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diff --git a/src/algebra/ffrac.as.pamphlet b/src/algebra/ffrac.as.pamphlet deleted file mode 100644 index d038a101..00000000 --- a/src/algebra/ffrac.as.pamphlet +++ /dev/null @@ -1,204 +0,0 @@ -\documentclass{article} -\usepackage{open-axiom} -\begin{document} -\title{\$SPAD/src/algebra ffrac.as} -\author{Michael Richardson} -\maketitle -\begin{abstract} -\end{abstract} -\eject -\tableofcontents -\eject -\begin{verbatim} - --- FormalFraction - --- N.B. ndftip.as inlines this, must be recompiled if this is. - --- To test: --- sed '1,/^#if NeverAssertThis/d;/#endif/d' < ffrac.as > ffrac.input --- axiom --- )set nag host <some machine running nagd> --- )r ffrac.input - -\end{verbatim} -\section{FormalFraction} -<<FormalFraction>>= - -#include "axiom.as" - -FFRAC ==> FormalFraction ; - -OF ==> OutputForm ; -SC ==> SetCategory ; -FRAC ==> Fraction ; -ID ==> IntegralDomain ; - -+++ Author: M.G. Richardson -+++ Date Created: 1996 Jan. 23 -+++ Date Last Updated: -+++ Basic Functions: -+++ Related Constructors: Fraction -+++ Also See: -+++ AMS Classifications: -+++ Keywords: -+++ References: -+++ Description: -+++ This type represents formal fractions - that is, pairs displayed as -+++ fractions with no simplification. -+++ -+++ If the elements of the pair have a type X which is an integral -+++ domain, a FFRAC X can be coerced to a FRAC X, provided that this -+++ is a valid type. A FRAC X can always be coerced to a FFRAC X. -+++ If the type of the elements is a Field, a FFRAC X can be coerced -+++ to X. -+++ -+++ Formal fractions are used to return results from numerical methods -+++ which determine numerator and denominator separately, to enable -+++ users to inspect these components and recognise, for example, -+++ ratios of very small numbers as potentially indeterminate. - -FormalFraction(X : SC) : SC with { - --- Could generalise further to allow numerator and denominator to be of --- different types, X and Y, both SCs. "Left as an exercise." - - / : (X,X) -> % ; -++ / forms the formal quotient of two items. - - numer : % -> X ; -++ numer returns the numerator of a FormalFraction. - - denom : % -> X ; -++ denom returns the denominator of a FormalFraction. - - if X has ID then { - - coerce : % -> FRAC(X pretend ID) ; -++ coerce x converts a FormalFraction over an IntegralDomain to a -++ Fraction over that IntegralDomain. - - coerce : FRAC(X pretend ID) -> % ; -++ coerce converts a Fraction to a FormalFraction. - - } - - if X has Field then coerce : % -> (X pretend Field) ; - -} == add { - - import from Record(num : X, den : X) ; - - Rep == Record(num : X, den : X) ; -- representation - - ((x : %) = (y : %)) : Boolean == - ((rep(x).num = rep(y).num) and (rep(x).den = rep(y).den)) ; - - ((n : X)/(d : X)) : % == per(record(n,d)) ; - - coerce(r : %) : OF == (rep(r).num :: OF) / (rep(r).den :: OF) ; - - numer(r : %) : X == rep(r).num ; - - denom(r : %) : X == rep(r).den ; - - if X has ID then { - - coerce(r : %) : FRAC(X pretend ID) - == ((rep(r).num)/(rep(r).den)) @ (FRAC(X pretend ID)) ; - - coerce(x : FRAC(X pretend ID)) : % == x pretend % ; - - } - - if X has Field then coerce(r : %) : (X pretend Field) - == ((rep(r).num)/(rep(r).den)) $ (X pretend Field) ; - -} - -#if NeverAssertThis - -)lib ffrac - -f1 : FormalFraction Integer -f1 := 6/3 - --- 6 --- - --- 3 - -f2 := (3.6/2.4)$FormalFraction Float - --- 3.6 --- --- --- 2.4 - -numer f1 - --- 6 - -denom f2 - --- 2.4 - -f1 :: FRAC INT - --- 2 - -% :: FormalFraction Integer - --- 2 --- - --- 1 - -f2 :: Float - --- 1.5 - -output "End of tests" - -#endif -@ -\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>> - -<<FormalFraction>> -@ -\eject -\begin{thebibliography}{99} -\bibitem{1} nothing -\end{thebibliography} -\end{document} |