--- /dev/null
+\input texinfo @c -*-texinfo-*-
+@c %**start of header
+@setfilename ginac.info
+@settitle GiNaC, an open framework for symbolic computation within the C++ programming language
+@setchapternewpage off
+@afourpaper
+@c %**end of header
+
+@include version.texi
+
+@direntry
+* ginac: (ginac). C++ library for symbolic computation.
+@end direntry
+
+@ifinfo
+This file documents GiNaC @value{VERSION}, an open framework for symbolic
+computation within the C++ programming language.
+
+Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+
+Permission is granted to make and distribute verbatim copies of
+this manual provided the copyright notice and this permission notice
+are preserved on all copies.
+
+@ignore
+Permission is granted to process this file through TeX and print the
+results, provided the printed document carries copying permission
+notice identical to this one except for the removal of this paragraph
+
+@end ignore
+Permission is granted to copy and distribute modified versions of this
+manual under the conditions for verbatim copying, provided that the entire
+resulting derived work is distributed under the terms of a permission
+notice identical to this one.
+@end ifinfo
+
+@titlepage
+@title GiNaC @value{VERSION}
+@subtitle An open framework for symbolic computation within the C++ programming language
+@author The GiNaC Group:
+@author Christian Bauer, Alexander Frink, Richard B. Kreckel
+
+@page
+@vskip 0pt plus 1filll
+Copyright @copyright{} 1999 Johannes Gutenberg University Mainz, Germany
+@sp 2
+Permission is granted to make and distribute verbatim copies of
+this manual provided the copyright notice and this permission notice
+are preserved on all copies.
+
+Permission is granted to copy and distribute modified versions of this
+manual under the conditions for verbatim copying, provided that the entire
+resulting derived work is distributed under the terms of a permission
+notice identical to this one.
+@end titlepage
+
+@page
+@contents
+
+@page
+
+
+@node Top, Introduction, (dir), (dir)
+@c node-name, next, previous, up
+@top GiNaC
+
+This file documents GiNaC @value{VERSION}, an open framework for symbolic
+computation within the C++ programming language.
+
+@menu
+* Introduction:: GiNaC's purpose.
+* A Tour of GiNaC:: A quick tour of the library.
+* Installation:: How to install the package.
+* Basic Concepts:: Description of fundamental classes.
+* Important Algorithms:: Algorithms for symbolic manipulations.
+* Extending GiNaC:: How to extend the library.
+* A Comparison With Other CAS:: Compares GiNaC to traditional CAS.
+* Bibliography::
+* Concept Index::
+@end menu
+
+
+@node Introduction, A Tour of GiNaC, Top, Top
+@c node-name, next, previous, up
+@chapter Introduction
+
+The motivation behind GiNaC derives from the observation that most
+present day computer algebra systems (CAS) are linguistically and
+semantically impoverished. It is an attempt to overcome the current
+situation by extending a well established and standardized computer
+language (C++) by some fundamental symbolic capabilities, thus
+allowing for integrated systems that embed symbolic manipulations
+together with more established areas of computer science (like
+computation-intense numeric applications, graphical interfaces, etc.)
+under one roof.
+
+This tutorial is intended for the novice user who is new to
+GiNaC but already has some background in C++ programming. However,
+since a hand made documentation like this one is difficult to keep in
+sync with the development the actual documentation is inside the
+sources in the form of comments. That documentation may be parsed by
+one of the many Javadoc-like documentation systems. If you fail at
+generating it you may access it from
+@uref{http://www.ginac.de/reference/, the GiNaC home page}.
+It is an invaluable resource not only for the advanced user who wishes
+to extend the system (or chase bugs) but for everybody who wants to
+comprehend the inner workings of GiNaC. This little tutorial on the
+other hand only covers the basic things that are unlikely to change in
+the near future.
+
+@section License
+The GiNaC framework for symbolic computation within the C++ programming
+language is Copyright @copyright{} 1999 Johannes Gutenberg University Mainz,
+Germany.
+
+This program is free software; you can redistribute it and/or
+modify it under the terms of the GNU General Public License as
+published by the Free Software Foundation; either version 2 of the
+License, or (at your option) any later version.
+
+This program is distributed in the hope that it will be useful, but
+WITHOUT ANY WARRANTY; without even the implied warranty of
+MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+General Public License for more details.
+
+You should have received a copy of the GNU General Public License
+along with this program; see the file COPYING. If not, write to the
+Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
+MA 02111-1307, USA.
+
+
+@node A Tour of GiNaC, How to use it from within C++, Introduction, Top
+@c node-name, next, previous, up
+@chapter A Tour of GiNaC
+
+This quick tour of GiNaC wants to rise your interest in the
+subsequent chapters by showing off a bit. Please excuse us if it
+leaves many open questions.
+
+@menu
+* How to use it from within C++:: Two simple examples.
+* What it can do for you:: A Tour of GiNaC's features.
+@end menu
+
+
+@node How to use it from within C++, What it can do for you, A Tour of GiNaC, A Tour of GiNaC
+@c node-name, next, previous, up
+@section How to use it from within C++
+
+The GiNaC open framework for symbolic computation within the C++ programming
+language does not try to define a language of it's own as conventional
+CAS do. Instead, it extends the capabilities of C++ by symbolic
+manipulations. Here is how to generate and print a simple (and
+pointless) bivariate polynomial with some large coefficients:
+
+@subheading My first GiNaC program (a bivariate polynomial)
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+int main()
+@{
+ symbol x("x"), y("y");
+ ex poly;
+
+ for (int i=0; i<3; ++i)
+ poly += factorial(i+16)*pow(x,i)*pow(y,2-i);
+
+ cout << poly << endl;
+ return 0;
+@}
+@end example
+
+Assuming the file is called @file{hello.cc}, on our system we can compile
+and run it like this:
+
+@example
+$ c++ hello.cc -o hello -lcln -lginac
+$ ./hello
+355687428096000*x*y+20922789888000*y^2+6402373705728000*x^2
+@end example
+
+Next, there is a more meaningful C++ program that calls a function which
+generates Hermite polynomials in a specified free variable.
+
+@subheading My second GiNaC program (Hermite polynomials)
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+ex HermitePoly(symbol x, int deg)
+@{
+ ex HKer=exp(-pow(x,2));
+ // uses the identity H_n(x) == (-1)^n exp(x^2) (d/dx)^n exp(-x^2)
+ return normal(pow(-1,deg) * diff(HKer, x, deg) / HKer);
+@}
+
+int main()
+@{
+ symbol z("z");
+
+ for (int i=0; i<6; ++i)
+ cout << "H_" << i << "(z) == " << HermitePoly(z,i) << endl;
+
+ return 0;
+@}
+@end example
+
+When run, this will type out
+
+@example
+H_0(z) == 1
+H_1(z) == 2*z
+H_2(z) == 4*z^2-2
+H_3(z) == -12*z+8*z^3
+H_4(z) == -48*z^2+16*z^4+12
+H_5(z) == 120*z-160*z^3+32*z^5
+@end example
+
+This method of generating the coefficients is of course far from
+optimal for production purposes.
+
+In order to show some more examples of what GiNaC can do we
+will now use @command{ginsh}, a simple GiNaC interactive
+shell that provides a convenient window into GiNaC's capabilities.
+
+
+@node What it can do for you, Installation, How to use it from within C++, A Tour of GiNaC
+@c node-name, next, previous, up
+@section What it can do for you
+
+After invoking @command{ginsh} one can test and experiment with GiNaC's
+features much like in other Computer Algebra Systems except that it does
+not provide programming constructs like loops or conditionals. For a
+concise description of the @command{ginsh} syntax we refer to its
+accompanied man page. Suffice to say that assignments and comparisons in
+@command{ginsh} are written as they are in C, i.e. @code{=} assigns and
+@code{==} compares.
+
+It can manipulate arbitrary precision integers in a very fast
+way. Rational numbers are automatically converted to fractions of
+coprime integers:
+
+@example
+> x=3^150;
+369988485035126972924700782451696644186473100389722973815184405301748249
+> y=3^149;
+123329495011708990974900260817232214728824366796574324605061468433916083
+> x/y;
+3
+> y/x;
+1/3
+@end example
+
+All numbers occuring in GiNaC's expressions can be converted into floating
+point numbers with the @code{evalf} method, to arbitrary accuracy:
+
+@example
+> evalf(1/7);
+0.14285714285714285714
+> Digits=150;
+150
+> evalf(1/7);
+0.1428571428571428571428571428571428571428571428571428571428571428571428
+5714285714285714285714285714285714285
+@end example
+
+Exact numbers other than rationals that can be manipulated in GiNaC
+include predefined constants like Archimedes' @code{Pi}. They can both
+be used in symbolic manipulations (as an exact number) as well as in
+numeric expressions (as an inexact number):
+
+@example
+> a=Pi^2+x;
+x+Pi^2
+> evalf(a);
+x+9.869604401089358619L0
+> x=2;
+2
+> evalf(a);
+11.869604401089358619L0
+@end example
+
+Built-in functions evaluate immediately to exact numbers if
+this is possible. Conversions that can be safely performed are done
+immediately; conversions that are not generally valid are not done:
+
+@example
+> cos(42*Pi);
+1
+> cos(acos(x));
+x
+> acos(cos(x));
+acos(cos(x))
+@end example
+
+(Note that converting the last input to @code{x} would allow one to
+conclude that @code{42*Pi} is equal to @code{0}.)
+
+Linear equation systems can be solved along with basic linear
+algebra manipulations over symbolic expressions. In C++ GiNaC offers
+a matrix class for this purpose but we can see what it can do using
+@command{ginsh}'s notation of double brackets to type them in:
+
+@example
+> lsolve(a+x*y==z,x);
+y^(-1)*(z-a);
+lsolve([3*x+5*y == 7, -2*x+10*y == -5], [x, y]);
+[x==19/8,y==-1/40]
+> M = [[ [[1, 3]], [[-3, 2]] ]];
+[[ [[1,3]], [[-3,2]] ]]
+> determinant(M);
+11
+> charpoly(M,lambda);
+lambda^2-3*lambda+11
+@end example
+
+Multivariate polynomials and rational functions may be expanded,
+collected and normalized (i.e. converted to a ratio of two coprime
+polynomials):
+
+@example
+> a = x^4 + 2*x^2*y^2 + 4*x^3*y + 12*x*y^3 - 3*y^4;
+-3*y^4+x^4+12*x*y^3+2*x^2*y^2+4*x^3*y
+> b = x^2 + 4*x*y - y^2;
+-y^2+x^2+4*x*y
+> expand(a*b);
+3*y^6+x^6-24*x*y^5+43*x^2*y^4+16*x^3*y^3+17*x^4*y^2+8*x^5*y
+> collect(a*b,x);
+3*y^6+48*x*y^4+2*x^2*y^2+x^4*(-y^2+x^2+4*x*y)+4*x^3*y*(-y^2+x^2+4*x*y)
+> normal(a/b);
+3*y^2+x^2
+@end example
+
+You can differentiate functions and expand them as Taylor or
+Laurent series (the third argument of series is the evaluation point,
+the fourth defines the order):
+
+@example
+> diff(tan(x),x);
+tan(x)^2+1
+> series(sin(x),x,0,4);
+x-1/6*x^3+Order(x^4)
+> series(1/tan(x),x,0,4);
+x^(-1)-1/3*x+Order(x^2)
+@end example
+
+If you ever wanted to convert units in C or C++ and found this
+is cumbersome, here is the solution. Symbolic types can always be
+used as tags for different types of objects. Converting from wrong
+units to the metric system is therefore easy:
+
+@example
+> in=.0254*m;
+0.0254*m
+> lb=.45359237*kg;
+0.45359237*kg
+> 200*lb/in^2;
+140613.91592783185568*kg*m^(-2)
+@end example
+
+
+@node Installation, Prerequisites, What it can do for you, Top
+@c node-name, next, previous, up
+@chapter Installation
+
+GiNaC's installation follows the spirit of most GNU software. It is
+easily installed on your system by three steps: configuration, build,
+installation.
+
+@menu
+* Prerequisites:: Packages upon which GiNaC depends.
+* Configuration:: How to configure GiNaC.
+* Building GiNaC:: How to compile GiNaC.
+* Installing GiNaC:: How to install GiNaC on your system.
+@end menu
+
+
+@node Prerequisites, Configuration, Installation, Installation
+@c node-name, next, previous, up
+@section Prerequisites
+
+In order to install GiNaC on your system, some prerequistes need
+to be met. First of all, you need to have a C++-compiler adhering to
+the ANSI-standard @cite{ISO/IEC 14882:1998(E)}. We used @acronym{GCC} for
+development so if you have a different compiler you are on your own.
+For the configuration to succeed you need a Posix compliant shell
+installed in @file{/bin/sh}, GNU @command{bash} is fine. Perl is needed
+by the built process as well, since some of the source files are automatically
+generated by Perl scripts. Last but not least, Bruno Haible's library
+@acronym{CLN} is extensively used and needs to be installed on your system.
+Please get it from @uref{ftp://ftp.santafe.edu/pub/gnu/} or from
+@uref{ftp://ftp.ilog.fr/pub/Users/haible/gnu/, Bruno Haible's FTP site}
+(it is covered by GPL) and install it prior to trying to install GiNaC.
+The configure script checks if it can find it and if it cannot
+it will refuse to continue.
+
+
+@node Configuration, Building GiNaC, Prerequisites, Installation
+@c node-name, next, previous, up
+@section Configuration
+
+To configure GiNaC means to prepare the source distribution for
+building. It is done via a shell script called @command{configure}
+that is shipped with the sources. (Actually, this script is by itself
+created with GNU Autoconf from the files @file{configure.in} and
+@file{aclocal.m4}.) Since a configure script generated by
+GNU Autoconf never prompts, all customization must be done either via
+command line parameters or environment variables. It accepts a list
+of parameters, the complete set of which can be listed by calling it
+with the @option{--help} option. The most important ones will be
+shortly described in what follows:
+
+@itemize @bullet
+
+@item
+@option{--disable-shared}: When given, this option switches off the
+build of a shared library, i.e. a @file{.so} file. This may be convenient
+when developing because it considerably speeds up compilation.
+
+@item
+@option{--prefix=@var{PREFIX}}: The directory where the compiled library
+and headers are installed. It defaults to @file{/usr/local} which means
+that the library is installed in the directory @file{/usr/local/lib},
+the header files in @file{/usr/local/include/GiNaC} and the documentation
+(like this one) into @file{/usr/local/share/doc/GiNaC}.
+
+@item
+@option{--libdir=@var{LIBDIR}}: Use this option in case you want to have
+the library installed in some other directory than
+@file{@var{PREFIX}/lib/}.
+
+@item
+@option{--includedir=@var{INCLUDEDIR}}: Use this option in case you want
+to have the header files installed in some other directory than
+@file{@var{PREFIX}/include/ginac/}. For instance, if you specify
+@option{--includedir=/usr/include} you will end up with the header files
+sitting in the directory @file{/usr/include/ginac/}. Note that the
+subdirectory @file{GiNaC} is enforced by this process in order to
+keep the header files separated from others. This avoids some
+clashes and allows for an easier deinstallation of GiNaC. This ought
+to be considered A Good Thing (tm).
+
+@item
+@option{--datadir=@var{DATADIR}}: This option may be given in case you
+want to have the documentation installed in some other directory than
+@file{@var{PREFIX}/share/doc/GiNaC/}.
+
+@end itemize
+
+In addition, you may specify some environment variables.
+@env{CXX} holds the path and the name of the C++ compiler
+in case you want to override the default in your path. (The
+@command{configure} script searches your path for @command{c++},
+@command{g++}, @command{gcc}, @command{CC}, @command{cxx}
+and @command{cc++} in that order.) It may be very useful to
+define some compiler flags with the @env{CXXFLAGS} environment
+variable, like optimization, debugging information and warning
+levels. If omitted, it defaults to @option{-g -O2}.
+
+The whole process is illustrated in the following two
+examples. (Substitute @command{setenv @var{VARIABLE} @var{value}} for
+@command{export @var{VARIABLE}=@var{value}} if the Berkeley C shell is
+your login shell.)
+
+@subheading Sample sessions of how to call the configure script
+
+Simple configuration for a site-wide GiNaC library assuming everything
+is in default paths:
+
+@example
+$ export CXXFLAGS="-Wall -O2"
+$ ./configure
+@end example
+
+Configuration for a private static GiNaC library with several components
+sitting in custom places (site-wide @acronym{GCC} and private @acronym{CLN}),
+the compiler pursueded to be picky and full assertions switched on:
+
+@example
+$ export CXX=/usr/local/gnu/bin/c++
+$ export CPPFLAGS="$(CPPFLAGS) -I$(HOME)/include"
+$ export CXXFLAGS="$(CXXFLAGS) -DDO_GINAC_ASSERT -ggdb -Wall -ansi -pedantic -O2"
+$ export LDFLAGS="$(LDFLAGS) -L$(HOME)/lib"
+$ ./configure --disable-shared --prefix=$(HOME)
+@end example
+
+
+@node Building GiNaC, Installing GiNaC, Configuration, Installation
+@c node-name, next, previous, up
+@section Building GiNaC
+
+After proper configuration you should just build the whole
+library by typing
+@example
+$ make
+@end example
+at the command prompt and go for a cup of coffee.
+
+Just to make sure GiNaC works properly you may run a simple test
+suite by typing
+@example
+$ make check
+@end example
+This will compile some sample programs, run them and compare the output
+to reference output. Each of the checks should return a message @samp{passed}
+together with the CPU time used for that particular test. If it does
+not, something went wrong. This is mostly intended to be a QA-check
+if something was broken during the development, but not a sanity check
+of your system. Another intent is to allow people to fiddle around
+with optimization. If @acronym{CLN} was installed all right
+this step is unlikely to return any errors.
