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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra c06.spad}
+\author{Godfrey Nolan, Mike Dewar}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{package NAGC06 NagSeriesSummationPackage}
+<<package NAGC06 NagSeriesSummationPackage>>=
+)abbrev package NAGC06 NagSeriesSummationPackage
+++ Author: Godfrey Nolan and Mike Dewar
+++ Date Created: Jan 1994
+++ Date Last Updated: Thu May 12 17:44:30 1994
+++Description:
+++This package uses the NAG Library to calculate the discrete Fourier
+++transform of a sequence of real or complex data values, and
+++applies it to calculate convolutions and correlations.
+++See \downlink{Manual Page}{manpageXXc06}.
+
+NagSeriesSummationPackage(): Exports == Implementation where
+  S ==> Symbol
+  FOP ==> FortranOutputStackPackage
+
+  Exports ==> with
+    c06eaf : (Integer,Matrix DoubleFloat,Integer) -> Result 
+     ++ c06eaf(n,x,ifail)
+     ++ calculates the discrete Fourier transform of a sequence of
+     ++ n real data values. (No extra workspace required.)
+     ++ See \downlink{Manual Page}{manpageXXc06eaf}.
+    c06ebf : (Integer,Matrix DoubleFloat,Integer) -> Result 
+     ++ c06ebf(n,x,ifail)
+     ++ calculates the discrete Fourier transform of a Hermitian 
+     ++ sequence of n complex data values. (No extra workspace required.)
+     ++ See \downlink{Manual Page}{manpageXXc06ebf}.
+    c06ecf : (Integer,Matrix DoubleFloat,Matrix DoubleFloat,Integer) -> Result 
+     ++ c06ecf(n,x,y,ifail)
+     ++ calculates the discrete Fourier transform of a sequence of
+     ++ n complex data values. (No extra workspace required.)
+     ++ See \downlink{Manual Page}{manpageXXc06ecf}.
+    c06ekf : (Integer,Integer,Matrix DoubleFloat,Matrix DoubleFloat,_
+	Integer) -> Result 
+     ++ c06ekf(job,n,x,y,ifail)
+     ++ calculates the circular convolution of two 
+     ++ real vectors of period n. No extra workspace is required.
+     ++ See \downlink{Manual Page}{manpageXXc06ekf}.
+    c06fpf : (Integer,Integer,String,Matrix DoubleFloat,_
+	Matrix DoubleFloat,Integer) -> Result 
+     ++ c06fpf(m,n,init,x,trig,ifail)
+     ++ computes the discrete Fourier transforms of m sequences, 
+     ++ each containing n real data values. This routine is designed to 
+     ++ be particularly efficient on vector processors.
+     ++ See \downlink{Manual Page}{manpageXXc06fpf}.
+    c06fqf : (Integer,Integer,String,Matrix DoubleFloat,_
+	Matrix DoubleFloat,Integer) -> Result 
+     ++ c06fqf(m,n,init,x,trig,ifail)
+     ++ computes the discrete Fourier transforms of m Hermitian 
+     ++ sequences, each containing n complex data values. This routine is
+     ++ designed to be particularly efficient on vector processors.
+     ++ See \downlink{Manual Page}{manpageXXc06fqf}.
+    c06frf : (Integer,Integer,String,Matrix DoubleFloat,_
+	Matrix DoubleFloat,Matrix DoubleFloat,Integer) -> Result 
+     ++ c06frf(m,n,init,x,y,trig,ifail)
+     ++ computes the discrete Fourier transforms of m sequences, 
+     ++ each containing n complex data values. This routine is designed 
+     ++ to be particularly efficient on vector processors.
+     ++ See \downlink{Manual Page}{manpageXXc06frf}.
+    c06fuf : (Integer,Integer,String,Matrix DoubleFloat,_
+	Matrix DoubleFloat,Matrix DoubleFloat,Matrix DoubleFloat,Integer) -> Result 
+     ++ c06fuf(m,n,init,x,y,trigm,trign,ifail)
+     ++ computes the two-dimensional discrete Fourier transform of
+     ++ a bivariate sequence of complex data values. This routine is 
+     ++ designed to be particularly efficient on vector processors.
+     ++ See \downlink{Manual Page}{manpageXXc06fuf}.
+    c06gbf : (Integer,Matrix DoubleFloat,Integer) -> Result 
+     ++ c06gbf(n,x,ifail)
+     ++ forms the complex conjugate of n 
+     ++ data values.
+     ++ See \downlink{Manual Page}{manpageXXc06gbf}.
