mailing-list for TeXmacs Users

["Pablo S. Casas" <address@hidden>]

Hi TeXmacs users:

   I have 4 issues (in order of importance) I want to share with you.
I use TeXmacs-1.0.7.14 from Mandriva 2010.2 Linux.


I) Float big table in two columns document

The attached document float.tm presents a big table which is right
positioned when the document is formatted to 1 column. Instead if
Document -> Paragraph -> Number of columns -> 2 is set, then the big
table is formatted in one column, not in the whole document width. Is
it possible in two-column documents to have a float big table spanned
to two columns? If the big table is not float everything is OK.


II) TeXmacs-qt doesn't show .ps figures

In 1.0.7.14 still persists the problem of inserting .ps figures from
matplotlib. They are shown in a very small size in TeXmacs-qt,
compared to exported PDF or TeXmacs-x11, in which they have the
correct size.


III) TeXmacs crashes when inserting a footnote

The attached document carta_ejemplo.tm makes TeXmacs-1.0.7.14 crash
when trying to export it to pdf. It seems to be related to the
insertion of a footnote. The messages in ~/.xsession-errors are:

TeXmacs] Fatal error, zero lines in insertion
TeXmacs] Crash report saved in ~/.TeXmacs/system/crash/crash_report_38
TeXmacs] Current buffer report saved in 
~/.TeXmacs/system/crash/crash_report_38_tree
texmacs.bin: ./Typeset/Page/make_pages.cpp:50: box 
pager_rep::pages_format(array<page_item>, SI, SI, SI): Assertion `N(bs) != 0' 
failed.

Also attached files crash_report_38, crash_report_38_tree.


IV) TeXmacs crashes when using "Undo"

This happen unexpectedly in many different and varied situations, with
no clear pattern.

   The rest TeXmacs is almost perfect for me. Thanks a lot for your
patience.