+
+
+@node Installing GiNaC, Basic Concepts, Building GiNaC, Installation
+@c node-name, next, previous, up
+@section Installing GiNaC
+
+To install GiNaC on your system, simply type
+@example
+$ make install
+@end example
+
+As described in the section about configuration
+the files will be installed in the following directories (the
+directories will be created if they don't already exist):
+
+@itemize @bullet
+
+@item
+@file{libginac.a} will go into @file{@var{PREFIX}/lib/} (or
+@file{@var{LIBDIR}}) which defaults to @file{/usr/local/lib/}.
+So will @file{libginac.so} unless the configure script was
+given the option @option{--disable-shared}. The proper symlinks
+will be established as well.
+
+@item
+All the header files will be installed into @file{@var{PREFIX}/include/ginac/}
+(or @file{@var{INCLUDEDIR}/ginac/}, if specified).
+
+@item
+All documentation (HTML and Postscript) will be stuffed into
+@file{@var{PREFIX}/share/doc/GiNaC/} (or @file{@var{DATADIR}/doc/GiNaC/}, if
+specified).
+
+@end itemize
+
+Just for the record we will list some other useful make targets:
+@command{make clean} deletes all files generated by @command{make},
+i.e. all the object files. In addition @command{make distclean}
+removes all files generated by the configuration. And finally
+@command{make uninstall} removes the installed library and header
+files@footnote{Uninstallation does not work after you have called
+@command{make distclean} since the @file{Makefile} is itself generated
+by the configuration from @file{Makefile.in} and hence deleted by
+@command{make distclean}. There are two obvious ways out of this
+dilemma. First, you can run the configuration again with the same
+@var{PREFIX} thus creating a @file{Makefile} with a working
+@samp{uninstall} target. Second, you can do it by hand since you
+now know where all the files went during installation.}.
+
+@node Basic Concepts, Expressions, Installing GiNaC, Top
+@c node-name, next, previous, up
+@chapter Basic Concepts
+
+This chapter will describe the different fundamental objects
+that can be handled with GiNaC. But before doing so, it is worthwhile
+introducing you to the more commonly used class of expressions,
+representing a flexible meta-class for storing all mathematical
+objects.
+
+@menu
+* Expressions:: The fundamental GiNaC class.
+* The Class Hierarchy:: Overview of GiNaC's classes.
+* Symbols:: Symbolic objects.
+* Numbers:: Numerical objects.
+* Constants:: Pre-defined constants.
+* Fundamental operations:: The power, add and mul classes
+* Built-in functions:: Mathematical functions.
+@end menu
+
+
+@node Expressions, The Class Hierarchy, Basic Concepts, Basic Concepts
+@c node-name, next, previous, up
+@section Expressions
+
+The most common class of objects a user deals with is the
+expression @code{ex}, representing a mathematical object
+like a variable, number, function, sum, product, etc... Expressions
+may be put together to form new expressions, passed as arguments to
+functions, and so on. Here is a little collection of valid
+expressions:
+
+@subheading Examples of expressions
+@example
+ex MyEx1 = 5; // simple number
+ex MyEx2 = x + 2*y; // polynomial in x and y
+ex MyEx3 = (x + 1)/(x - 1); // rational expression
+ex MyEx4 = sin(x + 2*y) + 3*z + 41; // containing a function
+ex MyEx5 = MyEx4 + 1; // similar to above
+@end example
+
+Before describing the more fundamental objects that form the building
+blocks of expressions we'll have a quick look under the hood by
+describing how expressions are internally managed.
+
+@unnumberedsubsec Digression: Expressions are reference counted
+
+An expression is extremely light-weight since internally it
+works like a handle to the actual representation and really holds
+nothing more than a pointer to some other object. What this means in
+practice is that whenever you create two @code{ex} and set
+the second equal to the first no copying process is involved. Instead,
+the copying takes place as soon as you try to change the second.
+Consider the simple sequence of code:
+
+@subheading Simple copy-on-write semantics
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+int main()
+@{
+ symbol x("x"), y("y"), z("z");
+ ex e1, e2;
+
+ e1 = sin(x + 2*y) + 3*z + 41;
+ e2 = e1; // e2 points to same object as e1
+ cout << e2 << endl; // prints sin(x+2*y)+3*z+41
+ e2 += 1; // e2 is copied into a new object
+ cout << e2 << endl; // prints sin(x+2*y)+3*z+42
+ // ...
+@}
+@end example
+
+The line @code{e2 = e1;} creates a second expression pointing to the
+object held already by @code{e1}. The time involved for this operation
+is therefore constant, no matter how large @code{e1} was. Actual
+copying, however, must take place in the line @code{e2 += 1;} because
+@code{e1} and @code{e2} are not handles for the same object any more.
+This concept is called @dfn{copy-on-write semantics}. It increases
+performance considerably whenever one object occurs multiple times and
+represents a simple garbage collection scheme because when an @code{ex}
+runs out of scope its destructor checks whether other expressions handle
+the object it points to too and deletes the object from memory if that
+turns out not to be the case. A slightly less trivial example of
+differentiation using the chain-rule should make clear how powerful this
+can be.
+
+@subheading Advanced copy-on-write semantics
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+int main()
+@{
+ symbol x("x"), y("y");
+
+ ex e1 = x + 3*y;
+ ex e2 = pow(e1, 3);
+ ex e3 = diff(sin(e2), x); // first derivative of sin(e2) by x
+ cout << e1 << endl // prints x+3*y
+ << e2 << endl // prints (x+3*y)^3
+ << e3 << endl; // prints 3*(x+3*y)^2*cos((x+3*y)^3)
+ // ...
+@}
+@end example
+
+Here, @code{e1} will actually be referenced three times while @code{e2}
+will be referenced two times. When the power of an expression is built,
+that expression needs not be copied. Likewise, since the derivative of a
+power of an expression can be easily expressed in terms of that expression,
+no copying of @code{e1} is involved when @code{e3} is constructed. So,
+when @code{e3} is constructed it will print as
+@code{3*(x+3*y)^2*cos((x+3*y)^3)} but the argument of @code{cos()} only
+holds a reference to @code{e2} and the factor in front is just @code{3*e1^2}.
+
+As a user of GiNaC, you cannot see this mechanism of
+copy-on-write semantics. When you insert an expression into a second
+expression, the result behaves exactly as if the contents of the first
+expression were inserted. But it may be useful to remember that this
+is not what happens. Knowing this will enable you to write much more
+efficient code. If you still have an uncertain feeling with
+copy-on-write semantics, we recommend you have a look at the
+@uref{http://www.cerfnet.com/~mpcline/c++-faq-lite/, C++-FAQ lite} by
+Marshall Cline. Chapter 16 covers this issue and presents an
+implementation which is pretty close to the one in GiNaC.
+
+So much for expressions. But what exactly are these expressions
+handles of? This will be answered in the following sections.
+
+
+@node The Class Hierarchy, Symbols, Expressions, Basic Concepts
+@c node-name, next, previous, up
+@section The Class Hierarchy
+
+GiNaC's class hierarchy consists of several classes representing
+mathematical objects, all of which (except for @code{ex}
+and some helpers) are internally derived from one abstract base class
+called @code{basic}. You do not have to deal with objects
+of class @code{basic}, instead you'll be dealing with
+symbols and functions of symbols. You'll soon learn in this chapter
+how many of the functions on symbols are really classes. This is
+because simple symbolic arithmetic is not supported by languages like
+C++ so in a certain way GiNaC has to implement its own arithmetic.
+
+To give an idea about what kinds of symbolic composits may be
+built we have a look at the most important classes in the class
+hierarchy. The dashed line symbolizes a "points to" or "handles"
+relationship while the solid lines stand for "inherits from"
+relationships.
+
+@subheading The GiNaC class hierarchy
+@image{classhierarchy}
+
+Some of the classes shown here (the ones sitting in white boxes) are
+abstract base classes that are of no interest at all for the user.
+They are used internally in order to avoid code duplication if
+two or more classes derived from them share certain features. An
+example would be @code{expairseq}, which is a container
+for a sequence of pairs each consisting of one expression and a number
+(@code{numeric}). What @emph{is} visible to the user are the derived
+classes @code{add} and @code{mul}, representing sums of terms and products,
+respectively. We'll come back later to some more details about these
+two classes and motivate the use of pairs in sums and products here.
+
+@subsection Digression: Internal representation of products and sums
+
+Although it should be completely transparent for the user of
+GiNaC a short discussion of this topic helps to understand the sources
+and also explain performance to a large degree. Consider the symbolic
+expression @math{2*d^3*(4*a+5*b-3)} which could naively be represented
+by a tree of linear containers for addition and multiplication, one
+container for exponentiation with base and exponent and some atomic
+leaves of symbols and numbers in this fashion:
+
+@subheading Naive internal representation-tree for @math{2*d^3*(4*a+5*b-3)}
+@image{repnaive}
+
+However, doing so results in a rather deeply nested tree which will
+quickly become inefficient to manipulate. If we represent the sum
+instead as a sequence of terms, each having a purely numeric
+multiplicative coefficient and the multiplication as a sequence of
+terms, each having a numeric exponent, the tree becomes much more
+flat.
+
+@subheading Pair-wise internal representation-tree for @math{2*d^3*(4*a+5*b-3)}
+@image{reppair}
+
+The number @code{3} above the symbol @code{d} shows that @code{mul}
+objects are treated similarly where the coefficients are interpreted as
+@emph{exponents} now. Addition of sums of terms or multiplication of
+products with numerical exponents can be coded to be very efficient with
+such a pair-representation. Internally, this handling is done by many CAS in
+this way. It typically speeds up manipulations by an order of
+magnitude. The overall multiplicative factor @code{2} and
+the additive term @code{-3} look somewhat cumbersome in
+this representation, however, since they are still carrying a trivial
+exponent and multiplicative factor @code{1} respectively.
+Within GiNaC, this is avoided by adding a field that carries overall
+numeric coefficient.
+
+@subheading Realistic picture of GiNaC's representation-tree for @math{2*d^3*(4*a+5*b-3)}
+@image{repreal}
+
+This also allows for a better handling of numeric radicals, since
+@code{sqrt(2)} can now be carried along calculations. Now it should be
+clear, why both classes @code{add} and @code{mul} are derived from the
+same abstract class: the data representation is the same, only the
+semantics differs. In the class hierarchy, methods for polynomial
+expansion and such are reimplemented for @code{add} and @code{mul}, but
+the data structure is inherited from @code{expairseq}.
+
+
+@node Symbols, Numbers, The Class Hierarchy, Basic Concepts
+@c node-name, next, previous, up
+@section Symbols
+
+Symbols are for symbolic manipulation what atoms are for
+chemistry. You can declare objects of class @code{symbol}
+as any other object simply by saying @code{symbol x,y;}.
+There is, however, a catch in here having to do with the fact that C++
+is a compiled language. The information about the symbol's name is
+thrown away by the compiler but at a later stage you may want to print
+expressions holding your symbols. In order to avoid confusion GiNaC's
+symbols are able to know their own name. This is accomplished by
+declaring its name for output at construction time in the fashion
+@code{symbol x("x");}. If you declare a symbol using the
+default constructor (i.e. without string argument) the system will
+deal out a unique name. That name may not be suitable for printing
+but for internal routines when no output is desired it is often
+enough. We'll come across examples of such symbols later in this
+tutorial.
+
+This implies that the stings passed to symbols at construction
+time may not be used for comparing two of them. It is perfectly
+legitimate to write @code{symbol x("x"),y("x");} but it is
+likely to lead into trouble. Here, @code{x} and
+@code{y} are different symbols and statements like
+@code{x-y} will not be simplified to zero although the
+output @code{x-x} looks funny. Such output may also occur
+when there are two different symbols in two scopes, for instance when
+you call a function that declares a symbol with a name already
+existent in a symbol in the calling function. Again, comparing them
+(using @code{operator==} for instance) will always reveal
+their difference. Watch out, please.
+
+Although symbols can be assigned expressions for internal
+reasons, you should not do it (and we are not going to tell you how it
+is done). If you want to replace a symbol with something else in an
+expression, you can use the expression's @code{.subs()}
+method.
+
+
+@node Numbers, Constants, Symbols, Basic Concepts
+@c node-name, next, previous, up
+@section Numbers
+
+For storing numerical things, GiNaC uses Bruno Haible's library
+@acronym{CLN}. The classes therein serve as foundation
+classes for GiNaC. @acronym{CLN} stands for Class Library
+for Numbers or alternatively for Common Lisp Numbers. In order to
+find out more about @acronym{CLN}'s internals the reader is
+refered to the documentation of that library. Suffice to say that it
+is by itself build on top of another library, the GNU Multiple
+Precision library @acronym{GMP}, which is an extremely fast
+library for arbitrary long integers and rationals as well as arbitrary
+precision floating point numbers. It is very commonly used by several
+popular cryptographic applications. @acronym{CLN} extends
+@acronym{GMP} by several useful things: First, it introduces
+the complex number field over either reals (i.e. floating point
+numbers with arbitrary precision) or rationals. Second, it
+automatically converts rationals to integers if the denominator is
+unity and complex numbers to real numbers if the imaginary part
+vanishes and also correctly treats algebraic functions. Third it
+provides good implementations of state-of-the-art algorithms for all
+trigonometric and hyperbolic functions as well as for calculation of
+some useful constants.
+
+The user can construct an object of class @code{numeric} in several ways.
+The following example shows the four most important constructors: construction
+from C-integer, construction of fractions from two integers, construction
+from C-float and construction from a string.
+
+@subheading Construction of numbers
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+int main()
+@{
+ numeric two(2); // exact integer 2
+ numeric r(2,3); // exact fraction 2/3
+ numeric e(2.71828); // floating point number
+ numeric p("3.1415926535897932385"); // floating point number
+
+ cout << two*p << endl; // floating point 6.283...
+ // ...
+@}
+@end example
+
+Note that all those constructors are @emph{explicit} which means you are
+not allowed to write @code{numeric two=2;}. This is because the basic
+objects to be handled by GiNaC are the expressions @code{ex} and we want
+to keep things simple and wish objects like @code{pow(x,2)} to be
+handled the same way as @code{pow(x,a)}, which means that we need to allow
+a general @code{ex} as base and exponent. Therefore there is an implicit
+constructor from C-integers directly to expressions handling numerics at
+work in most of our examples. This design really becomes convenient when
+one declares own functions having more than one parameter but it forbids
+using implicit constructors because that would lead to ambiguities.
+
+It may be tempting to construct numbers writing @code{numeric r(3/2)}.
+This would, however, call C's built-in operator @code{/} for integers
+first and result in a numeric holding a plain integer 1. @strong{Never use
+@code{/} on integers!} Use the constructor from two integers instead, as
+shown in the example above. Writing @code{numeric(1)/2} may look funny but
+works also.
+
+We have seen now the distinction between exact numbers and
+floating point numbers. Clearly, the user should never have to worry
+about dynamically created exact numbers, since their "exactness"
+always determines how they ought to be handled. The situation is
+different for floating point numbers. Their accuracy is handled by
+one @emph{global} variable, called @code{Digits}. (For those readers
+who know about Maple: it behaves very much like Maple's @code{Digits}).
+All objects of class numeric that are constructed from then on will be
+stored with a precision matching that number of decimal digits:
+
+@subheading Controlling the precision of floating point numbers
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+void foo()
+@{
+ numeric three(3.0), one(1.0);
+ numeric x = one/three;
+
+ cout << "in " << Digits << " digits:" << endl;
+ cout << x << endl;
+ cout << Pi.evalf() << endl;
+@}
+
+int main()
+@{
+ foo();
+ Digits = 60;
+ foo();
+ return 0;
+@}
+@end example
+
+The above example prints the following output to screen:
+
+@example
+in 17 digits:
+0.333333333333333333
+3.14159265358979324
+in 60 digits:
+0.333333333333333333333333333333333333333333333333333333333333333333
+3.14159265358979323846264338327950288419716939937510582097494459231
+@end example
+
+It should be clear that objects of class @code{numeric} should be used
+for constructing numbers or for doing arithmetic with them. The objects
+one deals with most of the time are the polymorphic expressions @code{ex}.
+
+@subsection Tests on numbers
+
+Once you have declared some numbers, assigned them to
+expressions and done some arithmetic with them it is frequently
+desired to retrieve some kind of information from them like asking
+whether that number is integer, rational, real or complex. For those
+cases GiNaC provides several useful methods. (Internally, they fall
+back to invocations of certain CLN functions.)
+
+As an example, let's construct some rational number, multiply it
+with some multiple of its denominator and check what comes out:
+
+@subheading Sample test on objects of type numeric
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+// some very important constants:
+const numeric twentyone(21);
+const numeric ten(10);
+const numeric fife(5);
+
+int main()
+@{
+ numeric answer = twentyone;
+
+ answer /= five;
+ cout << answer.is_integer() << endl; // false, it's 21/5
+ answer *= ten;
+ cout << answer.is_integer() << endl; // true, it's 42 now!
+ // ...
+@}
+@end example
+
+Note that the variable @code{answer} is constructed here
+as an integer by @code{numeric}'s copy constructor but in
+an intermediate step it holds a rational number represented as integer
+numerator and integer denominator. When multiplied by 10, the
+denominator becomes unity and the result is automatically converted to
+a pure integer again. Internally, the underlying
+@acronym{CLN} is responsible for this behaviour and we refer
+the reader to @acronym{CLN}'s documentation. Suffice to say
+that the same behaviour applies to complex numbers as well as return
+values of certain functions. Complex numbers are automatically
+converted to real numbers if the imaginary part becomes zero. The
+full set of tests that can be applied is listed in the following
+table.
