/n/12 ]\OML/cmm/m/it/12 ; v\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 j; \OT1/cmr/m
/n/12 0 :])\OML/cmm/m/it/12 forjinrange\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 i\OT1/
cmr/m/n/12 ))\OML/cmm/m/it/12 show\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 matrix[]lot
\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 A\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; axes \OT
1/cmr/m/n/12 =

Overfull \hbox (14.0397pt too wide) in paragraph at lines 481--511
\OT1/cmr/m/n/12 Sage Wiki (In-ter-acts) by Pablo An-gulo.  def animate$[]\OML/c
mm/m/it/12 ontraction\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 g; e; frames \OT1/cmr/m/
n/12 =

Overfull \hbox (136.07274pt too wide) in paragraph at lines 481--511
\OT1/cmr/m/n/12 12\OML/cmm/m/it/12 ; \OMS/cmsy/m/n/12 ^^C ^^C \OML/cmm/m/it/12 
kwds\OT1/cmr/m/n/12 ) : \OML/cmm/m/it/12 v\OT1/cmr/m/n/12 1\OML/cmm/m/it/12 ; v
\OT1/cmr/m/n/12 2 = \OML/cmm/m/it/12 eifnotg:has[]dge\OT1/cmr/m/n/12 (\OML/cmm/
m/it/12 v\OT1/cmr/m/n/12 1\OML/cmm/m/it/12 ; v\OT1/cmr/m/n/12 2) : \OML/cmm/m/i
t/12 raiseValueError; \OT1/cmr/m/n/12 "\OML/cmm/m/it/12 GivenedgenotfoundonGrap
h\OT1/cmr/m/n/12 "\OML/cmm/m/it/12 ls \OT1/cmr/m/n/12 =

Overfull \hbox (27.62787pt too wide) in paragraph at lines 481--511
\OT1/cmr/m/n/12 []\OML/cmm/m/it/12 posd \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 g:ge
t[]os\OT1/cmr/m/n/12 ()\OML/cmm/m/it/12 forjinrange\OT1/cmr/m/n/12 (\OML/cmm/m/
it/12 frames\OT1/cmr/m/n/12 ) : \OML/cmm/m/it/12 gp \OT1/cmr/m/n/12 = \OML/cmm/
m/it/12 Graph\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 g\OT1/cmr/m/n/12 )\OML/cmm/m/it/
12 posdp \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 dict\OT1/cmr/m/n/12 (\OML/cmm/m/it/
12 posd\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 p\OT1/cmr/m/n/12 1 =

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\OML/cmm/m/it/12 posdp\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 v\OT1/cmr/m/n/12 1]\OML
/cmm/m/it/12 p\OT1/cmr/m/n/12 2 = \OML/cmm/m/it/12 posdp\OT1/cmr/m/n/12 [\OML/c
mm/m/it/12 v\OT1/cmr/m/n/12 2]\OML/cmm/m/it/12 posdp\OT1/cmr/m/n/12 [\OML/cmm/m
/it/12 v\OT1/cmr/m/n/12 2] = [\OML/cmm/m/it/12 a \OMS/cmsy/m/n/12 ^^C \OT1/cmr/
m/n/12 (\OML/cmm/m/it/12 frames \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 j\OT1/cmr
/m/n/12 )\OML/cmm/m/it/12 =frames \OT1/cmr/m/n/12 + \OML/cmm/m/it/12 b \OMS/cms
y/m/n/12 ^^C \OML/cmm/m/it/12 j=framesfora; binzip\OT1/cmr/m/n/12 (\OML/cmm/m/i
t/12 p\OT1/cmr/m/n/12 2\OML/cmm/m/it/12 ; p\OT1/cmr/m/n/12 1)]$ 
[5]
! Missing $ inserted.
<inserted text> 
                $
l.512         gp.set_
                     pos(posdp)
! Missing $ inserted.
<inserted text> 
                $
l.515 
      
! Missing $ inserted.
<inserted text> 
                $
l.516 def animate_
                  vertex_deletion(g, v, frames = 12, **kwds):
! Missing $ inserted.
<inserted text> 
                $
l.534 
      