   Pablo S. Casas

document -- [ 1 ]
  "" -- [ 1, 0 ]
  letter-header -- [ 1, 1 ]
    document -- [ 1, 1, 0 ]
      destination -- [ 1, 1, 0, 0 ]
        document -- [ 1, 1, 0, 0, 0 ]
          "D. bla bla bla" -- [ 1, 1, 0, 0, 0, 0 ]
          "bla bla bla" -- [ 1, 1, 0, 0, 0, 1 ]
          "36349 bla bla bla" -- [ 1, 1, 0, 0, 0, 2 ]
      "" -- [ 1, 1, 0, 1 ]
      "" -- [ 1, 1, 0, 2 ]
      address -- [ 1, 1, 0, 3 ]
        document -- [ 1, 1, 0, 3, 0 ]
          "El destino bla bla bla" -- [ 1, 1, 0, 3, 0, 0 ]
          "El destino bla bla bla" -- [ 1, 1, 0, 3, 0, 1 ]
          "23462 El destino bla bla bla" -- [ 1, 1, 0, 3, 0, 2 ]
      letter-date -- [ 1, 1, 0, 4 ]
        document -- [ 1, 1, 0, 4, 0 ]
          "Mi casa, a 28 de octubre de 2011" -- [ 1, 1, 0, 4, 0, 0 ]
  opening -- [ 1, 2 ]
    document -- [ 1, 2, 0 ]
      "Estimados bla bla:" -- [ 1, 2, 0, 0 ]
  with -- [ 1, 3 ]
    "par-first" -- [ 1, 3, 0 ]
    "2fn" -- [ 1, 3, 1 ]
    document -- [ 1, 3, 2 ]
      concat -- [ 1, 3, 2, 0 ]
        footnote -- [ 1, 3, 2, 0, 0 ]
          document -- [ 1, 3, 2, 0, 0, 0 ]
            "" -- [ 1, 3, 2, 0, 0, 0, 0 ]
        "." -- [ 1, 3, 2, 0, 1 ]
      "En coordenadas elípticas Jacobi demostró que el problema del billar es 
integrable, que es uno de los motivos de la importancia de estas coordenadas. 
También las utilizó para clasificar las simetrías permitidas y prohibidas 
para cada tipo de cáusticas. En coordenadas elípticas Jacobi demostró que el 
problema del billar es integrable, que es uno de los motivos." -- [ 1, 3, 2, 
1 ]
  concat -- [ 1, 4 ]
    tabular* -- [ 1, 4, 0 ]
      tformat -- [ 1, 4, 0, 0 ]
        cwith -- [ 1, 4, 0, 0, 0 ]
          "1" -- [ 1, 4, 0, 0, 0, 0 ]
          "-1" -- [ 1, 4, 0, 0, 0, 1 ]
          "1" -- [ 1, 4, 0, 0, 0, 2 ]
          "1" -- [ 1, 4, 0, 0, 0, 3 ]
          "cell-halign" -- [ 1, 4, 0, 0, 0, 4 ]
          "l" -- [ 1, 4, 0, 0, 0, 5 ]
        cwith -- [ 1, 4, 0, 0, 1 ]
          "1" -- [ 1, 4, 0, 0, 1, 0 ]
          "-1" -- [ 1, 4, 0, 0, 1, 1 ]
          "1" -- [ 1, 4, 0, 0, 1, 2 ]
          "1" -- [ 1, 4, 0, 0, 1, 3 ]
          "cell-width" -- [ 1, 4, 0, 0, 1, 4 ]
          "8.5cm" -- [ 1, 4, 0, 0, 1, 5 ]
        cwith -- [ 1, 4, 0, 0, 2 ]
          "1" -- [ 1, 4, 0, 0, 2, 0 ]
          "-1" -- [ 1, 4, 0, 0, 2, 1 ]
          "1" -- [ 1, 4, 0, 0, 2, 2 ]
          "1" -- [ 1, 4, 0, 0, 2, 3 ]
          "cell-hmode" -- [ 1, 4, 0, 0, 2, 4 ]
          "exact" -- [ 1, 4, 0, 0, 2, 5 ]
        table -- [ 1, 4, 0, 0, 3 ]
          row -- [ 1, 4, 0, 0, 3, 0 ]
            cell -- [ 1, 4, 0, 0, 3, 0, 0 ]
              concat -- [ 1, 4, 0, 0, 3, 0, 0, 0 ]
                space -- [ 1, 4, 0, 0, 3, 0, 0, 0, 0 ]
                  "0.7cm" -- [ 1, 4, 0, 0, 3, 0, 0, 0, 0, 0 ]
                "Atentamente," -- [ 1, 4, 0, 0, 3, 0, 0, 0, 1 ]
          row -- [ 1, 4, 0, 0, 3, 1 ]
            cell -- [ 1, 4, 0, 0, 3, 1, 0 ]
              "" -- [ 1, 4, 0, 0, 3, 1, 0, 0 ]
          row -- [ 1, 4, 0, 0, 3, 2 ]
            cell -- [ 1, 4, 0, 0, 3, 2, 0 ]
              "" -- [ 1, 4, 0, 0, 3, 2, 0, 0 ]
          row -- [ 1, 4, 0, 0, 3, 3 ]
            cell -- [ 1, 4, 0, 0, 3, 3, 0 ]
              "" -- [ 1, 4, 0, 0, 3, 3, 0, 0 ]
          row -- [ 1, 4, 0, 0, 3, 4 ]
            cell -- [ 1, 4, 0, 0, 3, 4, 0 ]
              "" -- [ 1, 4, 0, 0, 3, 4, 0, 0 ]
          row -- [ 1, 4, 0, 0, 3, 5 ]
            cell -- [ 1, 4, 0, 0, 3, 5, 0 ]
              "" -- [ 1, 4, 0, 0, 3, 5, 0, 0 ]
          row -- [ 1, 4, 0, 0, 3, 6 ]
            cell -- [ 1, 4, 0, 0, 3, 6, 0 ]
              "" -- [ 1, 4, 0, 0, 3, 6, 0, 0 ]
          row -- [ 1, 4, 0, 0, 3, 7 ]
            cell -- [ 1, 4, 0, 0, 3, 7, 0 ]
              "Fdo.: bla bla bla bla bla" -- [ 1, 4, 0, 0, 3, 7, 0, 0 ]
          row -- [ 1, 4, 0, 0, 3, 8 ]
            cell -- [ 1, 4, 0, 0, 3, 8, 0 ]
              "D.N.I.: XXXXXXXXX" -- [ 1, 4, 0, 0, 3, 8, 0, 0 ]
    " " -- [ 1, 4, 1 ]
    blanc-page -- [ 1, 4, 2 ]
Error message:
  zero lines in insertion

