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authordos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
committerdos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
commitab8cc85adde879fb963c94d15675783f2cf4b183 (patch)
treec202482327f474583b750b2c45dedfc4e4312b1d /src/algebra/equation1.spad.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra equation1.spad}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{category IEVALAB InnerEvalable}
+<<category IEVALAB InnerEvalable>>=
+)abbrev category IEVALAB InnerEvalable
+-- FOR THE BENEFIT OF LIBAX0 GENERATION
+++ Author:
+++ Date Created:
+++ Date Last Updated: June 3, 1991
+++ Basic Operations:
+++ Related Domains:
+++ Also See: Evalable
+++ AMS Classifications:
+++ Keywords: equation
+++ Examples:
+++ References:
+++ Description:
+++ This category provides \spadfun{eval} operations.
+++ A domain may belong to this category if it is possible to make
+++ ``evaluation'' substitutions. The difference between this
+++ and \spadtype{Evalable} is that the operations in this category
+++ specify the substitution as a pair of arguments rather than as
+++ an equation.
+InnerEvalable(A:SetCategory, B:Type): Category == with
+ eval: ($, A, B) -> $
+ ++ eval(f, x, v) replaces x by v in f.
+ eval: ($, List A, List B) -> $
+ ++ eval(f, [x1,...,xn], [v1,...,vn]) replaces xi by vi in f.
+ add
+ eval(f:$, x:A, v:B) == eval(f, [x], [v])
+
+@
+\section{category EVALAB Evalable}
+<<category EVALAB Evalable>>=
+)abbrev category EVALAB Evalable
+++ Author:
+++ Date Created:
+++ Date Last Updated: June 3, 1991
+++ Basic Operations:
+++ Related Domains:
+++ Also See: FullyEvalable
+++ AMS Classifications:
+++ Keywords: equation
+++ Examples:
+++ References:
+++ Description:
+++ This category provides \spadfun{eval} operations.
+++ A domain may belong to this category if it is possible to make
+++ ``evaluation'' substitutions.
+Evalable(R:SetCategory): Category == InnerEvalable(R,R) with
+ eval: ($, Equation R) -> $
+ ++ eval(f,x = v) replaces x by v in f.
+ eval: ($, List Equation R) -> $
+ ++ eval(f, [x1 = v1,...,xn = vn]) replaces xi by vi in f.
+ add
+ eval(f:$, eq:Equation R) == eval(f, [eq])
+ eval(f:$, xs:List R,vs:List R) == eval(f,[x=v for x in xs for v in vs])
+
+@
+\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 IEVALAB InnerEvalable>>
+<<category EVALAB Evalable>>
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}