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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/attreg.spad.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
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+\documentclass{article}
+\usepackage{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
+ finiteAggregate
+ ++ \spad{finiteAggregate} is true if it is an aggregate with a
+ ++ finite number of elements.
+ commutative("*")
+ ++ \spad{commutative("*")} is true if it has an operation
+ ++ \spad{"*": (D,D) -> D} which is commutative.
+ shallowlyMutable
+ ++ \spad{shallowlyMutable} is true if its values
+ ++ have immediate components that are updateable (mutable).
+ ++ Note: the properties of any component domain are irrevelant to the
+ ++ \spad{shallowlyMutable} proper.
+ unitsKnown
+ ++ \spad{unitsKnown} is true if a monoid (a multiplicative semigroup
+ ++ with a 1) has \spad{unitsKnown} means that
+ ++ the operation \spadfun{recip} can only return "failed"
+ ++ if its argument is not a unit.
+ leftUnitary
+ ++ \spad{leftUnitary} is true if \spad{1 * x = x} for all x.
+ rightUnitary
+ ++ \spad{rightUnitary} is true if \spad{x * 1 = x} for all x.
+ 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)}.
+ canonicalsClosed
+ ++ \spad{canonicalsClosed} is true if
+ ++ \spad{unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}.
+ arbitraryPrecision
+ ++ \spad{arbitraryPrecision} means the user can set the
+ ++ precision for subsequent calculations.
+ 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}.
+ central
+ ++ \spad{central} is true if, given an algebra over a ring R,
+ ++ the image of R is the center
+ ++ of the algebra, i.e. the set of members of the algebra which commute
+ ++ with all others is precisely the image of R in the algebra.
+ noetherian
+ ++ \spad{noetherian} is true if all of its ideals are finitely generated.
+ additiveValuation
+ ++ \spad{additiveValuation} implies
+ ++ \spad{euclideanSize(a*b)=euclideanSize(a)+euclideanSize(b)}.
+ multiplicativeValuation
+ ++ \spad{multiplicativeValuation} implies
+ ++ \spad{euclideanSize(a*b)=euclideanSize(a)*euclideanSize(b)}.
+ NullSquare
+ ++ \axiom{NullSquare} means that \axiom{[x,x] = 0} holds.
+ ++ See \axiomType{LieAlgebra}.
+ JacobiIdentity
+ ++ \axiom{JacobiIdentity} means that
+ ++ \axiom{[x,[y,z]]+[y,[z,x]]+[z,[x,y]] = 0} holds.
+ ++ See \axiomType{LieAlgebra}.
+ 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
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}