+
+@cartouche
+@multitable @columnfractions .33 .66
+@item Method @tab Returns true if@dots{}
+@item @code{.is_zero()}
+@tab object is equal to zero
+@item @code{.is_positive()}
+@tab object is not complex and greater than 0
+@item @code{.is_integer()}
+@tab object is a (non-complex) integer
+@item @code{.is_pos_integer()}
+@tab object is an integer and greater than 0
+@item @code{.is_nonneg_integer()}
+@tab object is an integer and greater equal 0
+@item @code{.is_even()}
+@tab object is an even integer
+@item @code{.is_odd()}
+@tab object is an odd integer
+@item @code{.is_prime()}
+@tab object is a prime integer (probabilistic primality test)
+@item @code{.is_rational()}
+@tab object is an exact rational number (integers are rational, too, as are complex extensions like @math{2/3+7/2*I})
+@item @code{.is_real()}
+@tab object is a real integer, rational or float (i.e. is not complex)
+@end multitable
+@end cartouche
+
+
+@node Constants, Fundamental operations, Numbers, Basic Concepts
+@c node-name, next, previous, up
+@section Constants
+
+Constants behave pretty much like symbols except that that they return
+some specific number when the method @code{.evalf()} is called.
+
+The predefined known constants are:
+
+@cartouche
+@multitable @columnfractions .14 .29 .57
+@item Name @tab Common Name @tab Numerical Value (35 digits)
+@item @code{Pi}
+@tab Archimedes' constant
+@tab 3.14159265358979323846264338327950288
+@item @code{Catalan}
+@tab Catalan's constant
+@tab 0.91596559417721901505460351493238411
+@item @code{EulerGamma}
+@tab Euler's (or Euler-Mascheroni) constant
+@tab 0.57721566490153286060651209008240243
+@end multitable
+@end cartouche
+
+
+@node Fundamental operations, Built-in functions, Constants, Basic Concepts
+@c node-name, next, previous, up
+@section Fundamental operations: the @code{power}, @code{add} and @code{mul} classes
+
+Simple polynomial expressions are written down in GiNaC pretty
+much like in other CAS. The necessary operators @code{+}, @code{-},
+@code{*} and @code{/} have been overloaded to achieve this goal.
+When you run the following program, the constructor for an object of
+type @code{mul} is automatically called to hold the product of @code{a}
+and @code{b} and then the constructor for an object of type @code{add}
+is called to hold the sum of that @code{mul} object and the number one:
+
+@subheading Construction of @code{add} and @code{mul} objects
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+int main()
+@{
+ symbol a("a"), b("b");
+ ex MyTerm = 1+a*b;
+ // ...
+@}
+@end example
+
+For exponentiation, you have already seen the somewhat clumsy (though C-ish)
+statement @code{pow(x,2);} to represent @code{x} squared. This direct
+construction is necessary since we cannot safely overload the constructor
+@code{^} in C++ to construct a @code{power} object. If we did, it would
+have several counterintuitive effects:
+
+@itemize
+@item
+Due to C's operator precedence, @code{2*x^2} would be parsed as @code{(2*x)^2}.
+@item
+Due to the binding of the operator @code{^}, @code{x^a^b} would result in
+@code{(x^a)^b}. This would be confusing since most (though not all) other CAS
+interpret this as @code{x^(a^b)}.
+@item
+Also, expressions involving integer exponents are very frequently used,
+which makes it even more dangerous to overload @code{^} since it is then
+hard to distinguish between the semantics as exponentiation and the one
+for exclusive or. (It would be embarassing to return @code{1} where one
+has requested @code{2^3}.)
+@end itemize
+
+All effects are contrary to mathematical notation and differ from the
+way most other CAS handle exponentiation, therefore overloading
+@code{^} is ruled out for GiNaC's C++ part. The situation
+is different in @command{ginsh}, there the exponentiation-@code{^}
+exists. (Also note, that the other frequently used exponentiation operator
+@code{**} does not exist at all in C++).
+
+To be somewhat more precise, objects of the three classes
+described here, are all containers for other expressions. An object
+of class @code{power} is best viewed as a container with
+two slots, one for the basis, one for the exponent. All valid GiNaC
+expressions can be inserted. However, basic transformations like
+simplifying @code{pow(pow(x,2),3)} to @code{x^6} automatically are only
+performed when this is mathematically possible. If we replace the
+outer exponent three in the example by some symbols @code{a}, the
+simplification is not safe and will not be performed, since @code{a}
+might be @code{1/2} and @code{x} negative.
+
+Objects of type @code{add} and @code{mul} are containers with an arbitrary
+number of slots for expressions to be inserted. Again, simple and safe
+simplifications are carried out like transforming @code{3*x+4-x} to
+@code{2*x+4}.
+
+The general rule is that when you construct such objects, GiNaC
+automatically creates them in canonical form, which might differ from
+the form you typed in your program. This allows for rapid comparison
+of expressions, since after all @code{a-a} is simply zero.
+Note, that the canonical form is not necessarily lexicographical
+ordering or in any way easily guessable. It is only guaranteed that
+constructing the same expression twice, either implicitly or
+explicitly, results in the same canonical form.
+
+
+@node Built-in functions, Important Algorithms, Fundamental operations, Basic Concepts
+@c node-name, next, previous, up
+@section Built-in functions
+
+There are quite a number of useful functions built into GiNaC.
+They are all objects of class @code{function}. They
+accept one or more expressions as arguments and return one expression.
+If the arguments are not numerical, the evaluation of the functions
+may be halted, as it does in the next example:
+
+@subheading Evaluation of built-in functions
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+int main()
+@{
+ symbol x("x"), y("y");
+
+ ex foo = x+y/2;
+ cout << "gamma(" << foo << ") -> " << gamma(foo) << endl;
+ ex bar = foo.subs(y==1);
+ cout << "gamma(" << bar << ") -> " << gamma(bar) << endl;
+ ex foobar= bar.subs(x==7);
+ cout << "gamma(" << foobar << ") -> " << gamma(foobar) << endl;
+ // ...
+@}
+@end example
+
+This program will type out two times a function and then an
+expression that may be really useful:
+
+@example
+gamma(x+(1/2)*y) -> gamma(x+(1/2)*y)
+gamma(x+1/2) -> gamma(x+1/2)
+gamma(15/2) -> (135135/128)*Pi^(1/2)
+@end example
+
+Most of these functions can be differentiated, series expanded so on.
+Read the next chapter in order to learn more about this..
+
+
+@node Important Algorithms, Polynomial Expansion, Built-in functions, Top
+@c node-name, next, previous, up
+@chapter Important Algorithms
+
+In this chapter the most important algorithms provided by GiNaC
+will be described. Some of them are implemented as functions on
+expressions, others are implemented as methods provided by expression
+objects. If they are methods, there exists a wrapper function around
+it, so you can alternatively call it in a functional way as shown in
+the simple example:
+
+@subheading Methods vs. wrapper functions
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+int main()
+@{
+ ex x = numeric(1.0);
+
+ cout << "As method: " << sin(x).evalf() << endl;
+ cout << "As function: " << evalf(sin(x)) << endl;
+ // ...
+@}
+@end example
+
+The general rule is that wherever methods accept one or more
+parameters (@var{arg1}, @var{arg2}, @dots{}) the order of arguments
+the function wrapper accepts is the same but preceded by the object
+to act on (@var{object}, @var{arg1}, @var{arg2}, @dots{}). This
+approach is the most natural one in an OO model but it may lead to
+confusion for MapleV users because where they would type
+@code{A:=x+1; subs(x=2,A);} GiNaC would require
+@code{A=x+1; subs(A,x==2);} (after proper declaration of @code{A}
+and @code{x}). On the other hand, since MapleV returns 3 on
+@code{A:=x^2+3; coeff(A,x,0);} (GiNaC:
+@code{A=pow(x,2)+3; coeff(A,x,0);}) it is clear that
+MapleV is not trying to be consistent here. Also, users of MuPAD will
+in most cases feel more comfortable with GiNaC's convention. All
+function wrappers are always implemented as simple inline functions
+which just call the corresponding method and are only provided for
+users uncomfortable with OO who are dead set to avoid method
+invocations. Generally, a chain of function wrappers is much harder
+to read than a chain of methods and should therefore be avoided if
+possible. On the other hand, not everything in GiNaC is a method on
+class @code{ex} and sometimes calling a function cannot be
+avoided.
+
+@menu
+* Polynomial Expansion::
+* Collecting expressions::
+* Polynomial Arithmetic::
+* Symbolic Differentiation::
+* Series Expansion::
+@end menu
+
+
+@node Polynomial Expansion, Collecting expressions, Important Algorithms, Important Algorithms
+@c node-name, next, previous, up
+@section Polynomial Expansion
+
+A polynomial in one or more variables has many equivalent
+representations. Some useful ones serve a specific purpose. Consider
+for example the trivariate polynomial @math{4*x*y + x*z + 20*y^2 + 21*y*z + 4*z^2}.
+It is equivalent to the factorized polynomial @math{(x + 5*y + 4*z)*(4*y + z)}.
+Other representations are the recursive ones where one collects for
+exponents in one of the three variable. Since the factors are
+themselves polynomials in the remaining two variables the procedure
+can be repeated. In our expample, two possibilies would be
+@math{(4*y + z)*x + 20*y^2 + 21*y*z + 4*z^2} and
+@math{20*y^2 + (21*z + 4*x)*y + 4*z^2 + x*z}.
+
+To bring an expression into expanded form, its method
+@code{.expand()} may be called. In our example above,
+this corresponds to @math{4*x*y + x*z + 20*y^2 + 21*y*z + 4*z^2}.
+Again, since the canonical form in GiNaC is not easily guessable you
+should be prepared to see different orderings of terms in such sums!
+
+
+@node Collecting expressions, Polynomial Arithmetic, Polynomial Expansion, Important Algorithms
+@c node-name, next, previous, up
+@section Collecting expressions
+
+Another useful representation of multivariate polynomials is as
+a univariate polynomial in one of the variables with the coefficients
+being polynomials in the remaining variables. The method
+@code{collect()} accomplishes this task:
+
+@example
+#include <ginac/ginac.h>
+ex ex::collect(symbol const & s);
+@end example
+
+Note that the original polynomial needs to be in expanded form in
+order to be able to find the coefficients properly. The range of
+occuring coefficients can be checked using the two methods
+
+@example
+#include <ginac/ginac.h>
+int ex::degree(symbol const & s);
+int ex::ldegree(symbol const & s);
+@end example
+
+where @code{degree()} returns the highest coefficient and
+@code{ldegree()} the lowest one. These two methods work
+also reliably on non-expanded input polynomials. This is illustrated
+in the following example:
+
+@subheading Collecting expressions in multivariate polynomials
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+int main()
+@{
+ symbol x("x"), y("y");
+ ex PolyInp = 4*pow(x,3)*y + 5*x*pow(y,2) + 3*y
+ - pow(x+y,2) + 2*pow(y+2,2) - 8;
+ ex Poly = PolyInp.expand();
+
+ for (int i=Poly.ldegree(x); i<=Poly.degree(x); ++i) @{
+ cout << "The x^" << i << "-coefficient is "
+ << Poly.coeff(x,i) << endl;
+ @}
+ cout << "As polynomial in y: "
+ << Poly.collect(y) << endl;
+ // ...
+@}
+@end example
+
+When run, it returns an output in the following fashion:
+
+@example
+The x^0-coefficient is y^2+11*y
+The x^1-coefficient is 5*y^2-2*y
+The x^2-coefficient is -1
+The x^3-coefficient is 4*y
+As polynomial in y: -x^2+(5*x+1)*y^2+(-2*x+4*x^3+11)*y
+@end example
+
+As always, the exact output may vary between different versions of
+GiNaC or even from run to run since the internal canonical ordering is
+not within the user's sphere of influence.
+
+
+@node Polynomial Arithmetic, Symbolic Differentiation, Collecting expressions, Important Algorithms
+@c node-name, next, previous, up
+@section Polynomial Arithmetic
+
+@subsection GCD and LCM
+
+The functions for polynomial greatest common divisor and least common
+multiple have the synopsis:
+
+@example
+#include <GiNaC/normal.h>
+ex gcd(const ex & a, const ex & b);
+ex lcm(const ex & a, const ex & b);
+@end example
+
+The functions @code{gcd()} and @code{lcm()} accept two expressions
+@code{a} and @code{b} as arguments and return
+a new expression, their greatest common divisor or least common
+multiple, respectively. If the polynomials @code{a} and
+@code{b} are coprime @code{gcd(a,b)} returns 1 and @code{lcm(a,b)}
+returns the product of @code{a} and @code{b}.
+
+@subheading Polynomal GCD/LCM
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+int main()
+@{
+ symbol x("x"), y("y"), z("z");
+ ex P_a = 4*x*y + x*z + 20*pow(y, 2) + 21*y*z + 4*pow(z, 2);
+ ex P_b = x*y + 3*x*z + 5*pow(y, 2) + 19*y*z + 12*pow(z, 2);
+
+ ex P_gcd = gcd(P_a, P_b);
+ // x + 5*y + 4*z
+ ex P_lcm = lcm(P_a, P_b);
+ // 4*x*y^2 + 13*y*x*z + 20*y^3 + 81*y^2*z + 67*y*z^2 + 3*x*z^2 + 12*z^3
+ // ...
+@}
+@end example
+
+@subsection The @code{normal} method
+
+While in common symbolic code @code{gcd()} and @code{lcm()} are not too
+heavily used, simplification occurs frequently. Therefore @code{.normal()},
+which provides some basic form of simplification, has become a method of
+class @code{ex}, just like @code{.expand()}.
+It converts a rational function into an equivalent rational function
+where numererator and denominator are coprime. This means, it finds
+the GCD of numerator and denominator and cancels it. If it encounters
+some object which does not belong to the domain of rationals (a
+function for instance), that object is replaced by a temporary symbol.
+This means that both expressions @code{t1} and
+@code{t2} are indeed simplified in this little program:
+
+@subheading Cancellation of polynomial GCD (with obstacles)
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+int main()
+@{
+ symbol x("x");
+ ex t1 = (pow(x,2) + 2*x + 1)/(x + 1);
+ ex t2 = (pow(sin(x),2) + 2*sin(x) + 1)/(sin(x) + 1);
+ cout << "t1 is " << t1.normal() << endl;
+ cout << "t2 is " << t2.normal() << endl;
+ // ...
+@}
+@end example
+
+Of course this works for multivariate polynomials too, so the ratio of
+the sample-polynomials from the section about GCD and LCM above would
+be normalized to @code{P_a/P_b} = @code{(4*y+z)/(y+3*z)}.
+
+
+@node Symbolic Differentiation, Series Expansion, Polynomial Arithmetic, Important Algorithms
+@c node-name, next, previous, up
+@section Symbolic Differentiation
+
+GiNaC's objects know how to differentiate themselves. Thus, a
+polynomial (class @code{add}) knows that its derivative is
+the sum of the derivatives of all the monomials:
+
+@subheading Simple polynomial differentiation
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+int main()
+@{
+ symbol x("x"), y("y"), z("z");
+ ex P = pow(x, 5) + pow(x, 2) + y;
+
+ cout << P.diff(x,2) << endl; // 20*x^3 + 2
+ cout << P.diff(y) << endl; // 1
+ cout << P.diff(z) << endl; // 0
+ // ...
+@}
+@end example
+
+If a second integer parameter @var{n} is given, the @code{diff} method
+returns the @var{n}th derivative.
+
+If @emph{every} object and every function is told
+what its derivative is, all derivatives of composed objects can be
+calculated using the chain rule and the product rule. Consider, for
+instance the expression @code{1/cosh(x)}. Since the
+derivative of @code{cosh(x)} is @code{sinh(x)}
+and the derivative of @code{pow(x,-1)} is
+@code{-pow(x,-2)}, GiNaC can readily compute the
+composition. It turns out that the composition is the generating
+function for Euler Numbers, i.e. the so called
+@var{n}th Euler number is the coefficient of @code{x^n/n!} in
+the expansion of @code{1/cosh(x)}. We may use this identity to code a
+function that generates Euler numbers in just three lines:
+
+@subheading Differentiation with nontrivial functions: Euler numbers
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+ex EulerNumber(unsigned n)
+@{
+ symbol x;
+ ex generator = pow(cosh(x),-1);
+ return generator.diff(x,n).subs(x==0);
+@}
+
+int main()
+@{
+ for (unsigned i=0; i<11; i+=2)
+ cout << EulerNumber(i) << endl;
+ return 0;
+@}
+@end example
+
+When you run it, it produces the sequence @code{1}, @code{-1}, @code{5},
+@code{-61}, @code{1385}, @code{-50521}. We increment the loop variable
+@code{i} by two since all odd Euler numbers vanish anyways.
+
+
+@node Series Expansion, Extending GiNaC, Symbolic Differentiation, Important Algorithms
+@c node-name, next, previous, up
+@section Series Expansion
+
+Expressions know how to expand themselves as a Taylor series or
+(more generally) a Laurent series. As in most conventional Computer
+Algebra Systems no distinction is made between those two. There is a
+class of its own for storing such series as well as a class for
+storing the order of the series. A sample program could read:
+
+@subheading Series expansion
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+int main()
+@{
+ symbol x("x");
+ numeric point(0);
+ ex MyExpr1 = sin(x);
+ ex MyExpr2 = 1/(x - pow(x, 2) - pow(x, 3));
+ ex MyTailor, MySeries;
+
+ MyTailor = MyExpr1.series(x, point, 5);
+ cout << MyExpr1 << " == " << MyTailor
+ << " for small " << x << endl;
+ MySeries = MyExpr2.series(x, point, 7);
+ cout << MyExpr2 << " == " << MySeries
+ << " for small " << x << endl;
+ // ...
+@}
+@end example
+
+As an instructive application, let us calculate the numerical
+value of Archimedes' constant (for which there already exists the
+built-in constant @code{Pi}) using M@'echain's
+mysterious formula @code{Pi==16*atan(1/5)-4*atan(1/239)}.
+We may expand the arcus tangent around @code{0} and insert
+the fractions @code{1/5} and @code{1/239}.
+But, as we have seen, a series in GiNaC carries an order term with it.