System information:
  TeXmacs version  : 1.0.7.14
  Built by         : jpablo
  Building date    : Tue Nov  8 10:39:03 CET 2011
  Operating system : linux-gnu
  Vendor           : mandriva
  Processor        : x86_64
  Crash date       : mar nov  8 11:18:09 CET 2011

Editor status:
  Root path          : [ 1 ]
  Current path       : [ 1, 3, 2, 1, 360 ]
  Shifted path       : [ 1, 3, 2, 1, 360 ]
  Physical selection : [ 1, 3, 2, 1, 360 ] -- [ 1, 3, 2, 1, 360 ]
  Logical selection  : [ 1, 3, 2, 1, 360 ] -- [ 1, 3, 2, 1, 360 ]

Backtrace of C++ stack:
  texmacs.bin() [0x81c6c9]
  texmacs.bin() [0x81ce8e]
  texmacs.bin() [0x706212]
  texmacs.bin() [0x707e66]
  texmacs.bin() [0x706e23]
  texmacs.bin() [0x708e16]
  texmacs.bin() [0x70981c]
  texmacs.bin() [0x76b826]
  texmacs.bin() [0x88b481]
  texmacs.bin() [0x88b8a4]
  texmacs.bin() [0x568bea]
  texmacs.bin() [0x566146]
  texmacs.bin() [0x692153]
  /usr/lib64/libguile.so.17 : () + 0x507a2
  /usr/lib64/libguile.so.17 : scm_dapply() + 0x808
  /usr/lib64/libguile.so.17 : scm_c_with_throw_handler() + 0x126
  /usr/lib64/libguile.so.17 : scm_c_catch() + 0x14d
  /usr/lib64/libguile.so.17 : scm_internal_catch() + 0x14
  texmacs.bin() [0x61eb33]
  texmacs.bin() [0x730248]
  texmacs.bin() [0x7321c0]
  texmacs.bin() [0x82fc93]
  texmacs.bin() [0x9087cd]
  texmacs.bin() [0x7f65a2]
  /usr/lib64/libguile.so.17 : () + 0x667ff
  /usr/lib64/libguile.so.17 : () + 0x3cb0a
  /usr/lib64/libguile.so.17 : scm_c_catch() + 0x14d
  /usr/lib64/libguile.so.17 : scm_i_with_continuation_barrier() + 0xb7
  /usr/lib64/libguile.so.17 : scm_c_with_continuation_barrier() + 0x30
  /usr/lib64/libguile.so.17 : scm_i_with_guile_and_parent() + 0x34
  /usr/lib64/libguile.so.17 : scm_boot_guile() + 0x25
  texmacs.bin() [0x7f5be9]
  /lib64/libc.so.6 : __libc_start_main() + 0xfd
  texmacs.bin() [0x404df9]
<TeXmacs|1.0.7.14>

<style|letter>

<\body>
  \;

  <\letter-header>
    <\destination>
      D. bla bla bla

      bla bla bla

      36349 bla bla bla
    </destination>

    \;

    \;

    <\address>
      El destino bla bla bla

      El destino bla bla bla

      23462 El destino bla bla bla
    </address>

    <\letter-date>
      Mi casa, a 28 de octubre de 2011
    </letter-date>
  </letter-header>

  <\opening>
    Estimados bla bla:
  </opening>

  <\with|par-first|2fn>
    <\footnote>
      \;
    </footnote>.