+    c06gcf : (Integer,Matrix DoubleFloat,Integer) -> Result 
+     ++ c06gcf(n,y,ifail)
+     ++ forms the complex conjugate of a sequence of n data 
+     ++ values.
+     ++ See \downlink{Manual Page}{manpageXXc06gcf}.
+    c06gqf : (Integer,Integer,Matrix DoubleFloat,Integer) -> Result 
+     ++ c06gqf(m,n,x,ifail)
+     ++ forms the complex conjugates, 
+     ++ each containing n data values.
+     ++ See \downlink{Manual Page}{manpageXXc06gqf}.
+    c06gsf : (Integer,Integer,Matrix DoubleFloat,Integer) -> Result 
+     ++ c06gsf(m,n,x,ifail)
+     ++ takes m Hermitian sequences, each containing n data 
+     ++ values, and forms the real and imaginary parts of the m 
+     ++ corresponding complex sequences.
+     ++ See \downlink{Manual Page}{manpageXXc06gsf}.
+  Implementation ==> add
+
+    import Lisp
+    import DoubleFloat
+    import Any
+    import Record
+    import Integer
+    import Matrix DoubleFloat
+    import Boolean
+    import NAGLinkSupportPackage
+    import AnyFunctions1(Integer)
+    import AnyFunctions1(String)
+    import AnyFunctions1(Matrix DoubleFloat)
+
+
+    c06eaf(nArg:Integer,xArg:Matrix DoubleFloat,ifailArg:Integer): Result == 
+	[(invokeNagman(NIL$Lisp,_
+	"c06eaf",_
+	["n"::S,"ifail"::S,"x"::S]$Lisp,_
+	[]$Lisp,_
+	[["double"::S,["x"::S,"n"::S]$Lisp]$Lisp_
+	,["integer"::S,"n"::S,"ifail"::S]$Lisp_
+	]$Lisp,_
+	["x"::S,"ifail"::S]$Lisp,_
+	[([nArg::Any,ifailArg::Any,xArg::Any ])_
+	@List Any]$Lisp)$Lisp)_
+	pretend List (Record(key:Symbol,entry:Any))]$Result
+
+
+    c06ebf(nArg:Integer,xArg:Matrix DoubleFloat,ifailArg:Integer): Result == 
+	[(invokeNagman(NIL$Lisp,_
+	"c06ebf",_
+	["n"::S,"ifail"::S,"x"::S]$Lisp,_
+	[]$Lisp,_
+	[["double"::S,["x"::S,"n"::S]$Lisp]$Lisp_
+	,["integer"::S,"n"::S,"ifail"::S]$Lisp_
+	]$Lisp,_
+	["x"::S,"ifail"::S]$Lisp,_
+	[([nArg::Any,ifailArg::Any,xArg::Any ])_
+	@List Any]$Lisp)$Lisp)_
+	pretend List (Record(key:Symbol,entry:Any))]$Result
+
+    c06ecf(nArg:Integer,xArg:Matrix DoubleFloat,yArg:Matrix DoubleFloat,_
+	ifailArg:Integer): Result == 
+	[(invokeNagman(NIL$Lisp,_
+	"c06ecf",_
+	["n"::S,"ifail"::S,"x"::S,"y"::S]$Lisp,_
+	[]$Lisp,_
+	[["double"::S,["x"::S,"n"::S]$Lisp,["y"::S,"n"::S]$Lisp_
+	]$Lisp_
+	,["integer"::S,"n"::S,"ifail"::S]$Lisp_
+	]$Lisp,_
+	["x"::S,"y"::S,"ifail"::S]$Lisp,_
+	[([nArg::Any,ifailArg::Any,xArg::Any,yArg::Any ])_
+	@List Any]$Lisp)$Lisp)_
+	pretend List (Record(key:Symbol,entry:Any))]$Result
+
+    c06ekf(jobArg:Integer,nArg:Integer,xArg:Matrix DoubleFloat,_
+	yArg:Matrix DoubleFloat,ifailArg:Integer): Result == 
+	[(invokeNagman(NIL$Lisp,_
+	"c06ekf",_
+	["job"::S,"n"::S,"ifail"::S,"x"::S,"y"::S]$Lisp,_
+	[]$Lisp,_
+	[["double"::S,["x"::S,"n"::S]$Lisp,["y"::S,"n"::S]$Lisp_
+	]$Lisp_
+	,["integer"::S,"job"::S,"n"::S,"ifail"::S]$Lisp_
+	]$Lisp,_
+	["x"::S,"y"::S,"ifail"::S]$Lisp,_