+The function @code{series_to_poly()} may be used to strip
+this off:
+
+@subheading Series expansion using M@'echain's formula for @code{Pi}
+@example
+#include <ginac/ginac.h>
+using namespace GiNaC;
+
+ex mechain_pi(int degr)
+@{
+ symbol x;
+ ex pi_expansion = series_to_poly(atan(x).series(x,0,degr));
+ ex pi_approx = 16*pi_expansion.subs(x==numeric(1,5))
+ -4*pi_expansion.subs(x==numeric(1,239));
+ return pi_approx;
+@}
+
+int main()
+@{
+ ex pi_frac;
+ for (int i=2; i<12; i+=2) @{
+ pi_frac = mechain_pi(i);
+ cout << i << ":\t" << pi_frac << endl
+ << "\t" << pi_frac.evalf() << endl;
+ @}
+ return 0;
+@}
+@end example
+
+When you run this program, it will type out:
+
+@example
+2: 3804/1195
+ 3.1832635983263598326
+4: 5359397032/1706489875
+ 3.1405970293260603143
+6: 38279241713339684/12184551018734375
+ 3.141621029325034425
+8: 76528487109180192540976/24359780855939418203125
+ 3.141591772182177295
+10: 327853873402258685803048818236/104359128170408663038552734375
+ 3.1415926824043995174
+@end example
+
+
+@node Extending GiNaC, What does not belong into GiNaC, Series Expansion, Top
+@c node-name, next, previous, up
+@chapter Extending GiNaC
+
+By reading so far you should have gotten a fairly good
+understanding of GiNaC's design-patterns. From here on you should
+start reading the sources. All we can do now is issue some
+recommendations how to tackle GiNaC's many loose ends in order to
+fulfill everybody's dreams.
+
+@menu
+* What does not belong into GiNaC:: What to avoid.
+* Symbolic functions:: Implementing symbolic functions.
+@end menu
+
+
+@node What does not belong into GiNaC, Symbolic functions, Extending GiNaC, Extending GiNaC
+@c node-name, next, previous, up
+@section What doesn't belong into GiNaC
+
+First of all, GiNaC's name must be read literally. It is
+designed to be a library for use within C++. The tiny
+@command{ginsh} accompanying GiNaC makes this even more
+clear: it doesn't even attempt to provide a language. There are no
+loops or conditional expressions in @command{ginsh}, it is
+merely a window into the library for the programmer to test stuff (or
+to show off). Still, the design of a complete CAS with a language of
+its own, graphical capabilites and all this on top of GiNaC is
+possible and is without doubt a nice project for the future.
+
+There are many built-in functions in GiNaC that do not know how
+to evaluate themselves numerically to a precision declared at runtime
+(using @code{Digits}). Some may be evaluated at certain
+points, but not generally. This ought to be fixed. However, doing
+numerical computations with GiNaC's quite abstract classes is doomed
+to be inefficient. For this purpose, the underlying bignum-package
+@acronym{CLN} is much better suited.
+
+
+@node Symbolic functions, A Comparison With Other CAS, What does not belong into GiNaC, Extending GiNaC
+@c node-name, next, previous, up
+@section Symbolic functions
+
+The easiest and most instructive way to start with is probably
+to implement your own function. Objects of class
+@code{function} are inserted into the system via a kind of
+"registry". They get a serial number that is used internally to
+identify them but you usually need not worry about this. What you
+have to care for are functions that are called when the user invokes
+certain methods. These are usual C++-functions accepting a number of
+@code{ex} as arguments and returning one
+@code{ex}. As an example, if we have a look at a
+simplified implementation of the cosine trigonometric function, we
+first need a function that is called when one wishes to
+@code{eval} it. It could look something like this:
+
+@example
+static ex cos_eval_method(ex const & x)
+@{
+ // if x%2*Pi return 1
+ // if x%Pi return -1
+ // if x%Pi/2 return 0
+ // care for other cases...
+ return cos(x).hold();
+@}
+@end example
+
+The last line returns @code{cos(x)} if we don't know what
+else to do and stops a potential recursive evaluation by saying
+@code{.hold()}. We should also implement a method for
+numerical evaluation and since we are lazy we sweep the problem under
+the rug by calling someone else's function that does so, in this case
+the one in class @code{numeric}:
+
+@example
+static ex cos_evalf_method(ex const & x)
+@{
+ return sin(ex_to_numeric(x));
+@}
+@end example
+
+Differentiation will surely turn up and so we need to tell
+@code{sin} how to differentiate itself:
+
+@example
+static ex cos_diff_method(ex const & x, unsigned diff_param)
+@{
+ return cos(x);
+@}
+@end example
+
+The second parameter is obligatory but uninteresting at this point.
+It is used for correct handling of the product rule only. For Taylor
+expansion, it is enough to know how to differentiate. But if the
+function you want to implement does have a pole somewhere in the
+complex plane, you need to write another method for Laurent expansion
+around that point.
+
+Now that everything has been written for @code{cos},
+we need to tell the system about it. This is done by a macro and we
+are not going to descibe how it expands, please consult your
+preprocessor if you are curious:
+
+@example
+REGISTER_FUNCTION(cos, cos_eval_method, cos_evalf_method, cos_diff, NULL);
+@end example
+
+The first argument is the function's name, the second, third and
+fourth bind the corresponding methods to this objects and the fifth is
+a slot for inserting a method for series expansion. Also, the new
+function needs to be declared somewhere. This may also be done by a
+convenient preprocessor macro:
+
+@example
+DECLARE_FUNCTION_1P(cos)
+@end example
+
+The suffix @code{_1P} stands for @emph{one parameter}. Of course, this
+implementation of @code{cos} is very incomplete and lacks several safety
+mechanisms. Please, have a look at the real implementation in GiNaC.
+(By the way: in case you are worrying about all the macros above we
+can assure you that functions are GiNaC's most macro-intense classes.
+We have done our best to avoid them where we can.)
+
+That's it. May the source be with you!
+
+
+@node A Comparison With Other CAS, Bibliography, Symbolic functions, Top
+@c node-name, next, previous, up
+@chapter A Comparison With Other CAS
+
+This chapter will give you some information on how GiNaC
+compares to other, traditional Computer Algebra Systems, like
+@emph{Maple}, @emph{Mathematica} or @emph{Reduce}, where it has
+advantages and disadvantages over these systems.
+
+
+@heading Advantages
+
+GiNaC has several advantages over traditional Computer
+Algebra Systems, like
+
+@itemize
+
+@item
+familiar language: all common CAS implement their own
+proprietary grammar which you have to learn first (and maybe learn
+again when your vendor chooses to "enhance" it). With GiNaC you
+can write your program in common C++, which is standardized.
+
+@item
+structured data types: you can build up structured data
+types using @code{struct}s or @code{class}es
+together with STL features instead of using unnamed lists of lists
+of lists.
+
+@item
+strongly typed: in CAS, you usually have only one kind of
+variables which can hold contents of an arbitrary type. This
+4GL like feature is nice for novice programmers, but dangerous.
+
+@item
+development tools: powerful development tools exist for
+C++, like fancy editors (e.g. with automatic
+indentation and syntax highlighting), debuggers, visualization
+tools, documentation tools...
+
+@item
+modularization: C++ programs can
+easily be split into modules by separating interface and
+implementation.
+
+@item
+price: GiNaC is distributed under the GNU Public License
+which means that it is free and available with source code. And
+there are excellent C++-compilers for free, too.
+
+@item
+extendable: you can add your own classes to GiNaC, thus
+extending it on a very low level. Compare this to a traditional
+CAS that you can usually only extend on a high level by writing in
+the language defined by the parser. In particular, it turns out
+to be almost impossible to fix bugs in a traditional system.
+
+@item
+seemless integration: it is somewhere between difficult
+and impossible to call CAS functions from within a program
+written in C++ or any other programming
+language and vice versa. With GiNaC, your symbolic routines
+are part of your program. You can easily call third party
+libraries, e.g. for numerical evaluation or graphical
+interaction. All other approaches are much more cumbersome: they
+range from simply ignoring the problem (i.e. @emph{Maple}) to providing a
+method for "embedding" the system (i.e. @emph{Yacas}).
+
+@item
+efficiency: often large parts of a program do not need
+symbolic calculations at all. Why use large integers for loop
+variables or arbitrary precision arithmetics where double
+accuracy is sufficient? For pure symbolic applications,
+GiNaC is comparable in speed with other CAS.
+
+@end itemize
+
+
+@heading Disadvantages
+
+Of course it also has some disadvantages
+
+@itemize
+
+@item
+not interactive: GiNaC programs have to be written in
+an editor, compiled and executed. You cannot play with
+expressions interactively. However, such an extension is not
+inherently forbidden by design. In fact, two interactive
+interfaces are possible: First, a simple shell that exposes GiNaC's
+types to a command line can readily be written (and has been
+written) and second, as a more consistent approach we plan
+an integration with the @acronym{CINT} C++ interpreter.
+
+@item
+advanced features: GiNaC cannot compete with a program
+like @emph{Reduce} which exists for more than
+30 years now or @emph{Maple} which grows since
+1981 by the work of dozens of programmers, with respect to
+mathematical features. Integration, factorization, non-trivial
+simplifications, limits etc. are missing in GiNaC (and are not
+planned for the near future).
+
+@item
+portability: While the GiNaC library itself is designed
+to avoid any platform dependent features (it should compile
+on any ANSI compliant C++ compiler), the
+currently used version of the CLN library (fast large integer and
+arbitrary precision arithmetics) can be compiled only on systems
+with a recently new C++ compiler from the
+GNU Compiler Collection (@acronym{GCC}). GiNaC uses
+recent language features like explicit constructors, mutable
+members, RTTI, @code{dynamic_cast}s and STL, so ANSI compliance is meant
+literally. Recent @acronym{GCC} versions starting at
+2.95, although itself not yet ANSI compliant, support all needed
+features.
+
+@end itemize
+
+
+@heading Why C++?
+
+Why did we choose to implement GiNaC in C++ instead of Java or any other
+language? C++ is not perfect: type checking is not strict
+(casting is possible), separation between interface and implementation
+is not complete, object oriented design is not enforced. The main
+reason is the often scolded feature of operator overloading in
+C++. While it may be true that operating on classes
+with a @code{+} operator is rarely meaningful, it is
+perfectly suited for algebraic expressions. Writing @math{3x+5y} as
+@code{3*x+5*y} instead of @code{x.times(3).plus(y.times(5))} looks much more
+natural. Furthermore, the main developers are more familiar with
+C++ than with any other programming language.
+
+
+@node Bibliography, Concept Index, A Comparison With Other CAS, Top
+@c node-name, next, previous, up
+@chapter Bibliography
+
+@itemize @minus{}
+
+@item
+@cite{ISO/IEC 14882:1998: Programming Languages: C++}
+
+@item
+@cite{CLN: A Class Library for Numbers}, @email{haible@@ilog.fr, Bruno Haible}
+
+@item
+@cite{The C++ Programming Language}, Bjarne Stroustrup, 3rd Edition, ISBN 0-201-88954-4, Addison Wesley
+
+@item
+@cite{C++ FAQs}, Marshall Cline, ISBN 0-201-58958-3, 1995, Addison Wesley
+
+@item
+@cite{Algorithms for Computer Algebra}, Keith O. Geddes, Stephen R. Czapor,
+and George Labahn, ISBN 0-7923-9259-0, 1992, Kluwer Academic Publishers, Norwell, Massachusetts
+
+@item
+@cite{Computer Algebra: Systems and Algorithms for Algebraic Computation},
+J.H. Davenport, Y. Siret, and E. Tournier, ISBN 0-12-204230-1, 1988,
+Academic Press, London
+
+@end itemize
+
+
+@node Concept Index, , Bibliography, Top
+@c node-name, next, previous, up
+@unnumbered Concept Index
+
+@printindex cp
+
+@bye
+
--- /dev/null
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+%
+% This texinfo.tex file is distributed in the hope that it will be
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+
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+\def\loggingall{\tracingcommands3 \tracingstats2
+ \tracingpages1 \tracingoutput1 \tracinglostchars1
+ \tracingmacros2 \tracingparagraphs1 \tracingrestores1
+ \tracingscantokens1 \tracingassigns1 \tracingifs1
+ \tracinggroups1 \tracingnesting2
+ \showboxbreadth\maxdimen\showboxdepth\maxdimen
+}%
+\fi
+
+% For @cropmarks command.
+% Do @cropmarks to get crop marks.
+%
+\newif\ifcropmarks
+\let\cropmarks = \cropmarkstrue
+%
+% Dimensions to add cropmarks at corners.
+% Added by P. A. MacKay, 12 Nov. 1986
+%
+\newdimen\outerhsize \newdimen\outervsize % set by the paper size routines
+\newdimen\cornerlong \cornerlong=1pc
+\newdimen\cornerthick \cornerthick=.3pt
+\newdimen\topandbottommargin \topandbottommargin=.75in
+
+% Main output routine.
+\chardef\PAGE = 255
+\output = {\onepageout{\pagecontents\PAGE}}
+
+\newbox\headlinebox
+\newbox\footlinebox
+
+% \onepageout takes a vbox as an argument. Note that \pagecontents
+% does insertions, but you have to call it yourself.
+\def\onepageout#1{%
+ \ifcropmarks \hoffset=0pt \else \hoffset=\normaloffset \fi
+ %
+ \ifodd\pageno \advance\hoffset by \bindingoffset
+ \else \advance\hoffset by -\bindingoffset\fi
+ %
+ % Do this outside of the \shipout so @code etc. will be expanded in
+ % the headline as they should be, not taken literally (outputting ''code).
+ \setbox\headlinebox = \vbox{\let\hsize=\pagewidth \makeheadline}%
+ \setbox\footlinebox = \vbox{\let\hsize=\pagewidth \makefootline}%
+ %
+ {%
+ % Have to do this stuff outside the \shipout because we want it to
+ % take effect in \write's, yet the group defined by the \vbox ends
+ % before the \shipout runs.
+ %
+ \escapechar = `\\ % use backslash in output files.
+ \indexdummies % don't expand commands in the output.
+ \normalturnoffactive % \ in index entries must not stay \, e.g., if
+ % the page break happens to be in the middle of an example.
+ \shipout\vbox{%
+ \ifcropmarks \vbox to \outervsize\bgroup
+ \hsize = \outerhsize
+ \vskip-\topandbottommargin
+ \vtop to0pt{%
+ \line{\ewtop\hfil\ewtop}%
+ \nointerlineskip
+ \line{%
+ \vbox{\moveleft\cornerthick\nstop}%
+ \hfill
+ \vbox{\moveright\cornerthick\nstop}%
+ }%
+ \vss}%
+ \vskip\topandbottommargin
+ \line\bgroup
+ \hfil % center the page within the outer (page) hsize.
+ \ifodd\pageno\hskip\bindingoffset\fi
+ \vbox\bgroup
+ \fi
+ %
+ \unvbox\headlinebox
+ \pagebody{#1}%
+ \ifdim\ht\footlinebox > 0pt
+ % Only leave this space if the footline is nonempty.
+ % (We lessened \vsize for it in \oddfootingxxx.)
+ % The \baselineskip=24pt in plain's \makefootline has no effect.
+ \vskip 2\baselineskip
+ \unvbox\footlinebox
+ \fi
+ %
+ \ifcropmarks
+ \egroup % end of \vbox\bgroup
+ \hfil\egroup % end of (centering) \line\bgroup
+ \vskip\topandbottommargin plus1fill minus1fill
+ \boxmaxdepth = \cornerthick
+ \vbox to0pt{\vss
+ \line{%
+ \vbox{\moveleft\cornerthick\nsbot}%
+ \hfill
+ \vbox{\moveright\cornerthick\nsbot}%
+ }%
+ \nointerlineskip
+ \line{\ewbot\hfil\ewbot}%
+ }%
+ \egroup % \vbox from first cropmarks clause
+ \fi
+ }% end of \shipout\vbox
+ }% end of group with \turnoffactive
+ \advancepageno
+ \ifnum\outputpenalty>-20000 \else\dosupereject\fi
+}
+
+\newinsert\margin \dimen\margin=\maxdimen
+
+\def\pagebody#1{\vbox to\pageheight{\boxmaxdepth=\maxdepth #1}}
+{\catcode`\@ =11
+\gdef\pagecontents#1{\ifvoid\topins\else\unvbox\topins\fi
+% marginal hacks, juha@viisa.uucp (Juha Takala)
+\ifvoid\margin\else % marginal info is present
+ \rlap{\kern\hsize\vbox to\z@{\kern1pt\box\margin \vss}}\fi
+\dimen@=\dp#1 \unvbox#1
+\ifvoid\footins\else\vskip\skip\footins\footnoterule \unvbox\footins\fi
+\ifr@ggedbottom \kern-\dimen@ \vfil \fi}
+}
+
+% Here are the rules for the cropmarks. Note that they are
+% offset so that the space between them is truly \outerhsize or \outervsize
+% (P. A. MacKay, 12 November, 1986)
+%
+\def\ewtop{\vrule height\cornerthick depth0pt width\cornerlong}
+\def\nstop{\vbox
+ {\hrule height\cornerthick depth\cornerlong width\cornerthick}}
+\def\ewbot{\vrule height0pt depth\cornerthick width\cornerlong}
+\def\nsbot{\vbox
+ {\hrule height\cornerlong depth\cornerthick width\cornerthick}}
+
+% Parse an argument, then pass it to #1. The argument is the rest of
+% the input line (except we remove a trailing comment). #1 should be a
+% macro which expects an ordinary undelimited TeX argument.
+%
+\def\parsearg#1{%
+ \let\next = #1%
+ \begingroup
+ \obeylines
+ \futurelet\temp\parseargx
+}
+
+% If the next token is an obeyed space (from an @example environment or
+% the like), remove it and recurse. Otherwise, we're done.
+\def\parseargx{%
+ % \obeyedspace is defined far below, after the definition of \sepspaces.
+ \ifx\obeyedspace\temp
+ \expandafter\parseargdiscardspace
+ \else
+ \expandafter\parseargline
+ \fi
+}
+
+% Remove a single space (as the delimiter token to the macro call).
