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author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
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committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/algebra/attreg.spad.pamphlet | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/algebra/attreg.spad.pamphlet')
-rw-r--r-- | src/algebra/attreg.spad.pamphlet | 127 |
1 files changed, 127 insertions, 0 deletions
diff --git a/src/algebra/attreg.spad.pamphlet b/src/algebra/attreg.spad.pamphlet new file mode 100644 index 00000000..221d387a --- /dev/null +++ b/src/algebra/attreg.spad.pamphlet @@ -0,0 +1,127 @@ +\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} |