Overfull \hbox (124.57397pt too wide) in paragraph at lines 516--534
[]\OT1/cmr/m/n/12 def animate$[]\OML/cmm/m/it/12 ertex[]eletion\OT1/cmr/m/n/12 
(\OML/cmm/m/it/12 g; v; frames \OT1/cmr/m/n/12 = 12\OML/cmm/m/it/12 ; \OMS/cmsy
/m/n/12 ^^C ^^C \OML/cmm/m/it/12 kwds\OT1/cmr/m/n/12 ) : \OML/cmm/m/it/12 kwds\
OT1/cmr/m/n/12 2 = \OML/cmm/m/it/12 dict\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 kwds\
OT1/cmr/m/n/12 )\OML/cmm/m/it/12 if[]vertex[]olors[]inkwds \OT1/cmr/m/n/12 :

Overfull \hbox (20.49643pt too wide) in paragraph at lines 516--534
\OML/cmm/m/it/12 cs \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 dict\OT1/cmr/m/n/12 (\OM
L/cmm/m/it/12 kwds\OT1/cmr/m/n/12 [[]\OML/cmm/m/it/12 vertex[]olors[]\OT1/cmr/m
/n/12 ])\OML/cmm/m/it/12 forc; vsinkwds\OT1/cmr/m/n/12 [[]\OML/cmm/m/it/12 vert
ex[]olors[]\OT1/cmr/m/n/12 ]\OML/cmm/m/it/12 :items\OT1/cmr/m/n/12 () : \OML/cm
m/m/it/12 ifvinvs \OT1/cmr/m/n/12 :

Overfull \hbox (216.78722pt too wide) in paragraph at lines 516--534
\OML/cmm/m/it/12 kwds\OT1/cmr/m/n/12 2 = \OML/cmm/m/it/12 dict\OT1/cmr/m/n/12 (
\OML/cmm/m/it/12 kwds\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 g\OT1/cmr/m/n/12 2 = \OM
L/cmm/m/it/12 Graph\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 g\OT1/cmr/m/n/12 )\OML/cmm
/m/it/12 posd \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 dict\OT1/cmr/m/n/12 (\OML/cmm/
m/it/12 g:get[]os\OT1/cmr/m/n/12 ())\OML/cmm/m/it/12 delposd\OT1/cmr/m/n/12 [\O
ML/cmm/m/it/12 v\OT1/cmr/m/n/12 ]\OML/cmm/m/it/12 g\OT1/cmr/m/n/12 2\OML/cmm/m/
it/12 :delete[]ertex\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 v\OT1/cmr/m/n/12 )\OML/cm
m/m/it/12 g\OT1/cmr/m/n/12 2\OML/cmm/m/it/12 :set[]os\OT1/cmr/m/n/12 (\OML/cmm/
m/it/12 posd\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 return\OT1/cmr/m/n/12 [\OML/cmm/m
/it/12 plot\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 g; \OMS/cmsy/m/n/12 ^^C ^^C
! Missing $ inserted.
<inserted text> 
                $
l.535 def animate_
                  edge_deletion(g, e, frames = 12, **kwds):
! Missing $ inserted.
<inserted text> 
                $
l.540 
      

Overfull \hbox (33.546pt too wide) in paragraph at lines 535--540
\OML/cmm/m/it/12 Graph\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 g\OT1/cmr/m/n/12 )\OML/
cmm/m/it/12 g\OT1/cmr/m/n/12 2\OML/cmm/m/it/12 :delete[]dge\OT1/cmr/m/n/12 (\OM
L/cmm/m/it/12 e\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 return\OT1/cmr/m/n/12 [\OML/cm
m/m/it/12 plot\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 g; \OMS/cmsy/m/n/12 ^^C ^^C \OM
L/cmm/m/it/12 kwds\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; plot\OT1/cmr/m/n/12 (\OML
/cmm/m/it/12 g\OT1/cmr/m/n/12 2\OML/cmm/m/it/12 ; \OMS/cmsy/m/n/12 ^^C ^^C \OML
/cmm/m/it/12 kwds\OT1/cmr/m/n/12 )] \OMS/cmsy/m/n/12 ^^C \OML/cmm/m/it/12 int\O
T1/cmr/m/n/12 (\OML/cmm/m/it/12 frames=\OT1/cmr/m/n/12 2)$ 
! Missing $ inserted.
<inserted text> 
                $
l.541 def animate_
                  glide(g, pos1, pos2, frames = 12, **kwds):
! Missing $ inserted.
<inserted text> 
                $
l.554 
      