    En coordenadas elípticas Jacobi demostró que el problema del billar es
    integrable, que es uno de los motivos de la importancia de estas
    coordenadas. También las utilizó para clasificar las simetrías permitidas
    y prohibidas para cada tipo de cáusticas. En coordenadas elípticas Jacobi
    demostró que el problema del billar es integrable, que es uno de los
    motivos.
  </with>

  
<tabular*|<tformat|<cwith|1|-1|1|1|cell-halign|l>|<cwith|1|-1|1|1|cell-width|8.5cm>|<cwith|1|-1|1|1|cell-hmode|exact>|<table|<row|<cell|<space|0.7cm>Atentamente,>>|<row|<cell|>>|<row|<cell|>>|<row|<cell|>>|<row|<cell|>>|<row|<cell|>>|<row|<cell|>>|<row|<cell|Fdo.:
  bla bla bla bla bla>>|<row|<cell|D.N.I.: XXXXXXXXX>>>>> <blanc-page>
</body>

<\initial>
  <\collection>
    <associate|font-base-size|14>
    <associate|language|spanish>
    <associate|page-show-hf|true>
    <associate|preamble|false>
  </collection>
</initial>

<\references>
  <\collection>
    <associate|footnote-1|<tuple|1|1>>
    <associate|footnr-1|<tuple|1|1>>
  </collection>
</references><TeXmacs|1.0.7.14>

<style|<tuple|article|mismacros|maxima|varsession>>

<\body>
  <section|Conclusiones>

  \;

  <subsection|Trozos>

  <\float|float|t>
    
<big-table|<tabular*|<tformat|<cwith|1|-1|1|1|cell-rborder|1ln>|<cwith|1|1|1|-1|cell-bborder|1ln>|<cwith|1|1|1|-1|cell-bborder|1ln>|<cwith|1|-1|1|1|cell-lborder|0ln>|<cwith|1|-1|1|1|cell-halign|l>|<cwith|1|-1|2|2|cell-halign|l>|<cwith|1|-1|2|2|cell-lborder|1ln>|<cwith|1|-1|2|2|cell-rborder|0ln>|<cwith|1|-1|3|3|cell-lborder|1ln>|<cwith|1|-1|3|3|cell-halign|l>|<cwith|4|4|1|-1|cell-tborder|1ln>|<cwith|6|6|1|-1|cell-tborder|1ln>|<cwith|8|8|1|-1|cell-tborder|1ln>|<cwith|10|10|1|-1|cell-tborder|1ln>|<cwith|12|12|1|-1|cell-tborder|1ln>|<cwith|13|13|1|-1|cell-bborder|1ln>|<cwith|6|6|1|-1|cell-halign|l>|<cwith|2|2|1|1|cell-row-span|2>|<cwith|1|-1|1|1|cell-valign|c>|<cwith|1|-1|2|2|cell-valign|c>|<cwith|2|2|2|2|cell-row-span|2>|<cwith|4|4|1|1|cell-row-span|2>|<cwith|4|4|2|2|cell-row-span|2>|<cwith|6|6|1|1|cell-row-span|2>|<cwith|6|6|2|2|cell-row-span|2>|<cwith|8|8|1|1|cell-row-span|2>|<cwith|8|8|2|2|cell-row-span|2>|<cwith|10|10|1|1|cell-row-span|2>|<cwith|10|10|2|2|cell-row-span|2>|<cwith|12|12|1|1|cell-row-span|2>|<cwith|12|12|2|2|cell-row-span|2>|<cwith|12|12|1|-1|cell-bborder|1ln>|<cwith|13|13|1|-1|cell-tborder|0ln>|<cwith|13|13|3|3|cell-tborder|0ln>|<cwith|12|12|3|3|cell-bborder|0ln>|<table|<row|<cell|<math|<around*|(|e,h<rsub|1>,h<rsub|2>|)>>>|<cell|Reversor>|<cell|<math|q=<around*|(|x,y,z|)>>,
    
