\documentclass{article}
\usepackage{axiom}
\begin{document}
\title{\$SPAD/src/algebra functions.spad}
\author{Brian Dupee}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{domain BFUNCT BasicFunctions}
<<domain BFUNCT BasicFunctions>>=
)abbrev domain BFUNCT BasicFunctions
++ Author: Brian Dupee
++ Date Created: August 1994
++ Date Last Updated: April 1996
++ Basic Operations: bfKeys, bfEntry
++ Description: A Domain which implements a table containing details of 
++ points at which particular functions have evaluation problems.
DF	==> DoubleFloat
SDF	==> Stream DoubleFloat
RS	==> Record(zeros: SDF, ones: SDF, singularities: SDF)

BasicFunctions():  E == I where 
  E ==> SetCategory with
    bfKeys:() -> List Symbol
      ++ bfKeys() returns the names of each function in the
      ++ \axiomType{BasicFunctions} table 
    bfEntry:Symbol -> RS
      ++ bfEntry(k) returns the entry in the \axiomType{BasicFunctions} table 
      ++ corresponding to \spad{k}
    finiteAggregate

  I ==> add 

    Rep := Table(Symbol,RS)
    import Rep, SDF

    f(x:DF):DF ==
      positive?(x) => -x
      -x+1

    bf():$ ==
      import RS
      dpi := pi()$DF
      ndpi:SDF := map(#1*dpi,(z := generate(f,0))) -- [n pi for n in Z]
      n1dpi:SDF := map(-(2*(#1)-1)*dpi/2,z) -- [(n+1) pi /2]
      n2dpi:SDF := map(2*#1*dpi,z) -- [2 n pi for n in Z]
      n3dpi:SDF := map(-(4*(#1)-1)*dpi/4,z)
      n4dpi:SDF := map(-(4*(#1)-1)*dpi/2,z)
      sinEntry:RS := [ndpi, n4dpi, empty()$SDF]
      cosEntry:RS := [n1dpi, n2dpi, esdf := empty()$SDF]
      tanEntry:RS := [ndpi, n3dpi, n1dpi]
      asinEntry:RS := [construct([0$DF])$SDF,
                        construct([float(8414709848078965,-16,10)$DF]), esdf]
      acosEntry:RS := [construct([1$DF])$SDF,
                        construct([float(54030230586813977,-17,10)$DF]), esdf]
      atanEntry:RS := [construct([0$DF])$SDF,
                        construct([float(15574077246549023,-16,10)$DF]), esdf]
      secEntry:RS := [esdf, n2dpi, n1dpi]
      cscEntry:RS := [esdf, n4dpi, ndpi]
      cotEntry:RS := [n1dpi, n3dpi, ndpi]
      logEntry:RS := [construct([1$DF])$SDF,esdf, construct([0$DF])$SDF]
      entryList:List(Record(key:Symbol,entry:RS)) :=
         [[sin@Symbol, sinEntry], [cos@Symbol, cosEntry],
           [tan@Symbol, tanEntry], [sec@Symbol, secEntry],
            [csc@Symbol, cscEntry], [cot@Symbol, cotEntry],
             [asin@Symbol, asinEntry], [acos@Symbol, acosEntry], 
              [atan@Symbol, atanEntry], [log@Symbol, logEntry]]
      construct(entryList)$Rep

    bfKeys():List Symbol == keys(bf())$Rep

    bfEntry(k:Symbol):RS == qelt(bf(),k)$Rep

@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
--    - Redistributions of source code must retain the above copyright
--      notice, this list of conditions and the following disclaimer.
--
--    - Redistributions in binary form must reproduce the above copyright
--      notice, this list of conditions and the following disclaimer in
--      the documentation and/or other materials provided with the
--      distribution.
--
--    - Neither the name of The Numerical ALgorithms Group Ltd. nor the
--      names of its contributors may be used to endorse or promote products
--      derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
@
<<*>>=
<<license>>

<<domain BFUNCT BasicFunctions>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}