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\documentclass[dvipdfmx]{book}
\newcommand{\VolumeName}{Volume 3: Axiom Programmers Guide}
\input{bookheader.tex}
\mainmatter
\setcounter{chapter}{0} % Chapter 1
\chapter{Details for Programmers}
Axiom maintains internal representations for domains.
There are functions for examining the internals of objects of
a particular domain.
\section{Examining Internals}
One useful function is {\bf devaluate} which takes an object
and returns a Lisp pair. The CAR of the pair is the Axiom type.
The CDR of the pair is the object representation.
For instances, consider the session where we create a list of
objects using the domain {\bf List(Any)}.
\begin{verbatim}
(1) -> w:=[1,7.2,"luanne",3*x^2+5,_
(3*x^2+5)::FRAC(POLY(INT)),_
(3*x^2+5)::POLY(FRAC(INT)),_
(3*x^2+5)::EXPR(INT)]$LIST(ANY)
2 2 2 2
(1) [1,7.2,"luanne",3x + 5,3x + 5,3x + 5,3x + 5]
Type: List(Any)
\end{verbatim}
The first object, {\bf 1} is a primitive object that has the domain
{\bf PI} and uses the underlying Lisp representation for the number.
\begin{verbatim}
(2) -> devaluate(1)$Lisp
(2) 1
Type: SExpression
\end{verbatim}
The second object, {\bf 7.2} is a primitive object that has the domain
{\bf FLOAT} and uses the underlying Lisp representation for the number,
in this case, itself a pair whose CAR is the floating point base and whose
CDR is the mantissa,
\begin{verbatim}
(3) -> devaluate(7.2)$Lisp
(3) (265633114661417543270 . - 65)
Type: SExpression
\end{verbatim}
The third object, {\tt {\bf "luanne"}} is from the domain {\bf STRING}
and uses the Lisp string representation.
\begin{verbatim}
(4) -> devaluate("luanne")$Lisp
(4) luanne
Type: SExpression
\end{verbatim}
Now we get more complicated. We illustrate various ways to store the
formula $3x^2+5$ in different domains. Each domain has a chosen
representation.
\begin{verbatim}
(5) -> devaluate(3*x^2+5)$Lisp
(5) (1 x (2 0 . 3) (0 0 . 5))
Type: SExpression
\end{verbatim}
The fourth object, $3x^2+5$ is from the domain {\bf POLY(INT)}. It is stored
as the list
\begin{verbatim}
(1 x (2 0 . 3) (0 0 . 5))
\end{verbatim}
From the domain {\bf POLY} (Vol 10.3, POLY) we see that
\begin{verbatim}
Polynomial(R:Ring): ...
== SparseMultivariatePolynomial(R, Symbol) add ...
\end{verbatim}
So objects from this domain are represented as {\bf SMP(INT,SYMBOL)}.
From this domain we ss that
\begin{verbatim}
SparseMultivariatePolynomial(R: Ring,VarSet: OrderedSet): ...
== add
--representations
D := SparseUnivariatePolynomial(%)
\end{verbatim}
So objects from this domain are represented as a {\bf SUP(INT)}
\begin{verbatim}
SparseUnivariatePolynomial(R:Ring): ...
== PolynomialRing(R,NonNegativeInteger) add
\end{verbatim}
So objects from this domain are represented as {\bf PR(INT,NNI)}
\begin{verbatim}
PolynomialRing(R:Ring,E:OrderedAbelianMonoid): ...
FreeModule(R,E) add
--representations
Term:= Record(k:E,c:R)
Rep:= List Term
\end{verbatim}
So objects from this domain are represented as {\bf FM(INT,NNI)}
\begin{verbatim}
FreeModule(R:Ring,S:OrderedSet):
== IndexedDirectProductAbelianGroup(R,S) add
--representations
Term:= Record(k:S,c:R)
Rep:= List Term
\end{verbatim}
So objects from this domain are represented as {\bf IDPAG(INT,NNI)}
\begin{verbatim}
IndexedDirectProductAbelianGroup(A:AbelianGroup,S:OrderedSet):
== IndexedDirectProductAbelianMonoid(A,S) add
\end{verbatim}
So objects from this domain are represented as {\bf IDPAM(INT,NNI)}
\begin{verbatim}
IndexedDirectProductAbelianMonoid(A:AbelianMonoid,S:OrderedSet):
== IndexedDirectProductObject(A,S) add
--representations
Term:= Record(k:S,c:A)
Rep:= List Term
\end{verbatim}
So objects from this domain are represented as {\bf IDPO(INT,NNI)}
\begin{verbatim}
IndexedDirectProductObject(A:SetCategory,S:OrderedSet):
== add
-- representations
Term:= Record(k:S,c:A)
Rep:= List Term
\end{verbatim}
\begin{verbatim}
(6) -> devaluate((3*x^2+5)::FRAC(POLY(INT)))$Lisp
(6) ((1 x (2 0 . 3) (0 0 . 5)) 0 . 1)
Type: SExpression
\end{verbatim}
\begin{verbatim}
(7) -> devaluate((3*x^2+5)::POLY(FRAC(INT)))$Lisp
(7) (1 x (2 0 3 . 1) (0 0 5 . 1))
Type: SExpression
\end{verbatim}
\begin{verbatim}
(8) -> devaluate((3*x^2+5)::EXPR(INT))$Lisp
(8) ((1 [[x,0,%symbol()()()],NIL,1,1024] (2 0 . 3) (0 0 . 5)) 0 . 1)
Type: SExpression
\end{verbatim}
\begin{verbatim}
(9) -> devaluate(w)$Lisp
(9)
(((PositiveInteger) . 1) ((Float) 265633114661417543270 . - 65)
((String) . luanne) ((Polynomial (Integer)) 1 x (2 0 . 3) (0 0 . 5))
((Fraction (Polynomial (Integer))) (1 x (2 0 . 3) (0 0 . 5)) 0 . 1)
((Polynomial (Fraction (Integer))) 1 x (2 0 3 . 1) (0 0 5 . 1))
((Expression (Integer))
(1 [[x,0,%symbol()()()],NIL,1,1024] (2 0 . 3) (0 0 . 5)) 0 . 1)
)
Type: SExpression
\end{verbatim}
\section{Makefile}
This book is actually a literate program\cite{Knut92} and can contain
executable source code. In particular, the Makefile for this book
is part of the source of the book and is included below.
\eject
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\cleardoublepage
\phantomsection
\addcontentsline{toc}{chapter}{Bibliography}
\bibliographystyle{axiom}
\bibliography{axiom}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\cleardoublepage
\phantomsection
\addcontentsline{toc}{chapter}{Index}
\printindex
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\end{document}
|