<math|p=<around*|(|u,v,w|)>>>>|<row|<cell|<math|<around*|(|0,\<lambda\><rsub|1>,\<lambda\><rsub|2>|)>>>|<cell|<math|R>>|<cell|<math|x<rsub|l><rsup|2>=<with|math-display|true|*<frac|a<rsub|l>*<around*|(|a<rsub|l>-\<lambda\><rsub|1>|)>*<around*|(|a<rsub|l>-\<lambda\><rsub|2>|)>|<around*|(|a<rsub|l>-a<rsub|m>|)>*<around*|(|a<rsub|l>-a<rsub|n>|)>>>>,>>|<row|<cell|>|<cell|>|<cell|<math|p=<sqrt|<with|math-display|true|<frac|a*b*c|\<lambda\><rsub|1>*\<lambda\><rsub|2>>>>*<around*|(|<with|math-display|true|<frac|x|a>>,<with|math-display|true|<frac|y|b>>,<with|math-display|true|<frac|z|c>>|)>>>>|<row|<cell|<math|e=0>,
    
<math|<around*|{|h<rsub|1>,h<rsub|2>|}>=<around*|{|a<rsub|l>,\<lambda\><rsub|j>|}>>>|<cell|<math|R<rsub|x<rsub|l>>>>|<cell|<math|x<rsub|l>=0>,
    
<math|x<rsub|m><rsup|2>\<nocomma\>=<with|math-display|true|<frac|a*<rsub|m><around*|(|a<rsub|m>-\<lambda\><rsub|j>|)>|a<rsub|m>-a<rsub|n>>>>,>>|<row|<cell|>|<cell|>|<cell|<math|u<rsub|l><rsup|2>=<with|math-display|true|<frac|a<rsub|l>-\<lambda\><rsub|k>|a<rsub|l>>>>,
    
<math|u<rsub|m>=a<rsub|n>x<rsub|m><sqrt|<with|math-display|true|<frac|\<lambda\><rsub|k>|a
    b c \<lambda\><rsub|j>>>>>>>|<row|<cell|<math|e=0>,
    
<math|<around*|{|h<rsub|1>,h<rsub|2>|}>=<around*|{|a<rsub|m>,a<rsub|n>|}>>>|<cell|<math|R<rsub|x<rsub|m>x<rsub|n>>>>|<cell|<math|x<rsub|l>=\<pm\><sqrt|a<rsub|l>>>,
    
<math|x<rsub|m>=x<rsub|n>=0>,>>|<row|<cell|>|<cell|>|<cell|<math|u<rsub|l><rsup|2>=<with|math-display|true|*<frac|\<lambda\><rsub|1>*\<lambda\><rsub|2>|a<rsub|m>*a<rsub|n>>>>,
    
<math|u<rsub|m><rsup|2>=<with|math-display|true|*<frac|<around*|(|a<rsub|m>-\<lambda\><rsub|1>|)>*<around*|(|a<rsub|m>-\<lambda\><rsub|2>|)>|a<rsub|m>*<around*|(|a<rsub|m>-a<rsub|n>|)>>>>>>|<row|<cell|<math|<around*|{|e,h<rsub|1>,h<rsub|2>|}>=<around*|{|a<rsub|l>,\<lambda\><rsub|1>,\<lambda\><rsub|2>|}>>>|<cell|<math|f\<circ\>R<rsub|x<rsub|l>>>>|<cell|<math|x<rsub|l><rsup|2>=<with|math-display|true|*<frac|a<rsub|l>*\<lambda\><rsub|1>*\<lambda\><rsub|2>|a<rsub|m>a<rsub|n>>>>,
    
<math|x<rsub|m><rsup|2>=<with|math-display|true|*<frac|<around*|(|a<rsub|m>-\<lambda\><rsub|1>|)>*<around*|(|a<rsub|m>-\<lambda\><rsub|2>|)>|a<rsub|m>-a<rsub|n>>>>,>>|<row|<cell|>|<cell|>|<cell|<math|u<rsub|l>=\<pm\>1>,
    