+{\obeyspaces %
+ \gdef\parseargdiscardspace {\futurelet\temp\parseargx}}
+
+{\obeylines %
+ \gdef\parseargline#1^^M{%
+ \endgroup % End of the group started in \parsearg.
+ %
+ % First remove any @c comment, then any @comment.
+ % Result of each macro is put in \toks0.
+ \argremovec #1\c\relax %
+ \expandafter\argremovecomment \the\toks0 \comment\relax %
+ %
+ % Call the caller's macro, saved as \next in \parsearg.
+ \expandafter\next\expandafter{\the\toks0}%
+ }%
+}
+
+% Since all \c{,omment} does is throw away the argument, we can let TeX
+% do that for us. The \relax here is matched by the \relax in the call
+% in \parseargline; it could be more or less anything, its purpose is
+% just to delimit the argument to the \c.
+\def\argremovec#1\c#2\relax{\toks0 = {#1}}
+\def\argremovecomment#1\comment#2\relax{\toks0 = {#1}}
+
+% \argremovec{,omment} might leave us with trailing spaces, though; e.g.,
+% @end itemize @c foo
+% will have two active spaces as part of the argument with the
+% `itemize'. Here we remove all active spaces from #1, and assign the
+% result to \toks0.
+%
+% This loses if there are any *other* active characters besides spaces
+% in the argument -- _ ^ +, for example -- since they get expanded.
+% Fortunately, Texinfo does not define any such commands. (If it ever
+% does, the catcode of the characters in questionwill have to be changed
+% here.) But this means we cannot call \removeactivespaces as part of
+% \argremovec{,omment}, since @c uses \parsearg, and thus the argument
+% that \parsearg gets might well have any character at all in it.
+%
+\def\removeactivespaces#1{%
+ \begingroup
+ \ignoreactivespaces
+ \edef\temp{#1}%
+ \global\toks0 = \expandafter{\temp}%
+ \endgroup
+}
+
+% Change the active space to expand to nothing.
+%
+\begingroup
+ \obeyspaces
+ \gdef\ignoreactivespaces{\obeyspaces\let =\empty}
+\endgroup
+
+
+\def\flushcr{\ifx\par\lisppar \def\next##1{}\else \let\next=\relax \fi \next}
+
+%% These are used to keep @begin/@end levels from running away
+%% Call \inENV within environments (after a \begingroup)
+\newif\ifENV \ENVfalse \def\inENV{\ifENV\relax\else\ENVtrue\fi}
+\def\ENVcheck{%
+\ifENV\errmessage{Still within an environment; press RETURN to continue}
+\endgroup\fi} % This is not perfect, but it should reduce lossage
+
+% @begin foo is the same as @foo, for now.
+\newhelp\EMsimple{Press RETURN to continue.}
+
+\outer\def\begin{\parsearg\beginxxx}
+
+\def\beginxxx #1{%
+\expandafter\ifx\csname #1\endcsname\relax
+{\errhelp=\EMsimple \errmessage{Undefined command @begin #1}}\else
+\csname #1\endcsname\fi}
+
+% @end foo executes the definition of \Efoo.
+%
+\def\end{\parsearg\endxxx}
+\def\endxxx #1{%
+ \removeactivespaces{#1}%
+ \edef\endthing{\the\toks0}%
+ %
+ \expandafter\ifx\csname E\endthing\endcsname\relax
+ \expandafter\ifx\csname \endthing\endcsname\relax
+ % There's no \foo, i.e., no ``environment'' foo.
+ \errhelp = \EMsimple
+ \errmessage{Undefined command `@end \endthing'}%
+ \else
+ \unmatchedenderror\endthing
+ \fi
+ \else
+ % Everything's ok; the right environment has been started.
+ \csname E\endthing\endcsname
+ \fi
+}
+
+% There is an environment #1, but it hasn't been started. Give an error.
+%
+\def\unmatchedenderror#1{%
+ \errhelp = \EMsimple
+ \errmessage{This `@end #1' doesn't have a matching `@#1'}%
+}
+
+% Define the control sequence \E#1 to give an unmatched @end error.
+%
+\def\defineunmatchedend#1{%
+ \expandafter\def\csname E#1\endcsname{\unmatchedenderror{#1}}%
+}
+
+
+% Single-spacing is done by various environments (specifically, in
+% \nonfillstart and \quotations).
+\newskip\singlespaceskip \singlespaceskip = 12.5pt
+\def\singlespace{%
+ % Why was this kern here? It messes up equalizing space above and below
+ % environments. --karl, 6may93
+ %{\advance \baselineskip by -\singlespaceskip
+ %\kern \baselineskip}%
+ \setleading \singlespaceskip
+}
+
+%% Simple single-character @ commands
+
+% @@ prints an @
+% Kludge this until the fonts are right (grr).
+\def\@{{\tt\char64}}
+
+% This is turned off because it was never documented
+% and you can use @w{...} around a quote to suppress ligatures.
+%% Define @` and @' to be the same as ` and '
+%% but suppressing ligatures.
+%\def\`{{`}}
+%\def\'{{'}}
+
+% Used to generate quoted braces.
+\def\mylbrace {{\tt\char123}}
+\def\myrbrace {{\tt\char125}}
+\let\{=\mylbrace
+\let\}=\myrbrace
+\begingroup
+ % Definitions to produce actual \{ & \} command in an index.
+ \catcode`\{ = 12 \catcode`\} = 12
+ \catcode`\[ = 1 \catcode`\] = 2
+ \catcode`\@ = 0 \catcode`\\ = 12
+ @gdef@lbracecmd[\{]%
+ @gdef@rbracecmd[\}]%
+@endgroup
+
+% Accents: @, @dotaccent @ringaccent @ubaraccent @udotaccent
+% Others are defined by plain TeX: @` @' @" @^ @~ @= @v @H.
+\let\, = \c
+\let\dotaccent = \.
+\def\ringaccent#1{{\accent23 #1}}
+\let\tieaccent = \t
+\let\ubaraccent = \b
+\let\udotaccent = \d
+
+% Other special characters: @questiondown @exclamdown
+% Plain TeX defines: @AA @AE @O @OE @L (and lowercase versions) @ss.
+\def\questiondown{?`}
+\def\exclamdown{!`}
+
+% Dotless i and dotless j, used for accents.
+\def\imacro{i}
+\def\jmacro{j}
+\def\dotless#1{%
+ \def\temp{#1}%
+ \ifx\temp\imacro \ptexi
+ \else\ifx\temp\jmacro \j
+ \else \errmessage{@dotless can be used only with i or j}%
+ \fi\fi
+}
+
+% Be sure we're in horizontal mode when doing a tie, since we make space
+% equivalent to this in @example-like environments. Otherwise, a space
+% at the beginning of a line will start with \penalty -- and
+% since \penalty is valid in vertical mode, we'd end up putting the
+% penalty on the vertical list instead of in the new paragraph.
+{\catcode`@ = 11
+ % Avoid using \@M directly, because that causes trouble
+ % if the definition is written into an index file.
+ \global\let\tiepenalty = \@M
+ \gdef\tie{\leavevmode\penalty\tiepenalty\ }
+}
+
+% @: forces normal size whitespace following.
+\def\:{\spacefactor=1000 }
+
+% @* forces a line break.
+\def\*{\hfil\break\hbox{}\ignorespaces}
+
+% @. is an end-of-sentence period.
+\def\.{.\spacefactor=3000 }
+
+% @! is an end-of-sentence bang.
+\def\!{!\spacefactor=3000 }
+
+% @? is an end-of-sentence query.
+\def\?{?\spacefactor=3000 }
+
+% @w prevents a word break. Without the \leavevmode, @w at the
+% beginning of a paragraph, when TeX is still in vertical mode, would
+% produce a whole line of output instead of starting the paragraph.
+\def\w#1{\leavevmode\hbox{#1}}
+
+% @group ... @end group forces ... to be all on one page, by enclosing
+% it in a TeX vbox. We use \vtop instead of \vbox to construct the box
+% to keep its height that of a normal line. According to the rules for
+% \topskip (p.114 of the TeXbook), the glue inserted is
+% max (\topskip - \ht (first item), 0). If that height is large,
+% therefore, no glue is inserted, and the space between the headline and
+% the text is small, which looks bad.
+%
+\def\group{\begingroup
+ \ifnum\catcode13=\active \else
+ \errhelp = \groupinvalidhelp
+ \errmessage{@group invalid in context where filling is enabled}%
+ \fi
+ %
+ % The \vtop we start below produces a box with normal height and large
+ % depth; thus, TeX puts \baselineskip glue before it, and (when the
+ % next line of text is done) \lineskip glue after it. (See p.82 of
+ % the TeXbook.) Thus, space below is not quite equal to space
+ % above. But it's pretty close.
+ \def\Egroup{%
+ \egroup % End the \vtop.
+ \endgroup % End the \group.
+ }%
+ %
+ \vtop\bgroup
+ % We have to put a strut on the last line in case the @group is in
+ % the midst of an example, rather than completely enclosing it.
+ % Otherwise, the interline space between the last line of the group
+ % and the first line afterwards is too small. But we can't put the
+ % strut in \Egroup, since there it would be on a line by itself.
+ % Hence this just inserts a strut at the beginning of each line.
+ \everypar = {\strut}%
+ %
+ % Since we have a strut on every line, we don't need any of TeX's
+ % normal interline spacing.
+ \offinterlineskip
+ %
+ % OK, but now we have to do something about blank
+ % lines in the input in @example-like environments, which normally
+ % just turn into \lisppar, which will insert no space now that we've
+ % turned off the interline space. Simplest is to make them be an
+ % empty paragraph.
+ \ifx\par\lisppar
+ \edef\par{\leavevmode \par}%
+ %
+ % Reset ^^M's definition to new definition of \par.
+ \obeylines
+ \fi
+ %
+ % Do @comment since we are called inside an environment such as
+ % @example, where each end-of-line in the input causes an
+ % end-of-line in the output. We don't want the end-of-line after
+ % the `@group' to put extra space in the output. Since @group
+ % should appear on a line by itself (according to the Texinfo
+ % manual), we don't worry about eating any user text.
+ \comment
+}
+%
+% TeX puts in an \escapechar (i.e., `@') at the beginning of the help
+% message, so this ends up printing `@group can only ...'.
+%
+\newhelp\groupinvalidhelp{%
+group can only be used in environments such as @example,^^J%
+where each line of input produces a line of output.}
+
+% @need space-in-mils
+% forces a page break if there is not space-in-mils remaining.
+
+\newdimen\mil \mil=0.001in
+
+\def\need{\parsearg\needx}
+
+% Old definition--didn't work.
+%\def\needx #1{\par %
+%% This method tries to make TeX break the page naturally
+%% if the depth of the box does not fit.
+%{\baselineskip=0pt%
+%\vtop to #1\mil{\vfil}\kern -#1\mil\nobreak
+%\prevdepth=-1000pt
+%}}
+
+\def\needx#1{%
+ % Go into vertical mode, so we don't make a big box in the middle of a
+ % paragraph.
+ \par
+ %
+ % Don't add any leading before our big empty box, but allow a page
+ % break, since the best break might be right here.
+ \allowbreak
+ \nointerlineskip
+ \vtop to #1\mil{\vfil}%
+ %
+ % TeX does not even consider page breaks if a penalty added to the
+ % main vertical list is 10000 or more. But in order to see if the
+ % empty box we just added fits on the page, we must make it consider
+ % page breaks. On the other hand, we don't want to actually break the
+ % page after the empty box. So we use a penalty of 9999.
+ %
+ % There is an extremely small chance that TeX will actually break the
+ % page at this \penalty, if there are no other feasible breakpoints in
+ % sight. (If the user is using lots of big @group commands, which
+ % almost-but-not-quite fill up a page, TeX will have a hard time doing
+ % good page breaking, for example.) However, I could not construct an
+ % example where a page broke at this \penalty; if it happens in a real
+ % document, then we can reconsider our strategy.
+ \penalty9999
+ %
+ % Back up by the size of the box, whether we did a page break or not.
+ \kern -#1\mil
+ %
+ % Do not allow a page break right after this kern.
+ \nobreak
+}
+
+% @br forces paragraph break
+
+\let\br = \par
+
+% @dots{} output an ellipsis using the current font.
+% We do .5em per period so that it has the same spacing in a typewriter
+% font as three actual period characters.
+%
+\def\dots{%
+ \leavevmode
+ \hbox to 1.5em{%
+ \hskip 0pt plus 0.25fil minus 0.25fil
+ .\hss.\hss.%
+ \hskip 0pt plus 0.5fil minus 0.5fil
+ }%
+}
+
+% @enddots{} is an end-of-sentence ellipsis.
+%
+\def\enddots{%
+ \leavevmode
+ \hbox to 2em{%
+ \hskip 0pt plus 0.25fil minus 0.25fil
+ .\hss.\hss.\hss.%
+ \hskip 0pt plus 0.5fil minus 0.5fil
+ }%
+ \spacefactor=3000
+}
+
+
+% @page forces the start of a new page
+%
+\def\page{\par\vfill\supereject}
+
+% @exdent text....
+% outputs text on separate line in roman font, starting at standard page margin
+
+% This records the amount of indent in the innermost environment.
+% That's how much \exdent should take out.
+\newskip\exdentamount
+
+% This defn is used inside fill environments such as @defun.
+\def\exdent{\parsearg\exdentyyy}
+\def\exdentyyy #1{{\hfil\break\hbox{\kern -\exdentamount{\rm#1}}\hfil\break}}
+
+% This defn is used inside nofill environments such as @example.
+\def\nofillexdent{\parsearg\nofillexdentyyy}
+\def\nofillexdentyyy #1{{\advance \leftskip by -\exdentamount
+\leftline{\hskip\leftskip{\rm#1}}}}
+
+% @inmargin{TEXT} puts TEXT in the margin next to the current paragraph.
+
+\def\inmargin#1{%
+\strut\vadjust{\nobreak\kern-\strutdepth
+ \vtop to \strutdepth{\baselineskip\strutdepth\vss
+ \llap{\rightskip=\inmarginspacing \vbox{\noindent #1}}\null}}}
+\newskip\inmarginspacing \inmarginspacing=1cm
+\def\strutdepth{\dp\strutbox}
+
+%\hbox{{\rm#1}}\hfil\break}}
+
+% @include file insert text of that file as input.
+% Allow normal characters that we make active in the argument (a file name).
+\def\include{\begingroup
+ \catcode`\\=12
+ \catcode`~=12
+ \catcode`^=12
+ \catcode`_=12
+ \catcode`|=12
+ \catcode`<=12
+ \catcode`>=12
+ \catcode`+=12
+ \parsearg\includezzz}
+% Restore active chars for included file.
+\def\includezzz#1{\endgroup\begingroup
+ % Read the included file in a group so nested @include's work.
+ \def\thisfile{#1}%
+ \input\thisfile
+\endgroup}
+
+\def\thisfile{}
+
+% @center line outputs that line, centered
+
+\def\center{\parsearg\centerzzz}
+\def\centerzzz #1{{\advance\hsize by -\leftskip
+\advance\hsize by -\rightskip
+\centerline{#1}}}
+
+% @sp n outputs n lines of vertical space
+
+\def\sp{\parsearg\spxxx}
+\def\spxxx #1{\vskip #1\baselineskip}
+
+% @comment ...line which is ignored...
+% @c is the same as @comment
+% @ignore ... @end ignore is another way to write a comment
+
+\def\comment{\begingroup \catcode`\^^M=\other%
+\catcode`\@=\other \catcode`\{=\other \catcode`\}=\other%
+\commentxxx}
+{\catcode`\^^M=\other \gdef\commentxxx#1^^M{\endgroup}}
+
+\let\c=\comment
+
+% @paragraphindent is defined for the Info formatting commands only.
+\let\paragraphindent=\comment
+
+% Prevent errors for section commands.
+% Used in @ignore and in failing conditionals.
+\def\ignoresections{%
+\let\chapter=\relax
+\let\unnumbered=\relax
+\let\top=\relax
+\let\unnumberedsec=\relax
+\let\unnumberedsection=\relax
+\let\unnumberedsubsec=\relax
+\let\unnumberedsubsection=\relax
+\let\unnumberedsubsubsec=\relax
+\let\unnumberedsubsubsection=\relax
+\let\section=\relax
+\let\subsec=\relax
+\let\subsubsec=\relax
+\let\subsection=\relax
+\let\subsubsection=\relax
+\let\appendix=\relax
+\let\appendixsec=\relax
+\let\appendixsection=\relax
+\let\appendixsubsec=\relax
+\let\appendixsubsection=\relax
+\let\appendixsubsubsec=\relax
+\let\appendixsubsubsection=\relax
+\let\contents=\relax
+\let\smallbook=\relax
+\let\titlepage=\relax
+}
+
+% Used in nested conditionals, where we have to parse the Texinfo source
+% and so want to turn off most commands, in case they are used
+% incorrectly.
+%
+\def\ignoremorecommands{%
+ \let\defcodeindex = \relax
+ \let\defcv = \relax
+ \let\deffn = \relax
+ \let\deffnx = \relax
+ \let\defindex = \relax
+ \let\defivar = \relax
+ \let\defmac = \relax
+ \let\defmethod = \relax
+ \let\defop = \relax
+ \let\defopt = \relax
+ \let\defspec = \relax
+ \let\deftp = \relax
+ \let\deftypefn = \relax
+ \let\deftypefun = \relax
+ \let\deftypevar = \relax
+ \let\deftypevr = \relax
+ \let\defun = \relax
+ \let\defvar = \relax
+ \let\defvr = \relax
+ \let\ref = \relax
+ \let\xref = \relax
+ \let\printindex = \relax
+ \let\pxref = \relax
+ \let\settitle = \relax
+ \let\setchapternewpage = \relax
+ \let\setchapterstyle = \relax
+ \let\everyheading = \relax
+ \let\evenheading = \relax
+ \let\oddheading = \relax
+ \let\everyfooting = \relax
+ \let\evenfooting = \relax
+ \let\oddfooting = \relax
+ \let\headings = \relax
+ \let\include = \relax
+ \let\lowersections = \relax
+ \let\down = \relax
+ \let\raisesections = \relax
+ \let\up = \relax
+ \let\set = \relax
+ \let\clear = \relax
+ \let\item = \relax
+}
+
+% Ignore @ignore ... @end ignore.
