\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra attreg.spad}
\author{The Axiom Team}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{category ATTREG AttributeRegistry}
<<category ATTREG AttributeRegistry>>=
)abbrev category ATTREG AttributeRegistry

++ This category exports the attributes in the AXIOM Library
AttributeRegistry(): Category == with
  commutative("*")
    ++ \spad{commutative("*")} is true if it has an operation
    ++ \spad{"*": (D,D) -> D} which is commutative.
  noZeroDivisors
    ++ \spad{noZeroDivisors} is true if \spad{x * y \~~= 0} implies 
    ++ both x and y are non-zero.
  canonicalUnitNormal
    ++ \spad{canonicalUnitNormal} is true if we can choose a canonical
    ++ representative for each class of associate elements, that is
    ++ \spad{associates?(a,b)} returns true if and only if 
    ++ \spad{unitCanonical(a) = unitCanonical(b)}.
  partiallyOrderedSet
    ++ \spad{partiallyOrderedSet} is true if
    ++ a set with \spadop{<} which is transitive, 
    ++ but \spad{not(a < b or a = b)}
    ++ does not necessarily imply \spad{b<a}.
  additiveValuation
    ++ \spad{additiveValuation} implies
    ++ \spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.
  multiplicativeValuation
    ++ \spad{multiplicativeValuation} implies
    ++ \spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.
  canonical
    ++ \spad{canonical} is true if and only if distinct elements have 
    ++ distinct data structures. For example, a domain of mathematical objects 
    ++ which has the \spad{canonical} attribute means that two objects 
    ++ are mathematically
    ++ equal if and only if their data structures are equal.

@
\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 ATTREG AttributeRegistry>>
@
\eject
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\bibitem{1} nothing
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\end{document}