+	[([jobArg::Any,nArg::Any,ifailArg::Any,xArg::Any,yArg::Any ])_
+	@List Any]$Lisp)$Lisp)_
+	pretend List (Record(key:Symbol,entry:Any))]$Result
+
+    c06fpf(mArg:Integer,nArg:Integer,initArg:String,_
+	xArg:Matrix DoubleFloat,trigArg:Matrix DoubleFloat,ifailArg:Integer): Result == 
+	[(invokeNagman(NIL$Lisp,_
+	"c06fpf",_
+	["m"::S,"n"::S,"init"::S,"ifail"::S,"x"::S,"trig"::S,"work"::S]$Lisp,_
+	["work"::S]$Lisp,_
+	[["double"::S,["x"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp_
+	,["trig"::S,["*"::S,2$Lisp,"n"::S]$Lisp]$Lisp,["work"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp]$Lisp_
+	,["integer"::S,"m"::S,"n"::S,"ifail"::S]$Lisp_
+	,["character"::S,"init"::S]$Lisp_
+	]$Lisp,_
+	["x"::S,"trig"::S,"ifail"::S]$Lisp,_
+	[([mArg::Any,nArg::Any,initArg::Any,ifailArg::Any,xArg::Any,trigArg::Any ])_
+	@List Any]$Lisp)$Lisp)_
+	pretend List (Record(key:Symbol,entry:Any))]$Result
+
+    c06fqf(mArg:Integer,nArg:Integer,initArg:String,_
+	xArg:Matrix DoubleFloat,trigArg:Matrix DoubleFloat,ifailArg:Integer): Result == 
+	[(invokeNagman(NIL$Lisp,_
+	"c06fqf",_
+	["m"::S,"n"::S,"init"::S,"ifail"::S,"x"::S,"trig"::S,"work"::S]$Lisp,_
+	["work"::S]$Lisp,_
+	[["double"::S,["x"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp_
+	,["trig"::S,["*"::S,2$Lisp,"n"::S]$Lisp]$Lisp,["work"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp]$Lisp_
+	,["integer"::S,"m"::S,"n"::S,"ifail"::S]$Lisp_
+	,["character"::S,"init"::S]$Lisp_
+	]$Lisp,_
+	["x"::S,"trig"::S,"ifail"::S]$Lisp,_
+	[([mArg::Any,nArg::Any,initArg::Any,ifailArg::Any,xArg::Any,trigArg::Any ])_
+	@List Any]$Lisp)$Lisp)_
+	pretend List (Record(key:Symbol,entry:Any))]$Result
+
+    c06frf(mArg:Integer,nArg:Integer,initArg:String,_
+	xArg:Matrix DoubleFloat,yArg:Matrix DoubleFloat,trigArg:Matrix DoubleFloat,_
+	ifailArg:Integer): Result == 
+	[(invokeNagman(NIL$Lisp,_
+	"c06frf",_
+	["m"::S,"n"::S,"init"::S,"ifail"::S,"x"::S,"y"::S,"trig"::S,"work"::S]$Lisp,_
+	["work"::S]$Lisp,_
+	[["double"::S,["x"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp_
+	,["y"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp,["trig"::S,["*"::S,2$Lisp,"n"::S]$Lisp]$Lisp,["work"::S,["*"::S,["*"::S,2$Lisp,"m"::S]$Lisp,"n"::S]$Lisp]$Lisp_
+	]$Lisp_
+	,["integer"::S,"m"::S,"n"::S,"ifail"::S]$Lisp_
+	,["character"::S,"init"::S]$Lisp_
+	]$Lisp,_
+	["x"::S,"y"::S,"trig"::S,"ifail"::S]$Lisp,_
+	[([mArg::Any,nArg::Any,initArg::Any,ifailArg::Any,xArg::Any,yArg::Any,trigArg::Any ])_
+	@List Any]$Lisp)$Lisp)_
+	pretend List (Record(key:Symbol,entry:Any))]$Result
+
+    c06fuf(mArg:Integer,nArg:Integer,initArg:String,_
+	xArg:Matrix DoubleFloat,yArg:Matrix DoubleFloat,trigmArg:Matrix DoubleFloat,_
+	trignArg:Matrix DoubleFloat,ifailArg:Integer): Result == 
+	[(invokeNagman(NIL$Lisp,_
+	"c06fuf",_
+	["m"::S,"n"::S,"init"::S,"ifail"::S,"x"::S,"y"::S,"trigm"::S,"trign"::S,"work"::S_