Overfull \hbox (44.57045pt too wide) in paragraph at lines 541--554
[]\OT1/cmr/m/n/12 def animate$[]\OML/cmm/m/it/12 lide\OT1/cmr/m/n/12 (\OML/cmm/
m/it/12 g; pos\OT1/cmr/m/n/12 1\OML/cmm/m/it/12 ; pos\OT1/cmr/m/n/12 2\OML/cmm/
m/it/12 ; frames \OT1/cmr/m/n/12 = 12\OML/cmm/m/it/12 ; \OMS/cmsy/m/n/12 ^^C ^^
C \OML/cmm/m/it/12 kwds\OT1/cmr/m/n/12 ) : \OML/cmm/m/it/12 ls \OT1/cmr/m/n/12 
= []\OML/cmm/m/it/12 forjinrange\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 frames\OT1/cm
r/m/n/12 ) :

Overfull \hbox (89.74574pt too wide) in paragraph at lines 541--554
\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 b \OMS/cmsy/m/n/12 ^^C \OML/cmm/m/it/12 j=fra
mes \OT1/cmr/m/n/12 + \OML/cmm/m/it/12 a \OMS/cmsy/m/n/12 ^^C \OT1/cmr/m/n/12 (
\OML/cmm/m/it/12 frames \OMS/cmsy/m/n/12 ^^@ \OML/cmm/m/it/12 j\OT1/cmr/m/n/12 
)\OML/cmm/m/it/12 =framesfora; binzip\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 p\OT1/cm
r/m/n/12 1\OML/cmm/m/it/12 ; p\OT1/cmr/m/n/12 2)]\OML/cmm/m/it/12 gp:set[]os\OT
1/cmr/m/n/12 (\OML/cmm/m/it/12 pos\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ls:append\O
T1/cmr/m/n/12 (\OML/cmm/m/it/12 plot\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 gp; \OMS/
cmsy/m/n/12 ^^C ^^C
! Missing $ inserted.
<inserted text> 
                $
l.558 def new_
              color():
! Missing $ inserted.
<inserted text> 
                $
l.560 
      
! Missing $ inserted.
<inserted text> 
                $
l.561 def animate_
                  minor(g, m, frames = 12, pause = 50, step_time = 100):

LaTeX Warning: Command \' invalid in math mode on input line 562.

! Please use \mathaccent for accents in math mode.
\[email protected] [email protected] \spacefactor }\accent 
                                                  #1 #2\egroup \spacefactor ...
l.562     '''Crea una animació
                               n que muestra cómo un grafo tiene un menor m
! You can't use `\spacefactor' in math mode.
\[email protected] ...}\accent #1 #2\egroup \spacefactor 
                                                  \[email protected] 
l.562     '''Crea una animació
                               n que muestra cómo un grafo tiene un menor m

LaTeX Warning: Command \' invalid in math mode on input line 562.

! Please use \mathaccent for accents in math mode.
\[email protected] [email protected] \spacefactor }\accent 
                                                  #1 #2\egroup \spacefactor ...
l.562     '''Crea una animación que muestra có
                                                mo un grafo tiene un menor m
! You can't use `\spacefactor' in math mode.
\[email protected] ...}\accent #1 #2\egroup \spacefactor 
                                                  \[email protected] 
l.562     '''Crea una animación que muestra có
                                                mo un grafo tiene un menor m
! Missing $ inserted.
<inserted text> 
                $
l.572 
      

Overfull \hbox (327.68427pt too wide) in paragraph at lines 561--572
[]\OT1/cmr/m/n/12 def animate$[]\OML/cmm/m/it/12 inor\OT1/cmr/m/n/12 (\OML/cmm/
m/it/12 g; m; frames \OT1/cmr/m/n/12 = 12\OML/cmm/m/it/12 ; pause \OT1/cmr/m/n/
12 = 50\OML/cmm/m/it/12 ; step[]ime \OT1/cmr/m/n/12 = 100) :[] \OML/cmm/m/it/12
 Creaunaanimaci[]nquemuestrac[]moungrafotieneunmenorm[]posd \OT1/cmr/m/n/12 =