+%
+\def\ignore{\doignore{ignore}}
+
+% Ignore @ifinfo, @ifhtml, @ifnottex, @html, @menu, and @direntry text.
+%
+\def\ifinfo{\doignore{ifinfo}}
+\def\ifhtml{\doignore{ifhtml}}
+\def\ifnottex{\doignore{ifnottex}}
+\def\html{\doignore{html}}
+\def\menu{\doignore{menu}}
+\def\direntry{\doignore{direntry}}
+
+% @dircategory CATEGORY -- specify a category of the dir file
+% which this file should belong to. Ignore this in TeX.
+\let\dircategory = \comment
+
+% Ignore text until a line `@end #1'.
+%
+\def\doignore#1{\begingroup
+ % Don't complain about control sequences we have declared \outer.
+ \ignoresections
+ %
+ % Define a command to swallow text until we reach `@end #1'.
+ % This @ is a catcode 12 token (that is the normal catcode of @ in
+ % this texinfo.tex file). We change the catcode of @ below to match.
+ \long\def\doignoretext##1@end #1{\enddoignore}%
+ %
+ % Make sure that spaces turn into tokens that match what \doignoretext wants.
+ \catcode32 = 10
+ %
+ % Ignore braces, too, so mismatched braces don't cause trouble.
+ \catcode`\{ = 9
+ \catcode`\} = 9
+ %
+ % We must not have @c interpreted as a control sequence.
+ \catcode`\@ = 12
+ %
+ % Make the letter c a comment character so that the rest of the line
+ % will be ignored. This way, the document can have (for example)
+ % @c @end ifinfo
+ % and the @end ifinfo will be properly ignored.
+ % (We've just changed @ to catcode 12.)
+ \catcode`\c = 14
+ %
+ % And now expand that command.
+ \doignoretext
+}
+
+% What we do to finish off ignored text.
+%
+\def\enddoignore{\endgroup\ignorespaces}%
+
+\newif\ifwarnedobs\warnedobsfalse
+\def\obstexwarn{%
+ \ifwarnedobs\relax\else
+ % We need to warn folks that they may have trouble with TeX 3.0.
+ % This uses \immediate\write16 rather than \message to get newlines.
+ \immediate\write16{}
+ \immediate\write16{***WARNING*** for users of Unix TeX 3.0!}
+ \immediate\write16{This manual trips a bug in TeX version 3.0 (tex hangs).}
+ \immediate\write16{If you are running another version of TeX, relax.}
+ \immediate\write16{If you are running Unix TeX 3.0, kill this TeX process.}
+ \immediate\write16{ Then upgrade your TeX installation if you can.}
+ \immediate\write16{ (See ftp://ftp.gnu.org/pub/gnu/TeX.README.)}
+ \immediate\write16{If you are stuck with version 3.0, run the}
+ \immediate\write16{ script ``tex3patch'' from the Texinfo distribution}
+ \immediate\write16{ to use a workaround.}
+ \immediate\write16{}
+ \global\warnedobstrue
+ \fi
+}
+
+% **In TeX 3.0, setting text in \nullfont hangs tex. For a
+% workaround (which requires the file ``dummy.tfm'' to be installed),
+% uncomment the following line:
+%%%%%\font\nullfont=dummy\let\obstexwarn=\relax
+
+% Ignore text, except that we keep track of conditional commands for
+% purposes of nesting, up to an `@end #1' command.
+%
+\def\nestedignore#1{%
+ \obstexwarn
+ % We must actually expand the ignored text to look for the @end
+ % command, so that nested ignore constructs work. Thus, we put the
+ % text into a \vbox and then do nothing with the result. To minimize
+ % the change of memory overflow, we follow the approach outlined on
+ % page 401 of the TeXbook: make the current font be a dummy font.
+ %
+ \setbox0 = \vbox\bgroup
+ % Don't complain about control sequences we have declared \outer.
+ \ignoresections
+ %
+ % Define `@end #1' to end the box, which will in turn undefine the
+ % @end command again.
+ \expandafter\def\csname E#1\endcsname{\egroup\ignorespaces}%
+ %
+ % We are going to be parsing Texinfo commands. Most cause no
+ % trouble when they are used incorrectly, but some commands do
+ % complicated argument parsing or otherwise get confused, so we
+ % undefine them.
+ %
+ % We can't do anything about stray @-signs, unfortunately;
+ % they'll produce `undefined control sequence' errors.
+ \ignoremorecommands
+ %
+ % Set the current font to be \nullfont, a TeX primitive, and define
+ % all the font commands to also use \nullfont. We don't use
+ % dummy.tfm, as suggested in the TeXbook, because not all sites
+ % might have that installed. Therefore, math mode will still
+ % produce output, but that should be an extremely small amount of
+ % stuff compared to the main input.
+ %
+ \nullfont
+ \let\tenrm = \nullfont \let\tenit = \nullfont \let\tensl = \nullfont
+ \let\tenbf = \nullfont \let\tentt = \nullfont \let\smallcaps = \nullfont
+ \let\tensf = \nullfont
+ % Similarly for index fonts (mostly for their use in
+ % smallexample)
+ \let\indrm = \nullfont \let\indit = \nullfont \let\indsl = \nullfont
+ \let\indbf = \nullfont \let\indtt = \nullfont \let\indsc = \nullfont
+ \let\indsf = \nullfont
+ %
+ % Don't complain when characters are missing from the fonts.
+ \tracinglostchars = 0
+ %
+ % Don't bother to do space factor calculations.
+ \frenchspacing
+ %
+ % Don't report underfull hboxes.
+ \hbadness = 10000
+ %
+ % Do minimal line-breaking.
+ \pretolerance = 10000
+ %
+ % Do not execute instructions in @tex
+ \def\tex{\doignore{tex}}%
+ % Do not execute macro definitions.
+ % `c' is a comment character, so the word `macro' will get cut off.
+ \def\macro{\doignore{ma}}%
+}
+
+% @set VAR sets the variable VAR to an empty value.
+% @set VAR REST-OF-LINE sets VAR to the value REST-OF-LINE.
+%
+% Since we want to separate VAR from REST-OF-LINE (which might be
+% empty), we can't just use \parsearg; we have to insert a space of our
+% own to delimit the rest of the line, and then take it out again if we
+% didn't need it. Make sure the catcode of space is correct to avoid
+% losing inside @example, for instance.
+%
+\def\set{\begingroup\catcode` =10
+ \catcode`\-=12 \catcode`\_=12 % Allow - and _ in VAR.
+ \parsearg\setxxx}
+\def\setxxx#1{\setyyy#1 \endsetyyy}
+\def\setyyy#1 #2\endsetyyy{%
+ \def\temp{#2}%
+ \ifx\temp\empty \global\expandafter\let\csname SET#1\endcsname = \empty
+ \else \setzzz{#1}#2\endsetzzz % Remove the trailing space \setxxx inserted.
+ \fi
+ \endgroup
+}
+% Can't use \xdef to pre-expand #2 and save some time, since \temp or
+% \next or other control sequences that we've defined might get us into
+% an infinite loop. Consider `@set foo @cite{bar}'.
+\def\setzzz#1#2 \endsetzzz{\expandafter\gdef\csname SET#1\endcsname{#2}}
+
+% @clear VAR clears (i.e., unsets) the variable VAR.
+%
+\def\clear{\parsearg\clearxxx}
+\def\clearxxx#1{\global\expandafter\let\csname SET#1\endcsname=\relax}
+
+% @value{foo} gets the text saved in variable foo.
+%
+{
+ \catcode`\_ = \active
+ %
+ % We might end up with active _ or - characters in the argument if
+ % we're called from @code, as @code{@value{foo-bar_}}. So \let any
+ % such active characters to their normal equivalents.
+ \gdef\value{\begingroup
+ \catcode`\-=12 \catcode`\_=12
+ \indexbreaks \let_\normalunderscore
+ \valuexxx}
+}
+\def\valuexxx#1{\expandablevalue{#1}\endgroup}
+
+% We have this subroutine so that we can handle at least some @value's
+% properly in indexes (we \let\value to this in \indexdummies). Ones
+% whose names contain - or _ still won't work, but we can't do anything
+% about that. The command has to be fully expandable, since the result
+% winds up in the index file. This means that if the variable's value
+% contains other Texinfo commands, it's almost certain it will fail
+% (although perhaps we could fix that with sufficient work to do a
+% one-level expansion on the result, instead of complete).
+%
+\def\expandablevalue#1{%
+ \expandafter\ifx\csname SET#1\endcsname\relax
+ {[No value for ``#1'']}%
+ \else
+ \csname SET#1\endcsname
+ \fi
+}
+
+% @ifset VAR ... @end ifset reads the `...' iff VAR has been defined
+% with @set.
+%
+\def\ifset{\parsearg\ifsetxxx}
+\def\ifsetxxx #1{%
+ \expandafter\ifx\csname SET#1\endcsname\relax
+ \expandafter\ifsetfail
+ \else
+ \expandafter\ifsetsucceed
+ \fi
+}
+\def\ifsetsucceed{\conditionalsucceed{ifset}}
+\def\ifsetfail{\nestedignore{ifset}}
+\defineunmatchedend{ifset}
+
+% @ifclear VAR ... @end ifclear reads the `...' iff VAR has never been
+% defined with @set, or has been undefined with @clear.
+%
+\def\ifclear{\parsearg\ifclearxxx}
+\def\ifclearxxx #1{%
+ \expandafter\ifx\csname SET#1\endcsname\relax
+ \expandafter\ifclearsucceed
+ \else
+ \expandafter\ifclearfail
+ \fi
+}
+\def\ifclearsucceed{\conditionalsucceed{ifclear}}
+\def\ifclearfail{\nestedignore{ifclear}}
+\defineunmatchedend{ifclear}
+
+% @iftex, @ifnothtml, @ifnotinfo always succeed; we read the text
+% following, through the first @end iftex (etc.). Make `@end iftex'
+% (etc.) valid only after an @iftex.
+%
+\def\iftex{\conditionalsucceed{iftex}}
+\def\ifnothtml{\conditionalsucceed{ifnothtml}}
+\def\ifnotinfo{\conditionalsucceed{ifnotinfo}}
+\defineunmatchedend{iftex}
+\defineunmatchedend{ifnothtml}
+\defineunmatchedend{ifnotinfo}
+
+% We can't just want to start a group at @iftex (for example) and end it
+% at @end iftex, since then @set commands inside the conditional have no
+% effect (they'd get reverted at the end of the group). So we must
+% define \Eiftex to redefine itself to be its previous value. (We can't
+% just define it to fail again with an ``unmatched end'' error, since
+% the @ifset might be nested.)
+%
+\def\conditionalsucceed#1{%
+ \edef\temp{%
+ % Remember the current value of \E#1.
+ \let\nece{prevE#1} = \nece{E#1}%
+ %
+ % At the `@end #1', redefine \E#1 to be its previous value.
+ \def\nece{E#1}{\let\nece{E#1} = \nece{prevE#1}}%
+ }%
+ \temp
+}
+
+% We need to expand lots of \csname's, but we don't want to expand the
+% control sequences after we've constructed them.
+%
+\def\nece#1{\expandafter\noexpand\csname#1\endcsname}
+
+% @asis just yields its argument. Used with @table, for example.
+%
+\def\asis#1{#1}
+
+% @math means output in math mode.
+% We don't use $'s directly in the definition of \math because control
+% sequences like \math are expanded when the toc file is written. Then,
+% we read the toc file back, the $'s will be normal characters (as they
+% should be, according to the definition of Texinfo). So we must use a
+% control sequence to switch into and out of math mode.
+%
+% This isn't quite enough for @math to work properly in indices, but it
+% seems unlikely it will ever be needed there.
+%
+\let\implicitmath = $
+\def\math#1{\implicitmath #1\implicitmath}
+
+% @bullet and @minus need the same treatment as @math, just above.
+\def\bullet{\implicitmath\ptexbullet\implicitmath}
+\def\minus{\implicitmath-\implicitmath}
+
+% @refill is a no-op.
+\let\refill=\relax
+
+% If working on a large document in chapters, it is convenient to
+% be able to disable indexing, cross-referencing, and contents, for test runs.
+% This is done with @novalidate (before @setfilename).
+%
+\newif\iflinks \linkstrue % by default we want the aux files.
+\let\novalidate = \linksfalse
+
+% @setfilename is done at the beginning of every texinfo file.
+% So open here the files we need to have open while reading the input.
+% This makes it possible to make a .fmt file for texinfo.
+\def\setfilename{%
+ \iflinks
+ \readauxfile
+ \fi % \openindices needs to do some work in any case.
+ \openindices
+ \fixbackslash % Turn off hack to swallow `\input texinfo'.
+ \global\let\setfilename=\comment % Ignore extra @setfilename cmds.
+ %
+ % If texinfo.cnf is present on the system, read it.
+ % Useful for site-wide @afourpaper, etc.
+ % Just to be on the safe side, close the input stream before the \input.
+ \openin 1 texinfo.cnf
+ \ifeof1 \let\temp=\relax \else \def\temp{\input texinfo.cnf }\fi
+ \closein1
+ \temp
+ %
+ \comment % Ignore the actual filename.
+}
+
+% Called from \setfilename.
+%
+\def\openindices{%
+ \newindex{cp}%
+ \newcodeindex{fn}%
+ \newcodeindex{vr}%
+ \newcodeindex{tp}%
+ \newcodeindex{ky}%
+ \newcodeindex{pg}%
+}
+
+% @bye.
+\outer\def\bye{\pagealignmacro\tracingstats=1\ptexend}
+
+
+\message{fonts,}
+% Font-change commands.
+
+% Texinfo sort of supports the sans serif font style, which plain TeX does not.
+% So we set up a \sf analogous to plain's \rm, etc.
+\newfam\sffam
+\def\sf{\fam=\sffam \tensf}
+\let\li = \sf % Sometimes we call it \li, not \sf.
+
+% We don't need math for this one.
+\def\ttsl{\tenttsl}
+
+% Use Computer Modern fonts at \magstephalf (11pt).
+\newcount\mainmagstep
+\mainmagstep=\magstephalf
+
+% Set the font macro #1 to the font named #2, adding on the
+% specified font prefix (normally `cm').
+% #3 is the font's design size, #4 is a scale factor
+\def\setfont#1#2#3#4{\font#1=\fontprefix#2#3 scaled #4}
+
+% Use cm as the default font prefix.
+% To specify the font prefix, you must define \fontprefix
+% before you read in texinfo.tex.
+\ifx\fontprefix\undefined
+\def\fontprefix{cm}
+\fi
+% Support font families that don't use the same naming scheme as CM.
+\def\rmshape{r}
+\def\rmbshape{bx} %where the normal face is bold
+\def\bfshape{b}
+\def\bxshape{bx}
+\def\ttshape{tt}
+\def\ttbshape{tt}
+\def\ttslshape{sltt}
+\def\itshape{ti}
+\def\itbshape{bxti}
+\def\slshape{sl}
+\def\slbshape{bxsl}
+\def\sfshape{ss}
+\def\sfbshape{ss}
+\def\scshape{csc}
+\def\scbshape{csc}
+
+\ifx\bigger\relax
+\let\mainmagstep=\magstep1
+\setfont\textrm\rmshape{12}{1000}
+\setfont\texttt\ttshape{12}{1000}
+\else
+\setfont\textrm\rmshape{10}{\mainmagstep}
+\setfont\texttt\ttshape{10}{\mainmagstep}
+\fi
+% Instead of cmb10, you many want to use cmbx10.
+% cmbx10 is a prettier font on its own, but cmb10
+% looks better when embedded in a line with cmr10.
+\setfont\textbf\bfshape{10}{\mainmagstep}
+\setfont\textit\itshape{10}{\mainmagstep}
+\setfont\textsl\slshape{10}{\mainmagstep}
+\setfont\textsf\sfshape{10}{\mainmagstep}
+\setfont\textsc\scshape{10}{\mainmagstep}
+\setfont\textttsl\ttslshape{10}{\mainmagstep}
+\font\texti=cmmi10 scaled \mainmagstep
+\font\textsy=cmsy10 scaled \mainmagstep
+
+% A few fonts for @defun, etc.
+\setfont\defbf\bxshape{10}{\magstep1} %was 1314
+\setfont\deftt\ttshape{10}{\magstep1}
+\def\df{\let\tentt=\deftt \let\tenbf = \defbf \bf}
+
+% Fonts for indices and small examples (9pt).
+% We actually use the slanted font rather than the italic,
+% because texinfo normally uses the slanted fonts for that.
+% Do not make many font distinctions in general in the index, since they
+% aren't very useful.
+\setfont\ninett\ttshape{9}{1000}
+\setfont\ninettsl\ttslshape{10}{900}
+\setfont\indrm\rmshape{9}{1000}
+\setfont\indit\itshape{9}{1000}
+\setfont\indsl\slshape{9}{1000}
+\let\indtt=\ninett
+\let\indttsl=\ninettsl
+\let\indsf=\indrm
+\let\indbf=\indrm
+\setfont\indsc\scshape{10}{900}
+\font\indi=cmmi9
+\font\indsy=cmsy9
+
+% Fonts for title page:
+\setfont\titlerm\rmbshape{12}{\magstep3}
+\setfont\titleit\itbshape{10}{\magstep4}
+\setfont\titlesl\slbshape{10}{\magstep4}
+\setfont\titlett\ttbshape{12}{\magstep3}
+\setfont\titlettsl\ttslshape{10}{\magstep4}
+\setfont\titlesf\sfbshape{17}{\magstep1}
+\let\titlebf=\titlerm
+\setfont\titlesc\scbshape{10}{\magstep4}
+\font\titlei=cmmi12 scaled \magstep3
+\font\titlesy=cmsy10 scaled \magstep4
+\def\authorrm{\secrm}
+
+% Chapter (and unnumbered) fonts (17.28pt).