<math|u<rsub|m>=0>>>|<row|<cell|<math|<around*|{|e,h<rsub|1>,h<rsub|2>|}>=<around*|{|a<rsub|m>,a<rsub|n>,\<lambda\><rsub|j>|}>>>|<cell|<math|f\<circ\>R<rsub|x<rsub|m>x<rsub|n>>>>|<cell|<math|x<rsub|l><rsup|2>=a<rsub|l>-\<lambda\><rsub|k>>,
    <math|x<rsub|m>=u<rsub|m><sqrt|<with|math-display|true|<frac|a<rsub|m>
    a<rsub|n> \<lambda\><rsub|k>|a<rsub|l>
    \<lambda\><rsub|j>>>>>,>>|<row|<cell|>|<cell|>|<cell|<math|u<rsub|l>=0>,
    
<math|u<rsub|m><rsup|2>=<with|math-display|true|*<frac|a<rsub|m>-\<lambda\><rsub|j>|a<rsub|m>-a<rsub|n>>>>>>|<row|<cell|<math|<around*|(|c,b,a|)>>>|<cell|<math|f\<circ\>R<rsub|x*y*z>>>|<cell|<math|u<rsub|l><rsup|2>=<with|math-display|true|*<frac|<around*|(|a<rsub|l>-\<lambda\><rsub|1>|)>*<around*|(|a<rsub|l>-\<lambda\><rsub|2>|)>|<around*|(|a<rsub|l>-a<rsub|m>|)>*<around*|(|a<rsub|l>-a<rsub|n>|)>>>>,>>|<row|<cell|>|<cell|>|<cell|<math|q=<with|math-display|true|<sqrt|<frac|a*b*c|\<lambda\><rsub|1>*\<lambda\><rsub|2>>>>*<around*|(|u,v,w|)>>>>>>>|Likewise,
    we present the corresponding <math|<around*|(|q,p|)>> formulae.>
  </float>

  <subsection|Symmetries through elliptic coordinates>

  We give a complete classification of the symmetry sets, in connection with
  the vertexes in elliptic coordinates they come from. The next proposition
  is summarized in table <reference|vértices y reversores>.

  <\lemma>
    <dueto|Characterization of reversible maps> <label|lem:ReversibleMaps>A
    map <math|f> is reversible if and only if it can be factorized as the
    composition of two involutions, in which case both of them are reversors
    of <math|f>.\ 
  </lemma>

  <\duda>
    <\proof>
      Let us assume that <math|f> is <math|<wide|r|~>>-reversible. Then
      <math|<wide|r|^>=f\<circ\><wide|r|~>=<wide|r|~>\<circ\>f<rsup|-1>> is
      another reversor, because:

      <\enumerate-numeric>
        
<item><with|mode|math|f\<circ\><wide|r|^>=f\<circ\><wide|r|~>\<circ\>f<rsup|-1>=<wide|r|^>\<circ\>f<rsup|-1>>,

        
<item><with|mode|math|<wide|r|^><rsup|2>=<wide|r|^>\<circ\><wide|r|^>=<wide|r|~>\<circ\>f<rsup|-1>\<circ\>f\<circ\><wide|r|~>=<wide|r|~><rsup|2>=<Identity>>.
      </enumerate-numeric>

      Therefore, the map 
<math|f=f\<circ\><wide|r|~><rsup|2>=<wide|r|^>\<circ\><wide|r|~>>
      is the composition of two involutions.

      On the other hand, if <math|f=<wide|r|^>\<circ\><wide|r|~>> and
      <math|<wide|r|^><rsup|2>=<wide|r|~><rsup|2>=<Identity>>, then:

      <\enumerate-numeric>
        
<item><with|mode|math|f\<circ\><wide|r|~>\<circ\>f=<wide|r|^>\<circ\><wide|r|~><rsup|2>\<circ\><wide|r|^>\<circ\><wide|r|~>=<wide|r|^><rsup|2>\<circ\><wide|r|~>=<wide|r|~>>,

        
<item><with|mode|math|f\<circ\><wide|r|^>\<circ\>f=<wide|r|^>\<circ\><wide|r|~>\<circ\><wide|r|^><rsup|2>\<circ\><wide|r|~>=<wide|r|^>\<circ\><wide|r|~><rsup|2>=<wide|r|^>>,
      </enumerate-numeric>

      so both involutions <math|<wide|r|^>> and <math|<wide|r|~>> are
      reversors of the map <math|f>.
    </proof>
  </duda|El lema, ¾está publicado en alguna parte?|Según
  <cite|LambRoberts1998>, aparece en Birkhoff, G.D., (1915). The restricted
  problem of three bodies. Rend. Circ. Mat. Palermo 39, 265-334.>