Overfull \hbox (216.15955pt too wide) in paragraph at lines 561--572
\OML/cmm/m/it/12 max\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 max\OT1/cmr/m/n/12 (\OML/
cmm/m/it/12 xforx; yinposg\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; max\OT1/cmr/m/n/1
2 (\OML/cmm/m/it/12 xforx; yinposm\OT1/cmr/m/n/12 ))\OML/cmm/m/it/12 ymax \OT1/
cmr/m/n/12 = \OML/cmm/m/it/12 max\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 max\OT1/cmr/
m/n/12 (\OML/cmm/m/it/12 yforx; yinposg\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; max\
OT1/cmr/m/n/12 (\OML/cmm/m/it/12 yforx; yinposm\OT1/cmr/m/n/12 ))\OML/cmm/m/it/
12 xmin \OT1/cmr/m/n/12 =

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\OML/cmm/m/it/12 min\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 min\OT1/cmr/m/n/12 (\OML/
cmm/m/it/12 xforx; yinposg\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; min\OT1/cmr/m/n/1
2 (\OML/cmm/m/it/12 xforx; yinposm\OT1/cmr/m/n/12 ))\OML/cmm/m/it/12 ymin \OT1/
cmr/m/n/12 = \OML/cmm/m/it/12 min\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 min\OT1/cmr/
m/n/12 (\OML/cmm/m/it/12 yforx; yinposg\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; min\
OT1/cmr/m/n/12 (\OML/cmm/m/it/12 yforx; yinposm\OT1/cmr/m/n/12 ))\OML/cmm/m/it/
12 dd \OT1/cmr/m/n/12 =
! You can't use `macro parameter character #' in vertical mode.
l.573     #
           Set colors
! Missing $ inserted.
<inserted text> 
                $
l.574     m_
            colors = dict((v,new_color()) for v in m.vertices())
! Missing $ inserted.
<inserted text> 
                $
l.577 
      

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[]\OT1/cmr/m/n/12 Set col-ors m$[]\OML/cmm/m/it/12 olors \OT1/cmr/m/n/12 = \OML
/cmm/m/it/12 dict\OT1/cmr/m/n/12 ((\OML/cmm/m/it/12 v; new[]olor\OT1/cmr/m/n/12
 ())\OML/cmm/m/it/12 forvinm:vertices\OT1/cmr/m/n/12 ())\OML/cmm/m/it/12 g[]olo
rs \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 dict\OT1/cmr/m/n/12 ((\OML/cmm/m/it/12 m[
]olors\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 k\OT1/cmr/m/n/12 ]\OML/cmm/m/it/12 ; vs
\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 fork; vsindd:items\OT1/cmr/m/n/12 ())$ 
! Missing $ inserted.
<inserted text> 
                $
l.578     extra_
                vs = (set(g.vertices()) -
! Missing $ inserted.
<inserted text> 
                $
l.582 
      

Overfull \hbox (34.71065pt too wide) in paragraph at lines 578--582
[]\OT1/cmr/m/n/12 extra$[]\OML/cmm/m/it/12 s \OT1/cmr/m/n/12 = (\OML/cmm/m/it/1
2 set\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 g:vertices\OT1/cmr/m/n/12 ()) \OMS/cmsy/
m/n/12 ^^@ \OML/cmm/m/it/12 set\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 vforvsindd:val
ues\OT1/cmr/m/n/12 ()\OML/cmm/m/it/12 forvinvs\OT1/cmr/m/n/12 ))\OML/cmm/m/it/1
2 g[]olors\OT1/cmr/m/n/12 [(0\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 0\OML/cmm/m/it/
12 ; \OT1/cmr/m/n/12 0)] =
! You can't use `macro parameter character #' in vertical mode.
l.583     #
           pics contains the frames of the animation
! You can't use `macro parameter character #' in horizontal mode.
l.584     #
           no colors at the beggining
! You can't use `macro parameter character #' in vertical mode.
l.588     #
           First: eliminate extra vertices
! Missing $ inserted.
<inserted text> 
                $
l.589     for v in extra_
                         vs:
! Missing $ inserted.
<inserted text> 
                $
l.596 
      