+\setfont\chaprm\rmbshape{12}{\magstep2}
+\setfont\chapit\itbshape{10}{\magstep3}
+\setfont\chapsl\slbshape{10}{\magstep3}
+\setfont\chaptt\ttbshape{12}{\magstep2}
+\setfont\chapttsl\ttslshape{10}{\magstep3}
+\setfont\chapsf\sfbshape{17}{1000}
+\let\chapbf=\chaprm
+\setfont\chapsc\scbshape{10}{\magstep3}
+\font\chapi=cmmi12 scaled \magstep2
+\font\chapsy=cmsy10 scaled \magstep3
+
+% Section fonts (14.4pt).
+\setfont\secrm\rmbshape{12}{\magstep1}
+\setfont\secit\itbshape{10}{\magstep2}
+\setfont\secsl\slbshape{10}{\magstep2}
+\setfont\sectt\ttbshape{12}{\magstep1}
+\setfont\secttsl\ttslshape{10}{\magstep2}
+\setfont\secsf\sfbshape{12}{\magstep1}
+\let\secbf\secrm
+\setfont\secsc\scbshape{10}{\magstep2}
+\font\seci=cmmi12 scaled \magstep1
+\font\secsy=cmsy10 scaled \magstep2
+
+% \setfont\ssecrm\bxshape{10}{\magstep1} % This size an font looked bad.
+% \setfont\ssecit\itshape{10}{\magstep1} % The letters were too crowded.
+% \setfont\ssecsl\slshape{10}{\magstep1}
+% \setfont\ssectt\ttshape{10}{\magstep1}
+% \setfont\ssecsf\sfshape{10}{\magstep1}
+
+%\setfont\ssecrm\bfshape{10}{1315} % Note the use of cmb rather than cmbx.
+%\setfont\ssecit\itshape{10}{1315} % Also, the size is a little larger than
+%\setfont\ssecsl\slshape{10}{1315} % being scaled magstep1.
+%\setfont\ssectt\ttshape{10}{1315}
+%\setfont\ssecsf\sfshape{10}{1315}
+
+%\let\ssecbf=\ssecrm
+
+% Subsection fonts (13.15pt).
+\setfont\ssecrm\rmbshape{12}{\magstephalf}
+\setfont\ssecit\itbshape{10}{1315}
+\setfont\ssecsl\slbshape{10}{1315}
+\setfont\ssectt\ttbshape{12}{\magstephalf}
+\setfont\ssecttsl\ttslshape{10}{1315}
+\setfont\ssecsf\sfbshape{12}{\magstephalf}
+\let\ssecbf\ssecrm
+\setfont\ssecsc\scbshape{10}{\magstep1}
+\font\sseci=cmmi12 scaled \magstephalf
+\font\ssecsy=cmsy10 scaled 1315
+% The smallcaps and symbol fonts should actually be scaled \magstep1.5,
+% but that is not a standard magnification.
+
+% In order for the font changes to affect most math symbols and letters,
+% we have to define the \textfont of the standard families. Since
+% texinfo doesn't allow for producing subscripts and superscripts, we
+% don't bother to reset \scriptfont and \scriptscriptfont (which would
+% also require loading a lot more fonts).
+%
+\def\resetmathfonts{%
+ \textfont0 = \tenrm \textfont1 = \teni \textfont2 = \tensy
+ \textfont\itfam = \tenit \textfont\slfam = \tensl \textfont\bffam = \tenbf
+ \textfont\ttfam = \tentt \textfont\sffam = \tensf
+}
+
+
+% The font-changing commands redefine the meanings of \tenSTYLE, instead
+% of just \STYLE. We do this so that font changes will continue to work
+% in math mode, where it is the current \fam that is relevant in most
+% cases, not the current font. Plain TeX does \def\bf{\fam=\bffam
+% \tenbf}, for example. By redefining \tenbf, we obviate the need to
+% redefine \bf itself.
+\def\textfonts{%
+ \let\tenrm=\textrm \let\tenit=\textit \let\tensl=\textsl
+ \let\tenbf=\textbf \let\tentt=\texttt \let\smallcaps=\textsc
+ \let\tensf=\textsf \let\teni=\texti \let\tensy=\textsy \let\tenttsl=\textttsl
+ \resetmathfonts}
+\def\titlefonts{%
+ \let\tenrm=\titlerm \let\tenit=\titleit \let\tensl=\titlesl
+ \let\tenbf=\titlebf \let\tentt=\titlett \let\smallcaps=\titlesc
+ \let\tensf=\titlesf \let\teni=\titlei \let\tensy=\titlesy
+ \let\tenttsl=\titlettsl
+ \resetmathfonts \setleading{25pt}}
+\def\titlefont#1{{\titlefonts\rm #1}}
+\def\chapfonts{%
+ \let\tenrm=\chaprm \let\tenit=\chapit \let\tensl=\chapsl
+ \let\tenbf=\chapbf \let\tentt=\chaptt \let\smallcaps=\chapsc
+ \let\tensf=\chapsf \let\teni=\chapi \let\tensy=\chapsy \let\tenttsl=\chapttsl
+ \resetmathfonts \setleading{19pt}}
+\def\secfonts{%
+ \let\tenrm=\secrm \let\tenit=\secit \let\tensl=\secsl
+ \let\tenbf=\secbf \let\tentt=\sectt \let\smallcaps=\secsc
+ \let\tensf=\secsf \let\teni=\seci \let\tensy=\secsy \let\tenttsl=\secttsl
+ \resetmathfonts \setleading{16pt}}
+\def\subsecfonts{%
+ \let\tenrm=\ssecrm \let\tenit=\ssecit \let\tensl=\ssecsl
+ \let\tenbf=\ssecbf \let\tentt=\ssectt \let\smallcaps=\ssecsc
+ \let\tensf=\ssecsf \let\teni=\sseci \let\tensy=\ssecsy \let\tenttsl=\ssecttsl
+ \resetmathfonts \setleading{15pt}}
+\let\subsubsecfonts = \subsecfonts % Maybe make sssec fonts scaled magstephalf?
+\def\indexfonts{%
+ \let\tenrm=\indrm \let\tenit=\indit \let\tensl=\indsl
+ \let\tenbf=\indbf \let\tentt=\indtt \let\smallcaps=\indsc
+ \let\tensf=\indsf \let\teni=\indi \let\tensy=\indsy \let\tenttsl=\indttsl
+ \resetmathfonts \setleading{12pt}}
+
+% Set up the default fonts, so we can use them for creating boxes.
+%
+\textfonts
+
+% Define these so they can be easily changed for other fonts.
+\def\angleleft{$\langle$}
+\def\angleright{$\rangle$}
+
+% Count depth in font-changes, for error checks
+\newcount\fontdepth \fontdepth=0
+
+% Fonts for short table of contents.
+\setfont\shortcontrm\rmshape{12}{1000}
+\setfont\shortcontbf\bxshape{12}{1000}
+\setfont\shortcontsl\slshape{12}{1000}
+
+%% Add scribe-like font environments, plus @l for inline lisp (usually sans
+%% serif) and @ii for TeX italic
+
+% \smartitalic{ARG} outputs arg in italics, followed by an italic correction
+% unless the following character is such as not to need one.
+\def\smartitalicx{\ifx\next,\else\ifx\next-\else\ifx\next.\else\/\fi\fi\fi}
+\def\smartslanted#1{{\sl #1}\futurelet\next\smartitalicx}
+\def\smartitalic#1{{\it #1}\futurelet\next\smartitalicx}
+
+\let\i=\smartitalic
+\let\var=\smartslanted
+\let\dfn=\smartslanted
+\let\emph=\smartitalic
+\let\cite=\smartslanted
+
+\def\b#1{{\bf #1}}
+\let\strong=\b
+
+% We can't just use \exhyphenpenalty, because that only has effect at
+% the end of a paragraph. Restore normal hyphenation at the end of the
+% group within which \nohyphenation is presumably called.
+%
+\def\nohyphenation{\hyphenchar\font = -1 \aftergroup\restorehyphenation}
+\def\restorehyphenation{\hyphenchar\font = `- }
+
+\def\t#1{%
+ {\tt \rawbackslash \frenchspacing #1}%
+ \null
+}
+\let\ttfont=\t
+\def\samp#1{`\tclose{#1}'\null}
+\setfont\smallrm\rmshape{8}{1000}
+\font\smallsy=cmsy9
+\def\key#1{{\smallrm\textfont2=\smallsy \leavevmode\hbox{%
+ \raise0.4pt\hbox{\angleleft}\kern-.08em\vtop{%
+ \vbox{\hrule\kern-0.4pt
+ \hbox{\raise0.4pt\hbox{\vphantom{\angleleft}}#1}}%
+ \kern-0.4pt\hrule}%
+ \kern-.06em\raise0.4pt\hbox{\angleright}}}}
+% The old definition, with no lozenge:
+%\def\key #1{{\ttsl \nohyphenation \uppercase{#1}}\null}
+\def\ctrl #1{{\tt \rawbackslash \hat}#1}
+
+% @file, @option are the same as @samp.
+\let\file=\samp
+\let\option=\samp
+
+% @code is a modification of @t,
+% which makes spaces the same size as normal in the surrounding text.
+\def\tclose#1{%
+ {%
+ % Change normal interword space to be same as for the current font.
+ \spaceskip = \fontdimen2\font
+ %
+ % Switch to typewriter.
+ \tt
+ %
+ % But `\ ' produces the large typewriter interword space.
+ \def\ {{\spaceskip = 0pt{} }}%
+ %
+ % Turn off hyphenation.
+ \nohyphenation
+ %
+ \rawbackslash
+ \frenchspacing
+ #1%
+ }%
+ \null
+}
+
+% We *must* turn on hyphenation at `-' and `_' in \code.
+% Otherwise, it is too hard to avoid overfull hboxes
+% in the Emacs manual, the Library manual, etc.
+
+% Unfortunately, TeX uses one parameter (\hyphenchar) to control
+% both hyphenation at - and hyphenation within words.
+% We must therefore turn them both off (\tclose does that)
+% and arrange explicitly to hyphenate at a dash.
+% -- rms.
+{
+ \catcode`\-=\active
+ \catcode`\_=\active
+ %
+ \global\def\code{\begingroup
+ \catcode`\-=\active \let-\codedash
+ \catcode`\_=\active \let_\codeunder
+ \codex
+ }
+ %
+ % If we end up with any active - characters when handling the index,
+ % just treat them as a normal -.
+ \global\def\indexbreaks{\catcode`\-=\active \let-\realdash}
+}
+
+\def\realdash{-}
+\def\codedash{-\discretionary{}{}{}}
+\def\codeunder{\ifusingtt{\normalunderscore\discretionary{}{}{}}{\_}}
+\def\codex #1{\tclose{#1}\endgroup}
+
+%\let\exp=\tclose %Was temporary
+
+% @kbd is like @code, except that if the argument is just one @key command,
+% then @kbd has no effect.
+
+% @kbdinputstyle -- arg is `distinct' (@kbd uses slanted tty font always),
+% `example' (@kbd uses ttsl only inside of @example and friends),
+% or `code' (@kbd uses normal tty font always).
+\def\kbdinputstyle{\parsearg\kbdinputstylexxx}
+\def\kbdinputstylexxx#1{%
+ \def\arg{#1}%
+ \ifx\arg\worddistinct
+ \gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\ttsl}%
+ \else\ifx\arg\wordexample
+ \gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\tt}%
+ \else\ifx\arg\wordcode
+ \gdef\kbdexamplefont{\tt}\gdef\kbdfont{\tt}%
+ \fi\fi\fi
+}
+\def\worddistinct{distinct}
+\def\wordexample{example}
+\def\wordcode{code}
+
+% Default is kbdinputdistinct. (Too much of a hassle to call the macro,
+% the catcodes are wrong for parsearg to work.)
+\gdef\kbdexamplefont{\ttsl}\gdef\kbdfont{\ttsl}
+
+\def\xkey{\key}
+\def\kbdfoo#1#2#3\par{\def\one{#1}\def\three{#3}\def\threex{??}%
+\ifx\one\xkey\ifx\threex\three \key{#2}%
+\else{\tclose{\kbdfont\look}}\fi
+\else{\tclose{\kbdfont\look}}\fi}
+
+% For @url, @env, @command quotes seem unnecessary, so use \code.
+\let\url=\code
+\let\env=\code
+\let\command=\code
+
+% @uref (abbreviation for `urlref') takes an optional second argument
+% specifying the text to display. First (mandatory) arg is the url.
+% Perhaps eventually put in a hypertex \special here.
+%
+\def\uref#1{\urefxxx #1,,\finish}
+\def\urefxxx#1,#2,#3\finish{%
+ \setbox0 = \hbox{\ignorespaces #2}%
+ \ifdim\wd0 > 0pt
+ \unhbox0\ (\code{#1})%
+ \else
+ \code{#1}%
+ \fi
+}
+
+% rms does not like the angle brackets --karl, 17may97.
+% So now @email is just like @uref.
+%\def\email#1{\angleleft{\tt #1}\angleright}
+\let\email=\uref
+
+% Check if we are currently using a typewriter font. Since all the
+% Computer Modern typewriter fonts have zero interword stretch (and
+% shrink), and it is reasonable to expect all typewriter fonts to have
+% this property, we can check that font parameter.
+%
+\def\ifmonospace{\ifdim\fontdimen3\font=0pt }
+
+% Typeset a dimension, e.g., `in' or `pt'. The only reason for the
+% argument is to make the input look right: @dmn{pt} instead of @dmn{}pt.
+%
+\def\dmn#1{\thinspace #1}
+
+\def\kbd#1{\def\look{#1}\expandafter\kbdfoo\look??\par}
+
+% @l was never documented to mean ``switch to the Lisp font'',
+% and it is not used as such in any manual I can find. We need it for
+% Polish suppressed-l. --karl, 22sep96.
+%\def\l#1{{\li #1}\null}
+
+% Explicit font changes: @r, @sc, undocumented @ii.
+\def\r#1{{\rm #1}} % roman font
+\def\sc#1{{\smallcaps#1}} % smallcaps font
+\def\ii#1{{\it #1}} % italic font
+
+% @acronym downcases the argument and prints in smallcaps.
+\def\acronym#1{{\smallcaps \lowercase{#1}}}
+
+% @pounds{} is a sterling sign.
+\def\pounds{{\it\$}}
+
+
+\message{page headings,}
+
+\newskip\titlepagetopglue \titlepagetopglue = 1.5in
+\newskip\titlepagebottomglue \titlepagebottomglue = 2pc
+
+% First the title page. Must do @settitle before @titlepage.
+\newif\ifseenauthor
+\newif\iffinishedtitlepage
+
+% Do an implicit @contents or @shortcontents after @end titlepage if the
+% user says @setcontentsaftertitlepage or @setshortcontentsaftertitlepage.
+%
+\newif\ifsetcontentsaftertitlepage
+ \let\setcontentsaftertitlepage = \setcontentsaftertitlepagetrue
+\newif\ifsetshortcontentsaftertitlepage
+ \let\setshortcontentsaftertitlepage = \setshortcontentsaftertitlepagetrue
+
+\def\shorttitlepage{\parsearg\shorttitlepagezzz}
+\def\shorttitlepagezzz #1{\begingroup\hbox{}\vskip 1.5in \chaprm \centerline{#1}%
+ \endgroup\page\hbox{}\page}
+
+\def\titlepage{\begingroup \parindent=0pt \textfonts
+ \let\subtitlerm=\tenrm
+ \def\subtitlefont{\subtitlerm \normalbaselineskip = 13pt \normalbaselines}%
+ %
+ \def\authorfont{\authorrm \normalbaselineskip = 16pt \normalbaselines}%
+ %
+ % Leave some space at the very top of the page.
+ \vglue\titlepagetopglue
+ %
+ % Now you can print the title using @title.
+ \def\title{\parsearg\titlezzz}%
+ \def\titlezzz##1{\leftline{\titlefonts\rm ##1}
+ % print a rule at the page bottom also.
+ \finishedtitlepagefalse
+ \vskip4pt \hrule height 4pt width \hsize \vskip4pt}%
+ % No rule at page bottom unless we print one at the top with @title.
+ \finishedtitlepagetrue
+ %
+ % Now you can put text using @subtitle.
+ \def\subtitle{\parsearg\subtitlezzz}%
+ \def\subtitlezzz##1{{\subtitlefont \rightline{##1}}}%
+ %
+ % @author should come last, but may come many times.
+ \def\author{\parsearg\authorzzz}%
+ \def\authorzzz##1{\ifseenauthor\else\vskip 0pt plus 1filll\seenauthortrue\fi
+ {\authorfont \leftline{##1}}}%
+ %
+ % Most title ``pages'' are actually two pages long, with space
+ % at the top of the second. We don't want the ragged left on the second.
+ \let\oldpage = \page
+ \def\page{%
+ \iffinishedtitlepage\else
+ \finishtitlepage
+ \fi
+ \oldpage
+ \let\page = \oldpage
+ \hbox{}}%
+% \def\page{\oldpage \hbox{}}
+}
+
+\def\Etitlepage{%
+ \iffinishedtitlepage\else
+ \finishtitlepage
+ \fi
+ % It is important to do the page break before ending the group,
+ % because the headline and footline are only empty inside the group.
+ % If we use the new definition of \page, we always get a blank page
+ % after the title page, which we certainly don't want.
+ \oldpage
+ \endgroup
+ %
+ % If they want short, they certainly want long too.
