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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra ptranfn.spad}
\author{Clifton J. Williamson}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{category PTRANFN PartialTranscendentalFunctions}
<<category PTRANFN PartialTranscendentalFunctions>>=
)abbrev category PTRANFN PartialTranscendentalFunctions
++ Description of a package which provides partial transcendental
++ functions, i.e. functions which return an answer or "failed"
++ Author: Clifton J. Williamson
++ Date Created: 12 February 1990
++ Date Last Updated: 14 February 1990
++ Keywords:
++ Examples:
++ References:
++ Description:
++ This is the description of any package which provides partial
++ functions on a domain belonging to TranscendentalFunctionCategory.
PartialTranscendentalFunctions(K): Category == Definition where
K : TranscendentalFunctionCategory
NNI ==> NonNegativeInteger
Definition ==> with
--% Exponentials and Logarithms
nthRootIfCan: (K,NNI) -> Union(K,"failed")
++ nthRootIfCan(z,n) returns the nth root of z if possible,
++ and "failed" otherwise.
expIfCan: K -> Union(K,"failed")
++ expIfCan(z) returns exp(z) if possible, and "failed" otherwise.
logIfCan: K -> Union(K,"failed")
++ logIfCan(z) returns log(z) if possible, and "failed" otherwise.
--% TrigonometricFunctionCategory
sinIfCan : K -> Union(K,"failed")
++ sinIfCan(z) returns sin(z) if possible, and "failed" otherwise.
cosIfCan: K -> Union(K,"failed")
++ cosIfCan(z) returns cos(z) if possible, and "failed" otherwise.
tanIfCan: K -> Union(K,"failed")
++ tanIfCan(z) returns tan(z) if possible, and "failed" otherwise.
cotIfCan: K -> Union(K,"failed")
++ cotIfCan(z) returns cot(z) if possible, and "failed" otherwise.
secIfCan: K -> Union(K,"failed")
++ secIfCan(z) returns sec(z) if possible, and "failed" otherwise.
cscIfCan: K -> Union(K,"failed")
++ cscIfCan(z) returns csc(z) if possible, and "failed" otherwise.
--% ArcTrigonometricFunctionCategory
asinIfCan: K -> Union(K,"failed")
++ asinIfCan(z) returns asin(z) if possible, and "failed" otherwise.
acosIfCan: K -> Union(K,"failed")
++ acosIfCan(z) returns acos(z) if possible, and "failed" otherwise.
atanIfCan: K -> Union(K,"failed")
++ atanIfCan(z) returns atan(z) if possible, and "failed" otherwise.
acotIfCan: K -> Union(K,"failed")
++ acotIfCan(z) returns acot(z) if possible, and "failed" otherwise.
asecIfCan: K -> Union(K,"failed")
++ asecIfCan(z) returns asec(z) if possible, and "failed" otherwise.
acscIfCan: K -> Union(K,"failed")
++ acscIfCan(z) returns acsc(z) if possible, and "failed" otherwise.
--% HyperbolicFunctionCategory
sinhIfCan: K -> Union(K,"failed")
++ sinhIfCan(z) returns sinh(z) if possible, and "failed" otherwise.
coshIfCan: K -> Union(K,"failed")
++ coshIfCan(z) returns cosh(z) if possible, and "failed" otherwise.
tanhIfCan: K -> Union(K,"failed")
++ tanhIfCan(z) returns tanh(z) if possible, and "failed" otherwise.
cothIfCan: K -> Union(K,"failed")
++ cothIfCan(z) returns coth(z) if possible, and "failed" otherwise.
sechIfCan: K -> Union(K,"failed")
++ sechIfCan(z) returns sech(z) if possible, and "failed" otherwise.
cschIfCan: K -> Union(K,"failed")
++ cschIfCan(z) returns csch(z) if possible, and "failed" otherwise.
--% ArcHyperbolicFunctionCategory
asinhIfCan: K -> Union(K,"failed")
++ asinhIfCan(z) returns asinh(z) if possible, and "failed" otherwise.
acoshIfCan: K -> Union(K,"failed")
++ acoshIfCan(z) returns acosh(z) if possible, and "failed" otherwise.
atanhIfCan: K -> Union(K,"failed")
++ atanhIfCan(z) returns atanh(z) if possible, and "failed" otherwise.
acothIfCan: K -> Union(K,"failed")
++ acothIfCan(z) returns acoth(z) if possible, and "failed" otherwise.
asechIfCan: K -> Union(K,"failed")
++ asechIfCan(z) returns asech(z) if possible, and "failed" otherwise.
acschIfCan: K -> Union(K,"failed")
++ acschIfCan(z) returns acsch(z) if possible, and "failed" otherwise.
@
\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>>
<<category PTRANFN PartialTranscendentalFunctions>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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