Overfull \hbox (181.58517pt too wide) in paragraph at lines 588--596
[]\OT1/cmr/m/n/12 First: elim-i-nate ex-tra ver-tices for v in extra$[]\OML/cmm
/m/it/12 s \OT1/cmr/m/n/12 : \OML/cmm/m/it/12 pics:extend\OT1/cmr/m/n/12 (\OML/
cmm/m/it/12 animate[]ertex[]eletion\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 gg; v; fra
mes; vertex[]olors \OT1/cmr/m/n/12 =

Overfull \hbox (31.80675pt too wide) in paragraph at lines 588--596
\OML/cmm/m/it/12 g[]olors\OT1/cmr/m/n/12 ))\OML/cmm/m/it/12 gg:delete[]ertex\OT
1/cmr/m/n/12 (\OML/cmm/m/it/12 v\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 delposd\OT1/c
mr/m/n/12 [\OML/cmm/m/it/12 v\OT1/cmr/m/n/12 ]\OML/cmm/m/it/12 g[]olors\OT1/cmr
/m/n/12 [(0\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 0\OML/cmm/m/it/12 ; \OT1/cmr/m/n/
12 0)]\OML/cmm/m/it/12 :remove\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 v\OT1/cmr/m/n/1
2 )\OML/cmm/m/it/12 delg[]olors\OT1/cmr/m/n/12 [(0\OML/cmm/m/it/12 ; \OT1/cmr/m
/n/12 0\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 0)]$ 
! You can't use `macro parameter character #' in vertical mode.
l.597     #
           Second: contract edges
! Missing $ inserted.
<inserted text> 
                $
l.598     for color, vs in g_
                             colors.items():
! Missing $ inserted.
<inserted text> 
                $
l.612 
      

Overfull \hbox (293.51616pt too wide) in paragraph at lines 597--612
\OML/cmm/m/it/12 forjinxrange\OT1/cmr/m/n/12 (1\OML/cmm/m/it/12 ; len\OT1/cmr/m
/n/12 (\OML/cmm/m/it/12 vs\OT1/cmr/m/n/12 )) : \OML/cmm/m/it/12 ifgg:has[]dge\O
T1/cmr/m/n/12 (\OML/cmm/m/it/12 vs\OT1/cmr/m/n/12 [0]\OML/cmm/m/it/12 ; vs\OT1/
cmr/m/n/12 [\OML/cmm/m/it/12 j\OT1/cmr/m/n/12 ]) : \OML/cmm/m/it/12 breakpics:e
xtend\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 animate[]ontraction\OT1/cmr/m/n/12 (\OML
/cmm/m/it/12 gg; \OT1/cmr/m/n/12 (\OML/cmm/m/it/12 vs\OT1/cmr/m/n/12 [0]\OML/cm
m/m/it/12 ; vs\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 j\OT1/cmr/m/n/12 ])\OML/cmm/m/i
t/12 ; frames; vertex[]olors \OT1/cmr/m/n/12 =

Overfull \hbox (194.5743pt too wide) in paragraph at lines 597--612
\OML/cmm/m/it/12 g[]olors\OT1/cmr/m/n/12 ))\OML/cmm/m/it/12 forvingg:neighbors\
OT1/cmr/m/n/12 (\OML/cmm/m/it/12 vs\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 j\OT1/cmr/
m/n/12 ]) : \OML/cmm/m/it/12 gg:add[]dge\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 vs\OT
1/cmr/m/n/12 [0]\OML/cmm/m/it/12 ; v\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 gg:delete
[]ertex\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 vs\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 j\
OT1/cmr/m/n/12 ])\OML/cmm/m/it/12 delposd\OT1/cmr/m/n/12 [\OML/cmm/m/it/12 vs\O
T1/cmr/m/n/12 [\OML/cmm/m/it/12 j\OT1/cmr/m/n/12 ]]\OML/cmm/m/it/12 gg:set[]os\
OT1/cmr/m/n/12 (\OML/cmm/m/it/12 posd\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 posd \OT
1/cmr/m/n/12 =
! You can't use `macro parameter character #' in vertical mode.
l.613     #
           Relabel vertices of m so that they match with those of gg
! You can't use `macro parameter character #' in vertical mode.
l.620     #
           Third: glide to position in m
[6]
! Missing $ inserted.
<inserted text> 
                $
l.621     pos_
              m = m.get_pos()
! Missing $ inserted.
<inserted text> 
                $
l.626 
      

