mailing-list for TeXmacs Users

[Kris Kuhlman <address@hidden>]

Hi,

I have been using TeXmacs for a couple months now, and I must say I like 
it, but I have been having problems with equation numbers and 
referencing them in the text.  I put an equation in, number it using 
mathematics -> number equation, put a reference next to it (as is 
described in the help), then I put a reference to the same label in the 
text.  This puts a number down, but it is sometimes off by one, but 
elsewhere in the document, a reference to the same equation turns out 
correct. 

I don't want to do this manually... is there anything someone sees is 
missing?  I attached a copy of my first page, which illustrates my 
problem (bib not included, so citations don't work).  The problems are 
the last two paragraphs.  I write "Note that (<reference|eq:radialSep>) 
is the Cauchy-Euler 'equidimensional' equation." but it references eqn 
2, rather than eqn 3, and the same thing happens below that.

Thanks for any help.

Kris
<TeXmacs|1.0.3.7>

<style|generic>

<\body>
  <\make-title>
    <title|AEM Steady-State Circular Inclusions>
  </make-title>

  <section|Governing Equation: Laplace's Equation>

  In the following derivation <with|mode|math|h> is head, and
  <with|mode|math|K> is hydraulic conductivity. Beginning with the most
  general form of the steady-state groundwater flow equation

  <\equation*>
    <rsup|>\<nabla\>\<cdot\>(K\<nabla\>h)=0 \ <with|mode|text| or, when >K
    <with|mode|text| is uniform, > K\<nabla\><rsup|2>h=0
  </equation*>

  which, in familiar rectangular coordinates simply is

  <\equation*>
    
K<left|(><frac|\<partial\><rsup|2>h|\<partial\>x<rsup|2>>+<frac|\<partial\><rsup|2>h|\<partial\>y<rsup|2>>+<frac|\<partial\><rsup|2>h|\<partial\>z<rsup|2>><right|)>=0
  </equation*>

  To more efficiently deal with circular inclusions, the problem will be
  dealt with in cylindrical coordinates, instead of rectangular. In plane
  polar coordinates -- cylindrical coordinates invariant in the
  <with|mode|math|z> direction (<with|mode|math|r> is radial distance,
  <with|mode|math|\<theta\>> is the angle made with the positive x-axis) a
  convenient form of the Laplace equation is

  <\equation*>
    
K<left|(><frac|\<partial\><rsup|2>h|\<partial\>r<rsup|2>>+<frac|1|r><frac|\<partial\>h|\<partial\>r>+<frac|1|r<rsup|2>><frac|\<partial\><rsup|2><rsup|>h|\<partial\>\<theta\><rsup|2>><right|)>=0
  </equation*>

  expressed in terms of the confined aquifer discharge potential
  (<with|mode|math|\<Phi\>=h K>), this becomes

  <\equation>
    
<label|eq:Laplace.phi><frac|\<partial\><rsup|2>\<Phi\>|\<partial\>r<rsup|2>>+<frac|1|r><frac|\<partial\>\<Phi\>|\<partial\>r>+<frac|1|r<rsup|2>><frac|\<partial\><rsup|2><rsup|>\<Phi\>|\<partial\>\<theta\><rsup|2>>=0
  </equation>

  <section|Separation of Variables>

  This procedure is similar to those outlined in the literature
  (<cite|ozisikHC> Ÿ3-1 and <cite|GreenbergAdvEngMath> Ÿ20.3). \ First,
  (<reference|eq:Laplace.phi>) is separated into radial and azimuthal
  components, following the relationship

  <\equation>
    <label|eq:separation>\<Phi\>(r,\<theta\>)=R<rsub|>(r)\<Theta\>(\<theta\>).
  </equation>

  Substituting (<reference|eq:separation>) into (<reference|eq:Laplace.phi>),
  grouping the like components, and dividing by <with|mode|math|\<Phi\>>,
  leads to

  <\equation*>
    
<frac|1|R><left|(><frac|\<partial\><rsup|2>R|\<partial\>r<rsup|2>>+<frac|1|r><frac|\<partial\>R<rsub|>|\<partial\>r><right|)>+<frac|1|r<rsup|2>><frac|1|\<Theta\>><frac|\<partial\><rsup|2><rsup|>\<Theta\>|\<partial\>\<theta\><rsup|2>>=0.
  </equation*>