+	]$Lisp,_
+	["work"::S]$Lisp,_
+	[["double"::S,["x"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp_
+	,["y"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp,["trigm"::S,["*"::S,2$Lisp,"m"::S]$Lisp]$Lisp,["trign"::S,["*"::S,2$Lisp,"n"::S]$Lisp]$Lisp_
+	,["work"::S,["*"::S,["*"::S,2$Lisp,"m"::S]$Lisp,"n"::S]$Lisp]$Lisp]$Lisp_
+	,["integer"::S,"m"::S,"n"::S,"ifail"::S]$Lisp_
+	,["character"::S,"init"::S]$Lisp_
+	]$Lisp,_
+	["x"::S,"y"::S,"trigm"::S,"trign"::S,"ifail"::S]$Lisp,_
+	[([mArg::Any,nArg::Any,initArg::Any,ifailArg::Any,xArg::Any,yArg::Any,trigmArg::Any,trignArg::Any ])_
+	@List Any]$Lisp)$Lisp)_
+	pretend List (Record(key:Symbol,entry:Any))]$Result
+
+    c06gbf(nArg:Integer,xArg:Matrix DoubleFloat,ifailArg:Integer): Result == 
+	[(invokeNagman(NIL$Lisp,_
+	"c06gbf",_
+	["n"::S,"ifail"::S,"x"::S]$Lisp,_
+	[]$Lisp,_
+	[["double"::S,["x"::S,"n"::S]$Lisp]$Lisp_
+	,["integer"::S,"n"::S,"ifail"::S]$Lisp_
+	]$Lisp,_
+	["x"::S,"ifail"::S]$Lisp,_
+	[([nArg::Any,ifailArg::Any,xArg::Any ])_
+	@List Any]$Lisp)$Lisp)_
+	pretend List (Record(key:Symbol,entry:Any))]$Result
+
+    c06gcf(nArg:Integer,yArg:Matrix DoubleFloat,ifailArg:Integer): Result == 
+	[(invokeNagman(NIL$Lisp,_
+	"c06gcf",_
+	["n"::S,"ifail"::S,"y"::S]$Lisp,_
+	[]$Lisp,_
+	[["double"::S,["y"::S,"n"::S]$Lisp]$Lisp_
+	,["integer"::S,"n"::S,"ifail"::S]$Lisp_
+	]$Lisp,_
+	["y"::S,"ifail"::S]$Lisp,_
+	[([nArg::Any,ifailArg::Any,yArg::Any ])_
+	@List Any]$Lisp)$Lisp)_
+	pretend List (Record(key:Symbol,entry:Any))]$Result
+
+    c06gqf(mArg:Integer,nArg:Integer,xArg:Matrix DoubleFloat,_
+	ifailArg:Integer): Result == 
+	[(invokeNagman(NIL$Lisp,_
+	"c06gqf",_
+	["m"::S,"n"::S,"ifail"::S,"x"::S]$Lisp,_
+	[]$Lisp,_
+	[["double"::S,["x"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp_
+	]$Lisp_
+	,["integer"::S,"m"::S,"n"::S,"ifail"::S]$Lisp_
+	]$Lisp,_
+	["x"::S,"ifail"::S]$Lisp,_
+	[([mArg::Any,nArg::Any,ifailArg::Any,xArg::Any ])_
+	@List Any]$Lisp)$Lisp)_
+	pretend List (Record(key:Symbol,entry:Any))]$Result
+
+    c06gsf(mArg:Integer,nArg:Integer,xArg:Matrix DoubleFloat,_
+	ifailArg:Integer): Result == 
+	[(invokeNagman(NIL$Lisp,_
+	"c06gsf",_
+	["m"::S,"n"::S,"ifail"::S,"x"::S,"u"::S,"v"::S]$Lisp,_
+	["u"::S,"v"::S]$Lisp,_
+	[["double"::S,["x"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp_
+	,["u"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp,["v"::S,["*"::S,"m"::S,"n"::S]$Lisp]$Lisp]$Lisp_
+	,["integer"::S,"m"::S,"n"::S,"ifail"::S]$Lisp_
+	]$Lisp,_
+	["u"::S,"v"::S,"ifail"::S]$Lisp,_
+	[([mArg::Any,nArg::Any,ifailArg::Any,xArg::Any ])_
+	@List Any]$Lisp)$Lisp)_
+	pretend List (Record(key:Symbol,entry:Any))]$Result
+
+@
+\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>>
+
+<<package NAGC06 NagSeriesSummationPackage>>
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}