Overfull \hbox (276.85094pt too wide) in paragraph at lines 620--626
[]\OT1/cmr/m/n/12 Third: glide to po-si-tion in m pos$[] = \OML/cmm/m/it/12 m:g
et[]os\OT1/cmr/m/n/12 ()\OML/cmm/m/it/12 pos[] \OT1/cmr/m/n/12 = \OML/cmm/m/it/
12 gg:get[]os\OT1/cmr/m/n/12 ()\OML/cmm/m/it/12 pics:extend\OT1/cmr/m/n/12 (\OM
L/cmm/m/it/12 animate[]lide\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 gg; pos[]; pos[]; 
frames; vertex[]olors \OT1/cmr/m/n/12 =
! You can't use `macro parameter character #' in vertical mode.
l.627     #
           Fourth: delete redundant edges
! Missing $ inserted.
<inserted text> 
                $
l.629         if not m.has_
                           edge(e):
! Missing $ inserted.
<inserted text> 
                $
l.633 
      

Overfull \hbox (10.19482pt too wide) in paragraph at lines 627--633
\OT1/cmr/m/n/12 m.has$[]\OML/cmm/m/it/12 dge\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 e
\OT1/cmr/m/n/12 ) : \OML/cmm/m/it/12 pics:extend\OT1/cmr/m/n/12 (\OML/cmm/m/it/
12 animate[]dge[]eletion\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 gg; e; frames; vertex
[]olors \OT1/cmr/m/n/12 =
! You can't use `macro parameter character #' in vertical mode.
l.634     #
           And wait for a moment
! Missing $ inserted.
<inserted text> 
                $
l.635     pics.extend([plot(gg, vertex_
                                       colors = g_colors)]*frames)
! Missing $ inserted.
<inserted text> 
                $
l.636 
      

Overfull \hbox (8.26604pt too wide) in paragraph at lines 634--636
[]\OT1/cmr/m/n/12 And wait for a mo-ment pics.extend([plot(gg, vertex$[]\OML/cm
m/m/it/12 olors \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 g[]olors\OT1/cmr/m/n/12 )] \
OMS/cmsy/m/n/12 ^^C \OML/cmm/m/it/12 frames\OT1/cmr/m/n/12 )$ 

! LaTeX Error: \begin{document} on input line 20 ended by \end{sageverbatim}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.639 \end{sageverbatim}
                        

! LaTeX Error: Environment sageverbatim undefined.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.641 \begin{sageverbatim}
                          
! Missing $ inserted.
<inserted text> 
                $
l.642 graph_
            list = {'CompleteGraph4':graphs.CompleteGraph(4),

! LaTeX Error: \begin{document} on input line 20 ended by \end{sageverbatim}.

See the LaTeX manual or LaTeX Companion for explanation.
Type  H <return>  for immediate help.
 ...                                              
                                                  
l.671 \end{sageverbatim}
                        
! Missing $ inserted.
<inserted text> 
                $
l.671 \end{sageverbatim}
                        

Overfull \hbox (2187.3995pt too wide) in paragraph at lines 637--673
\OT1/cmr/m/n/12 0.1, ymax = ymax + 0.1)   graph$[]\OML/cmm/m/it/12 ist \OT1/cmr
/m/n/12 = []@\OML/cmm/m/it/12 interactdef[]u\OT1/cmr/m/n/12 1 =

Overfull \hbox (15.26898pt too wide) in paragraph at lines 637--673
\OML/cmm/m/it/12 text[]ontrol\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 value \OT1/cmr/m
/n/12 =[] \OML/cmm/m/it/12 Doesthisgraph[]\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; g
 \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 selector\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 g
raph[]ist:keys\OT1/cmr/m/n/12 ()\OML/cmm/m/it/12 ; buttons \OT1/cmr/m/n/12 =