  To satisfy this equality, both groups must be related through the arbitrary
  separation constant

  <\equation*>
    
<frac|1|\<Theta\>><frac|d<rsup|2><rsup|>\<Theta\>|d\<theta\><rsup|2>>=-v<rsup|2>
    <with|mode|text|, and > <frac|1|R><left|(><frac|d<rsup|2>R|d
    r<rsup|2>>+<frac|1|r><frac|d R|d r><right|)>-<frac|v<rsup|2>|r<rsup|2>>=0.
  </equation*>

  Re-arranging these equations leads to the following separated equations

  <\eqnarray*>
    
<tformat|<table|<row|<cell|<frac|d<rsup|2><rsup|>\<Theta\>|d\<theta\><rsup|2>>+v<rsup|2>\<Theta\>=0,>|<cell|>|<cell|>>|<row|<cell|<label|eq:radialSep><frac|d<rsup|2>R|d
    r<rsup|2>>+<frac|1|r><frac|d R|d 
r>-<frac|v<rsup|2>|r<rsup|2>>R=0.>|<cell|>|<cell|<eq-number>>>>>
  </eqnarray*>

  Note that (<reference|eq:radialSep>) is the Cauchy-Euler 'equidimensional'
  equation. These equations have the following general, orthogonal solutions
  for integer values of the separation constant (eigenvalues of the problem)

  <\eqnarray*>
    
<tformat|<table|<row|<cell|<label|eq:angGS>\<Theta\><rsub|v>(\<theta\>)=a<rsub|v>
    sin(v\<theta\>)+b<rsub|v> 
cos(v\<theta\>)>|<cell|>|<cell|<eq-number>>>|<row|<cell|<label|eq:radialGS>R<rsub|v>(r):<choice|<tformat|<table|<row|<cell|c<rsub|n>r<rsup|v>+d<rsub|n>r<rsup|-v>
    <with|mode|text| for >v\<neq\>0>>|<row|<cell|c<rsub|0>+d<rsub|0> ln r
    <with|mode|text| \ \ \ for >v=0>>>>>>|<cell|>|<cell|<eq-number>>>>>
  </eqnarray*>

  Utilizing the Sturm-Lioville theory, which states a quantity (e.g.,
  <with|mode|math|\<Phi\>>) can be represented using an infinite sum of
  orthogonal functions, put (<reference|eq:radialGS>) and
  (<reference|eq:angGS>) back into (<reference|eq:separation>) which gives
  the following form (sine and cosine evaluated at 0)

  \ 
</body>

<\initial>
  <\collection>
    <associate|language|english>
    <associate|page-bot|30mm>
    <associate|page-even|30mm>
    <associate|page-odd|30mm>
    <associate|page-reduce-bot|15mm>
    <associate|page-reduce-left|25mm>
    <associate|page-reduce-right|25mm>
    <associate|page-reduce-top|15mm>
    <associate|page-right|30mm>
    <associate|page-top|30mm>
    <associate|page-type|a4>
    <associate|par-width|150mm>
  </collection>
</initial>

<\references>
  <\collection>
    <associate|auto-1|<tuple|1|?>>
    <associate|auto-2|<tuple|2|?>>
    <associate|eq:1|<tuple|1|?>>
    <associate|eq:2|<tuple|2|?>>
    <associate|eq:Laplace.phi|<tuple|1|?>>
    <associate|eq:angGS|<tuple|3|?>>
    <associate|eq:radialGS|<tuple|4|?>>
    <associate|eq:radialSep|<tuple|2|?>>
    <associate|eq:separation|<tuple|2|?>>
  </collection>
</references>

<\auxiliary>
  <\collection>
    <\associate|bib>
      ozisikHC

      GreenbergAdvEngMath
    </associate>
    <\associate|toc>
      
<vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|Governing
      Equation: Laplace's Equation> 
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <pageref|auto-1><vspace|0.5fn>

      
<vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|Separation
      of Variables> 
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
      <pageref|auto-2><vspace|0.5fn>
    </associate>
  </collection>
</auxiliary>