  <\proposition>
    <label|clasificación de vértices>Let us denote
    <math|<with|math-font|cal**|C><rsub|T>> as the cuboid:

    <\equation*>
      
<with|math-font|cal**|C><rsub|T>=<choice|<tformat|<table|<row|<cell|<around*|[|0,\<lambda\><rsub|1>|]>\<times\><around*|[|c,\<lambda\><rsub|2>|]>\<times\><around*|[|b,a|]>,>|<cell|T=EH1,>>|<row|<cell|<around*|[|0,c|]>\<times\><around*|[|\<lambda\><rsub|1>,\<lambda\><rsub|2>|]>\<times\><around*|[|b,a|]>,>|<cell|T=<with|math-font-shape|right|H1H1>,>>|<row|<cell|<around*|[|0,\<lambda\><rsub|1>|]>\<times\><around*|[|c,b|]>\<times\><around*|[|\<lambda\><rsub|2>,a|]>,>|<cell|T=EH2,>>|<row|<cell|<around*|[|0,c|]>\<times\><around*|[|\<lambda\><rsub|1>,b|]>\<times\><around*|[|\<lambda\><rsub|2>,a|]>,>|<cell|T=<with|math-font-shape|right|H1H2>,>>>>>
    </equation*>

    where elliptic coordinates take place in a billiard trajectory. Then,
    every vertex of <math|<with|math-font|cal**|C><rsub|T>> corresponds to a
    SO.
  </proposition>

  \;

  \;
</body>

<\initial>
  <\collection>
    <associate|font-base-size|12>
    <associate|language|spanish>
    <associate|page-medium|paper>
    <associate|par-columns|1>
    <associate|preamble|false>
  </collection>
</initial>

<\references>
  <\collection>
    <associate|OPS en 2D|<tuple|1|9>>
    <associate|auto-1|<tuple|1|1>>
    <associate|auto-10|<tuple|9|6>>
    <associate|auto-11|<tuple|10|6>>
    <associate|auto-12|<tuple|10.1|6>>
    <associate|auto-13|<tuple|10.2|8>>
    <associate|auto-14|<tuple|10.3|9>>
    <associate|auto-15|<tuple|1|11>>
    <associate|auto-16|<tuple|11|12>>
    <associate|auto-17|<tuple|12|?>>
    <associate|auto-18|<tuple|11|?>>
    <associate|auto-19|<tuple|12|?>>
    <associate|auto-2|<tuple|1.1|1>>
    <associate|auto-3|<tuple|1|1>>
    <associate|auto-4|<tuple|1.2|1>>
    <associate|auto-5|<tuple|1|4>>
    <associate|auto-6|<tuple|2|3>>
    <associate|auto-7|<tuple|3|4>>
    <associate|auto-8|<tuple|4|5>>
    <associate|auto-9|<tuple|8|6>>
    <associate|clasificación de vértices|<tuple|4|2>>
    <associate|lem:ReversibleMaps|<tuple|3|1>>
    <associate|vértices y reversores|<tuple|1|2>>
  </collection>
</references>

<\auxiliary>
  <\collection>
    <\associate|table>
      <tuple|normal|Likewise, we present the corresponding
      <with|mode|<quote|math>|<around*|(|q,p|)>> formulae.|<pageref|auto-3>>
    </associate>
    <\associate|toc>
      
<vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|1<space|2spc>Conclusiones>
      
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-1><vspace|0.5fn>

      <with|par-left|<quote|1.5fn>|1.1<space|2spc>Trozos
      
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-2>>

      <with|par-left|<quote|1.5fn>|1.2<space|2spc>Symmetries through elliptic
      coordinates 
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <no-break><pageref|auto-4>>
    </associate>
  </collection>
</auxiliary>