Overfull \hbox (2.32649pt too wide) in paragraph at lines 637--673
\OML/cmm/m/it/12 True\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; u\OT1/cmr/m/n/12 2 = \
OML/cmm/m/it/12 text[]ontrol\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 value \OT1/cmr/m/
n/12 =[] \OML/cmm/m/it/12 haveaminorisomorphictothisothergraph \OT1/cmr/m/n/12 
:[]

Overfull \hbox (8.0012pt too wide) in paragraph at lines 637--673
\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; m \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 select
or\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 graph[]ist:keys\OT1/cmr/m/n/12 ()\OML/cmm/m
/it/12 ; buttons \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 True\OT1/cmr/m/n/12 )\OML/c
mm/m/it/12 ; u\OT1/cmr/m/n/12 3 = \OML/cmm/m/it/12 text[]ontrol\OT1/cmr/m/n/12 
(\OML/cmm/m/it/12 value \OT1/cmr/m/n/12 =[]

Overfull \hbox (38.6131pt too wide) in paragraph at lines 637--673
\OT1/cmr/m/n/12 ?\OML/cmm/m/it/12 Itishas; showittome; withananimationwiththefo
llowingparameters[]\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 ; frames \OT1/cmr/m/n/12 =


Overfull \hbox (59.41747pt too wide) in paragraph at lines 637--673
\OML/cmm/m/it/12 slider\OT1/cmr/m/n/12 (1\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 15\
OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 1\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 4\OML/cmm
/m/it/12 ; label \OT1/cmr/m/n/12 =[] \OML/cmm/m/it/12 Framespersecond[]\OT1/cmr
/m/n/12 )\OML/cmm/m/it/12 ; step[]ime \OT1/cmr/m/n/12 = \OML/cmm/m/it/12 slider
\OT1/cmr/m/n/12 (1\OML/cmm/m/it/12 =\OT1/cmr/m/n/12 10\OML/cmm/m/it/12 ; \OT1/c
mr/m/n/12 2\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 1\OML/cmm/m/it/12 =\OT1/cmr/m/n/1
2 10\OML/cmm/m/it/12 ; \OT1/cmr/m/n/12 1\OML/cmm/m/it/12 ; label \OT1/cmr/m/n/1
2 =[]

Overfull \hbox (104.56949pt too wide) in paragraph at lines 637--673
\OML/cmm/m/it/12 h\OT1/cmr/m/n/12 3 \OML/cmm/m/it/12 > Pleaseselecttwodifferent
graphs < =h\OT1/cmr/m/n/12 3 \OML/cmm/m/it/12 >[]\OT1/cmr/m/n/12 )\OML/cmm/m/it
/12 returntry \OT1/cmr/m/n/12 : \OML/cmm/m/it/12 a \OT1/cmr/m/n/12 = \OML/cmm/m
/it/12 animate[]inor\OT1/cmr/m/n/12 (\OML/cmm/m/it/12 g; m; frames \OT1/cmr/m/n
/12 =

Overfull \hbox (9.72966pt too wide) in paragraph at lines 637--673
\OML/cmm/m/it/12 frames\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 a:show\OT1/cmr/m/n/12 
(\OML/cmm/m/it/12 delay \OT1/cmr/m/n/12 = 100 \OMS/cmsy/m/n/12 ^^C \OML/cmm/m/i
t/12 step[]ime=frames\OT1/cmr/m/n/12 )\OML/cmm/m/it/12 exceptValueError \OT1/cm
r/m/n/12 : \OML/cmm/m/it/12 html\OT1/cmr/m/n/12 ([]\OML/cmm/m/it/12 <

Overfull \hbox (62.60728pt too wide) in paragraph at lines 637--673
\OML/cmm/m/it/12 h\OT1/cmr/m/n/12 3 \OML/cmm/m/it/12 > Thefirstgraphhave < stro
ng > NO < =strong > minorisomorphictothesecond <
[7] [8] [9] (./latex_ea332f494edd1d5b8c26114131d47768a1b51a5b_p.aux) )
(\end occurred inside a group at level 1)

### semi simple group (level 1) entered at line 20 (\begingroup)
### bottom level
(see the transcript file for additional information)
Output written on latex_ea332f494edd1d5b8c26114131d47768a1b51a5b_p.dvi (9 pages
, 25480 bytes).
Transcript written on latex_ea332f494edd1d5b8c26114131d47768a1b51a5b_p.log.

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