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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra setorder.spad}
\author{Manuel Bronstein}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{package UDPO UserDefinedPartialOrdering}
<<package UDPO UserDefinedPartialOrdering>>=
)abbrev package UDPO UserDefinedPartialOrdering
++ Author: Manuel Bronstein
++ Date Created: March 1990
++ Date Last Updated: 9 April 1991
++ Description:
++ Provides functions to force a partial ordering on any set.
UserDefinedPartialOrdering(S:SetCategory): with
setOrder : List S -> Void
++ setOrder([a1,...,an]) defines a partial ordering on S given by:
++ (1) \spad{a1 < a2 < ... < an}.
++ (2) \spad{b < ai for i = 1..n} and b not among the ai's.
++ (3) undefined on \spad{(b, c)} if neither is among the ai's.
setOrder : (List S, List S) -> Void
++ setOrder([b1,...,bm], [a1,...,an]) defines a partial
++ ordering on S given by:
++ (1) \spad{b1 < b2 < ... < bm < a1 < a2 < ... < an}.
++ (2) \spad{bj < c < ai} for c not among the ai's and bj's.
++ (3) undefined on \spad{(c,d)} if neither is among the ai's,bj's.
getOrder : () -> Record(low: List S, high: List S)
++ getOrder() returns \spad{[[b1,...,bm], [a1,...,an]]} such that the
++ partial ordering on S was given by
++ \spad{setOrder([b1,...,bm],[a1,...,an])}.
less? : (S, S) -> Union(Boolean, "failed")
++ less?(a, b) compares \spad{a} and b in the partial ordering induced by
++ setOrder.
less? : (S, S, (S, S) -> Boolean) -> Boolean
++ less?(a, b, fn) compares \spad{a} and b in the partial ordering induced
++ by setOrder, and returns \spad{fn(a, b)} if \spad{a}
++ and b are not comparable
++ in that ordering.
largest : (List S, (S, S) -> Boolean) -> S
++ largest(l, fn) returns the largest element of l where the partial
++ ordering induced by setOrder is completed into a total one by fn.
userOrdered?: () -> Boolean
++ userOrdered?() tests if the partial ordering induced by
++ \spadfunFrom{setOrder}{UserDefinedPartialOrdering} is not empty.
if S has OrderedSet then
largest: List S -> S
++ largest l returns the largest element of l where the partial
++ ordering induced by setOrder is completed into a total one by
++ the ordering on S.
more? : (S, S) -> Boolean
++ more?(a, b) compares \spad{a} and b in the partial ordering induced
++ by setOrder, and uses the ordering on S if \spad{a} and b are not
++ comparable in the partial ordering.
== add
llow :Reference List S := ref nil()
lhigh:Reference List S := ref nil()
userOrdered?() == not(empty? deref llow) or not(empty? deref lhigh)
getOrder() == [deref llow, deref lhigh]
setOrder l == setOrder(nil(), l)
setOrder(l, h) ==
setref(llow, removeDuplicates l)
setref(lhigh, removeDuplicates h)
less?(a, b, f) ==
(u := less?(a, b)) case "failed" => f(a, b)
u::Boolean
largest(x, f) ==
empty? x => error "largest: empty list"
empty? rest x => first x
a := largest(rest x, f)
less?(first x, a, f) => a
first x
less?(a, b) ==
for x in deref llow repeat
x = a => return(a ~= b)
x = b => return false
aa := bb := false$Boolean
for x in deref lhigh repeat
if x = a then
bb => return false
aa := true
if x = b then
aa => return(a ~= b)
bb := true
aa => false
bb => true
"failed"
if S has OrderedSet then
more?(a, b) == not less?(a, b, #1 <$S #2)
largest x == largest(x, #1 <$S #2)
@
\section{package UDVO UserDefinedVariableOrdering}
<<package UDVO UserDefinedVariableOrdering>>=
)abbrev package UDVO UserDefinedVariableOrdering
++ Author: Manuel Bronstein
++ Date Created: March 1990
++ Date Last Updated: 9 April 1991
++ Description:
++ This packages provides functions to allow the user to select the ordering
++ on the variables and operators for displaying polynomials,
++ fractions and expressions. The ordering affects the display
++ only and not the computations.
UserDefinedVariableOrdering(): with
setVariableOrder : List Symbol -> Void
++ setVariableOrder([a1,...,an]) defines an ordering on the
++ variables given by \spad{a1 > a2 > ... > an > other variables}.
setVariableOrder : (List Symbol, List Symbol) -> Void
++ setVariableOrder([b1,...,bm], [a1,...,an]) defines an ordering
++ on the variables given by
++ \spad{b1 > b2 > ... > bm >} other variables \spad{> a1 > a2 > ... > an}.
getVariableOrder : () -> Record(high:List Symbol, low:List Symbol)
++ getVariableOrder() returns \spad{[[b1,...,bm], [a1,...,an]]} such that
++ the ordering on the variables was given by
++ \spad{setVariableOrder([b1,...,bm], [a1,...,an])}.
resetVariableOrder: () -> Void
++ resetVariableOrder() cancels any previous use of
++ setVariableOrder and returns to the default system ordering.
== add
import UserDefinedPartialOrdering(Symbol)
setVariableOrder l == setOrder reverse l
setVariableOrder(l1, l2) == setOrder(reverse l2, reverse l1)
resetVariableOrder() == setVariableOrder(nil(), nil())
getVariableOrder() ==
r := getOrder()
[reverse(r.high), reverse(r.low)]
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
-- Copyright (C) 2007-2010, Gabriel Dos Reis.
-- 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>>
<<package UDPO UserDefinedPartialOrdering>>
<<package UDVO UserDefinedVariableOrdering>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
|
