This is TeX, Version 3.14159 (Web2C 7.3.1) (format=tex 2000.7.19)  13 APR 2001 09:13
**\nonstopmode\input algorithms.tex
(algorithms.tex
! Undefined control sequence.
l.1 \comment
            {
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   _
l.18 fixed modular degree notation m_
                                      instead of \delta_
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing { inserted.
<to be read again> 
                   \par 
l.19 
     
A left brace was mandatory here, so I've put one in.
You might want to delete and/or insert some corrections
so that I will find a matching right brace soon.
(If you're confused by all this, try typing `I}' now.)

! Missing $ inserted.
<inserted text> 
                $
<to be read again> 
                   \par 
l.19 
     
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.

! Missing } inserted.
<inserted text> 
                }
<to be read again> 
                   $
<to be read again> 
                   \par 
l.19 
     
I've inserted something that you may have forgotten.
(See the <inserted text> 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.

! Undefined control sequence.
l.34 \chapter
             {Applications of modular symbols}
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of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.35 \label
           {chap:computing}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.43 Sections~\ref
                  {sec:computingmk}--\ref{sec:decomposemodsym} of this
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.43 Sections~\ref{sec:computingmk}--\ref
                                         {sec:decomposemodsym} of this
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
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spelling (e.g., `I\hbox'). Otherwise just continue,
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! Undefined control sequence.
<recently read> \sM 
                    
l.45 spaces $\sM
                _k(N,\eps)$ of modular symbols.  In
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! Undefined control sequence.
l.45 spaces $\sM_k(N,\eps
                         )$ of modular symbols.  In
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spelling (e.g., `I\hbox'). Otherwise just continue,
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! Undefined control sequence.
l.46 Section~\ref
                 {sec:intersection} we observe that computing intersections
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<recently read> \Z 
                   
l.48 over~$\Z
             $ by viewing the abelian varieties as complex tori and
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of your error message was never \def'ed. If you have
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spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.50 Sections~\ref
                  {sec:ratperiod}, we continue this trend by pointing out
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
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spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.53 Section~\ref
                 {sec:torsionsubgroup}, we discuss well-known methods for
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.55 ...f certain abelian varieties.  Section~\ref
                                                  {sec:moddeg}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
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and I'll forget about whatever was undefined.

! Undefined control sequence.
l.59 In Section~\ref
                    {sec:ratpartformula} we aim squarely at the
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! Undefined control sequence.
l.61 conjecture\index
                     {BSD conjecture!and $L(A,j)/\Omega_j$}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
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! Undefined control sequence.
l.64 Section~\ref
                 {sec:maninconstant} we compare the ratio computed in the
The control sequence at the end of the top line
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spelling (e.g., `I\hbox'). Otherwise just continue,
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! Undefined control sequence.
l.66 Swinnerton-Dyer conjecture;\index
                                      {BSD conjecture}
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
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! Undefined control sequence.
l.67 the two numbers differ by a Manin\index
                                            {Manin}
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spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

! Undefined control sequence.
l.68 ... which we bound.  Finally, in Section~\ref
                                                  {sec:analytic} we
The control sequence at the end of the top line
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l.72 \section
             {Computing the space of modular symbols}%
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
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! Undefined control sequence.
l.73 \index
           {Modular symbols!computing}%
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
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! Undefined control sequence.
l.74 \label
           {sec:computingmk}%
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
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! Undefined control sequence.
l.75 \begin
           {definition}
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of your error message was never \def'ed. If you have
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! Undefined control sequence.
l.77 To \defn
             {compute} the quotient $V/W$ means to
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! Undefined control sequence.
l.78 ...a matrix representing the projection $V\ra
                                                   V/W$, with
The control sequence at the end of the top line
of your error message was never \def'ed. If you have
misspelled it (e.g., `\hobx'), type `I' and the correct
spelling (e.g., `I\hbox'). Otherwise just continue,
and I'll forget about whatever was undefined.

[1] )
Output written on algorithms.dvi (1 page, 4212 bytes).