+ \ifsetshortcontentsaftertitlepage
+ \shortcontents
+ \contents
+ \global\let\shortcontents = \relax
+ \global\let\contents = \relax
+ \fi
+ %
+ \ifsetcontentsaftertitlepage
+ \contents
+ \global\let\contents = \relax
+ \global\let\shortcontents = \relax
+ \fi
+ %
+ \HEADINGSon
+}
+
+\def\finishtitlepage{%
+ \vskip4pt \hrule height 2pt width \hsize
+ \vskip\titlepagebottomglue
+ \finishedtitlepagetrue
+}
+
+%%% Set up page headings and footings.
+
+\let\thispage=\folio
+
+\newtoks\evenheadline % headline on even pages
+\newtoks\oddheadline % headline on odd pages
+\newtoks\evenfootline % footline on even pages
+\newtoks\oddfootline % footline on odd pages
+
+% Now make Tex use those variables
+\headline={{\textfonts\rm \ifodd\pageno \the\oddheadline
+ \else \the\evenheadline \fi}}
+\footline={{\textfonts\rm \ifodd\pageno \the\oddfootline
+ \else \the\evenfootline \fi}\HEADINGShook}
+\let\HEADINGShook=\relax
+
+% Commands to set those variables.
+% For example, this is what @headings on does
+% @evenheading @thistitle|@thispage|@thischapter
+% @oddheading @thischapter|@thispage|@thistitle
+% @evenfooting @thisfile||
+% @oddfooting ||@thisfile
+
+\def\evenheading{\parsearg\evenheadingxxx}
+\def\oddheading{\parsearg\oddheadingxxx}
+\def\everyheading{\parsearg\everyheadingxxx}
+
+\def\evenfooting{\parsearg\evenfootingxxx}
+\def\oddfooting{\parsearg\oddfootingxxx}
+\def\everyfooting{\parsearg\everyfootingxxx}
+
+{\catcode`\@=0 %
+
+\gdef\evenheadingxxx #1{\evenheadingyyy #1@|@|@|@|\finish}
+\gdef\evenheadingyyy #1@|#2@|#3@|#4\finish{%
+\global\evenheadline={\rlap{\centerline{#2}}\line{#1\hfil#3}}}
+
+\gdef\oddheadingxxx #1{\oddheadingyyy #1@|@|@|@|\finish}
+\gdef\oddheadingyyy #1@|#2@|#3@|#4\finish{%
+\global\oddheadline={\rlap{\centerline{#2}}\line{#1\hfil#3}}}
+
+\gdef\everyheadingxxx#1{\oddheadingxxx{#1}\evenheadingxxx{#1}}%
+
+\gdef\evenfootingxxx #1{\evenfootingyyy #1@|@|@|@|\finish}
+\gdef\evenfootingyyy #1@|#2@|#3@|#4\finish{%
+\global\evenfootline={\rlap{\centerline{#2}}\line{#1\hfil#3}}}
+
+\gdef\oddfootingxxx #1{\oddfootingyyy #1@|@|@|@|\finish}
+\gdef\oddfootingyyy #1@|#2@|#3@|#4\finish{%
+ \global\oddfootline = {\rlap{\centerline{#2}}\line{#1\hfil#3}}%
+ %
+ % Leave some space for the footline. Hopefully ok to assume
+ % @evenfooting will not be used by itself.
+ \global\advance\pageheight by -\baselineskip
+ \global\advance\vsize by -\baselineskip
+}
+
+\gdef\everyfootingxxx#1{\oddfootingxxx{#1}\evenfootingxxx{#1}}
+%
+}% unbind the catcode of @.
+
+% @headings double turns headings on for double-sided printing.
+% @headings single turns headings on for single-sided printing.
+% @headings off turns them off.
+% @headings on same as @headings double, retained for compatibility.
+% @headings after turns on double-sided headings after this page.
+% @headings doubleafter turns on double-sided headings after this page.
+% @headings singleafter turns on single-sided headings after this page.
+% By default, they are off at the start of a document,
+% and turned `on' after @end titlepage.
+
+\def\headings #1 {\csname HEADINGS#1\endcsname}
+
+\def\HEADINGSoff{
+\global\evenheadline={\hfil} \global\evenfootline={\hfil}
+\global\oddheadline={\hfil} \global\oddfootline={\hfil}}
+\HEADINGSoff
+% When we turn headings on, set the page number to 1.
+% For double-sided printing, put current file name in lower left corner,
+% chapter name on inside top of right hand pages, document
+% title on inside top of left hand pages, and page numbers on outside top
+% edge of all pages.
+\def\HEADINGSdouble{
+\global\pageno=1
+\global\evenfootline={\hfil}
+\global\oddfootline={\hfil}
+\global\evenheadline={\line{\folio\hfil\thistitle}}
+\global\oddheadline={\line{\thischapter\hfil\folio}}
+\global\let\contentsalignmacro = \chapoddpage
+}
+\let\contentsalignmacro = \chappager
+
+% For single-sided printing, chapter title goes across top left of page,
+% page number on top right.
+\def\HEADINGSsingle{
+\global\pageno=1
+\global\evenfootline={\hfil}
+\global\oddfootline={\hfil}
+\global\evenheadline={\line{\thischapter\hfil\folio}}
+\global\oddheadline={\line{\thischapter\hfil\folio}}
+\global\let\contentsalignmacro = \chappager
+}
+\def\HEADINGSon{\HEADINGSdouble}
+
+\def\HEADINGSafter{\let\HEADINGShook=\HEADINGSdoublex}
+\let\HEADINGSdoubleafter=\HEADINGSafter
+\def\HEADINGSdoublex{%
+\global\evenfootline={\hfil}
+\global\oddfootline={\hfil}
+\global\evenheadline={\line{\folio\hfil\thistitle}}
+\global\oddheadline={\line{\thischapter\hfil\folio}}
+\global\let\contentsalignmacro = \chapoddpage
+}
+
+\def\HEADINGSsingleafter{\let\HEADINGShook=\HEADINGSsinglex}
+\def\HEADINGSsinglex{%
+\global\evenfootline={\hfil}
+\global\oddfootline={\hfil}
+\global\evenheadline={\line{\thischapter\hfil\folio}}
+\global\oddheadline={\line{\thischapter\hfil\folio}}
+\global\let\contentsalignmacro = \chappager
+}
+
+% Subroutines used in generating headings
+% Produces Day Month Year style of output.
+\def\today{\number\day\space
+\ifcase\month\or
+January\or February\or March\or April\or May\or June\or
+July\or August\or September\or October\or November\or December\fi
+\space\number\year}
+
+% Use this if you want the Month Day, Year style of output.
+%\def\today{\ifcase\month\or
+%January\or February\or March\or April\or May\or June\or
+%July\or August\or September\or October\or November\or December\fi
+%\space\number\day, \number\year}
+
+% @settitle line... specifies the title of the document, for headings
+% It generates no output of its own
+
+\def\thistitle{No Title}
+\def\settitle{\parsearg\settitlezzz}
+\def\settitlezzz #1{\gdef\thistitle{#1}}
+
+
+\message{tables,}
+% Tables -- @table, @ftable, @vtable, @item(x), @kitem(x), @xitem(x).
+
+% default indentation of table text
+\newdimen\tableindent \tableindent=.8in
+% default indentation of @itemize and @enumerate text
+\newdimen\itemindent \itemindent=.3in
+% margin between end of table item and start of table text.
+\newdimen\itemmargin \itemmargin=.1in
+
+% used internally for \itemindent minus \itemmargin
+\newdimen\itemmax
+
+% Note @table, @vtable, and @vtable define @item, @itemx, etc., with
+% these defs.
+% They also define \itemindex
+% to index the item name in whatever manner is desired (perhaps none).
+
+\newif\ifitemxneedsnegativevskip
+
+\def\itemxpar{\par\ifitemxneedsnegativevskip\nobreak\vskip-\parskip\nobreak\fi}
+
+\def\internalBitem{\smallbreak \parsearg\itemzzz}
+\def\internalBitemx{\itemxpar \parsearg\itemzzz}
+
+\def\internalBxitem "#1"{\def\xitemsubtopix{#1} \smallbreak \parsearg\xitemzzz}
+\def\internalBxitemx "#1"{\def\xitemsubtopix{#1} \itemxpar \parsearg\xitemzzz}
+
+\def\internalBkitem{\smallbreak \parsearg\kitemzzz}
+\def\internalBkitemx{\itemxpar \parsearg\kitemzzz}
+
+\def\kitemzzz #1{\dosubind {kw}{\code{#1}}{for {\bf \lastfunction}}%
+ \itemzzz {#1}}
+
+\def\xitemzzz #1{\dosubind {kw}{\code{#1}}{for {\bf \xitemsubtopic}}%
+ \itemzzz {#1}}
+
+\def\itemzzz #1{\begingroup %
+ \advance\hsize by -\rightskip
+ \advance\hsize by -\tableindent
+ \setbox0=\hbox{\itemfont{#1}}%
+ \itemindex{#1}%
+ \nobreak % This prevents a break before @itemx.
+ %
+ % If the item text does not fit in the space we have, put it on a line
+ % by itself, and do not allow a page break either before or after that
+ % line. We do not start a paragraph here because then if the next
+ % command is, e.g., @kindex, the whatsit would get put into the
+ % horizontal list on a line by itself, resulting in extra blank space.
+ \ifdim \wd0>\itemmax
+ %
+ % Make this a paragraph so we get the \parskip glue and wrapping,
+ % but leave it ragged-right.
+ \begingroup
+ \advance\leftskip by-\tableindent
+ \advance\hsize by\tableindent
+ \advance\rightskip by0pt plus1fil
+ \leavevmode\unhbox0\par
+ \endgroup
+ %
+ % We're going to be starting a paragraph, but we don't want the
+ % \parskip glue -- logically it's part of the @item we just started.
+ \nobreak \vskip-\parskip
+ %
+ % Stop a page break at the \parskip glue coming up. Unfortunately
+ % we can't prevent a possible page break at the following
+ % \baselineskip glue.
+ \nobreak
+ \endgroup
+ \itemxneedsnegativevskipfalse
+ \else
+ % The item text fits into the space. Start a paragraph, so that the
+ % following text (if any) will end up on the same line.
+ \noindent
+ % Do this with kerns and \unhbox so that if there is a footnote in
+ % the item text, it can migrate to the main vertical list and
+ % eventually be printed.
+ \nobreak\kern-\tableindent
+ \dimen0 = \itemmax \advance\dimen0 by \itemmargin \advance\dimen0 by -\wd0
+ \unhbox0
+ \nobreak\kern\dimen0
+ \endgroup
+ \itemxneedsnegativevskiptrue
+ \fi
+}
+
+\def\item{\errmessage{@item while not in a table}}
+\def\itemx{\errmessage{@itemx while not in a table}}
+\def\kitem{\errmessage{@kitem while not in a table}}
+\def\kitemx{\errmessage{@kitemx while not in a table}}
+\def\xitem{\errmessage{@xitem while not in a table}}
+\def\xitemx{\errmessage{@xitemx while not in a table}}
+
+% Contains a kludge to get @end[description] to work.
+\def\description{\tablez{\dontindex}{1}{}{}{}{}}
+
+% @table, @ftable, @vtable.
+\def\table{\begingroup\inENV\obeylines\obeyspaces\tablex}
+{\obeylines\obeyspaces%
+\gdef\tablex #1^^M{%
+\tabley\dontindex#1 \endtabley}}
+
+\def\ftable{\begingroup\inENV\obeylines\obeyspaces\ftablex}
+{\obeylines\obeyspaces%
+\gdef\ftablex #1^^M{%
+\tabley\fnitemindex#1 \endtabley
+\def\Eftable{\endgraf\afterenvbreak\endgroup}%
+\let\Etable=\relax}}
+
+\def\vtable{\begingroup\inENV\obeylines\obeyspaces\vtablex}
+{\obeylines\obeyspaces%
+\gdef\vtablex #1^^M{%
+\tabley\vritemindex#1 \endtabley
+\def\Evtable{\endgraf\afterenvbreak\endgroup}%
+\let\Etable=\relax}}
+
+\def\dontindex #1{}
+\def\fnitemindex #1{\doind {fn}{\code{#1}}}%
+\def\vritemindex #1{\doind {vr}{\code{#1}}}%
+
+{\obeyspaces %
+\gdef\tabley#1#2 #3 #4 #5 #6 #7\endtabley{\endgroup%
+\tablez{#1}{#2}{#3}{#4}{#5}{#6}}}
+
+\def\tablez #1#2#3#4#5#6{%
+\aboveenvbreak %
+\begingroup %
+\def\Edescription{\Etable}% Necessary kludge.
+\let\itemindex=#1%
+\ifnum 0#3>0 \advance \leftskip by #3\mil \fi %
+\ifnum 0#4>0 \tableindent=#4\mil \fi %
+\ifnum 0#5>0 \advance \rightskip by #5\mil \fi %
+\def\itemfont{#2}%
+\itemmax=\tableindent %
+\advance \itemmax by -\itemmargin %
+\advance \leftskip by \tableindent %
+\exdentamount=\tableindent
+\parindent = 0pt
+\parskip = \smallskipamount
+\ifdim \parskip=0pt \parskip=2pt \fi%
+\def\Etable{\endgraf\afterenvbreak\endgroup}%
+\let\item = \internalBitem %
+\let\itemx = \internalBitemx %
+\let\kitem = \internalBkitem %
+\let\kitemx = \internalBkitemx %
+\let\xitem = \internalBxitem %
+\let\xitemx = \internalBxitemx %
+}
+
+% This is the counter used by @enumerate, which is really @itemize
+
+\newcount \itemno
+
+\def\itemize{\parsearg\itemizezzz}
+
+\def\itemizezzz #1{%
+ \begingroup % ended by the @end itemize
+ \itemizey {#1}{\Eitemize}
+}
+
+\def\itemizey #1#2{%
+\aboveenvbreak %
+\itemmax=\itemindent %
+\advance \itemmax by -\itemmargin %
+\advance \leftskip by \itemindent %
+\exdentamount=\itemindent
+\parindent = 0pt %
+\parskip = \smallskipamount %
+\ifdim \parskip=0pt \parskip=2pt \fi%
+\def#2{\endgraf\afterenvbreak\endgroup}%
+\def\itemcontents{#1}%
+\let\item=\itemizeitem}
+
+% Set sfcode to normal for the chars that usually have another value.
+% These are `.?!:;,'
+\def\frenchspacing{\sfcode46=1000 \sfcode63=1000 \sfcode33=1000
+ \sfcode58=1000 \sfcode59=1000 \sfcode44=1000 }
+
+% \splitoff TOKENS\endmark defines \first to be the first token in
+% TOKENS, and \rest to be the remainder.
+%
+\def\splitoff#1#2\endmark{\def\first{#1}\def\rest{#2}}%
+
+% Allow an optional argument of an uppercase letter, lowercase letter,
+% or number, to specify the first label in the enumerated list. No
+% argument is the same as `1'.
+%
+\def\enumerate{\parsearg\enumeratezzz}
+\def\enumeratezzz #1{\enumeratey #1 \endenumeratey}
+\def\enumeratey #1 #2\endenumeratey{%
+ \begingroup % ended by the @end enumerate
+ %
+ % If we were given no argument, pretend we were given `1'.
+ \def\thearg{#1}%
+ \ifx\thearg\empty \def\thearg{1}\fi
+ %
+ % Detect if the argument is a single token. If so, it might be a
+ % letter. Otherwise, the only valid thing it can be is a number.
+ % (We will always have one token, because of the test we just made.
+ % This is a good thing, since \splitoff doesn't work given nothing at
+ % all -- the first parameter is undelimited.)
+ \expandafter\splitoff\thearg\endmark
+ \ifx\rest\empty
+ % Only one token in the argument. It could still be anything.
+ % A ``lowercase letter'' is one whose \lccode is nonzero.
+ % An ``uppercase letter'' is one whose \lccode is both nonzero, and
+ % not equal to itself.
+ % Otherwise, we assume it's a number.
+ %
+ % We need the \relax at the end of the \ifnum lines to stop TeX from
+ % continuing to look for a <number>.
+ %
+ \ifnum\lccode\expandafter`\thearg=0\relax
+ \numericenumerate % a number (we hope)
+ \else
+ % It's a letter.
+ \ifnum\lccode\expandafter`\thearg=\expandafter`\thearg\relax
+ \lowercaseenumerate % lowercase letter
+ \else
+ \uppercaseenumerate % uppercase letter
+ \fi
+ \fi
+ \else
+ % Multiple tokens in the argument. We hope it's a number.
+ \numericenumerate
+ \fi
+}
+
+% An @enumerate whose labels are integers. The starting integer is
+% given in \thearg.
+%
+\def\numericenumerate{%
+ \itemno = \thearg
+ \startenumeration{\the\itemno}%
+}
+
+% The starting (lowercase) letter is in \thearg.
+\def\lowercaseenumerate{%
+ \itemno = \expandafter`\thearg
+ \startenumeration{%
+ % Be sure we're not beyond the end of the alphabet.
+ \ifnum\itemno=0
+ \errmessage{No more lowercase letters in @enumerate; get a bigger
+ alphabet}%
+ \fi
+ \char\lccode\itemno
+ }%
+}
+
+% The starting (uppercase) letter is in \thearg.
+\def\uppercaseenumerate{%
+ \itemno = \expandafter`\thearg
+ \startenumeration{%
+ % Be sure we're not beyond the end of the alphabet.
+ \ifnum\itemno=0
+ \errmessage{No more uppercase letters in @enumerate; get a bigger
+ alphabet}
+ \fi
+ \char\uccode\itemno
+ }%
+}
+
+% Call itemizey, adding a period to the first argument and supplying the
+% common last two arguments. Also subtract one from the initial value in
+% \itemno, since @item increments \itemno.
+%
+\def\startenumeration#1{%
+ \advance\itemno by -1
+ \itemizey{#1.}\Eenumerate\flushcr
+}
+
+% @alphaenumerate and @capsenumerate are abbreviations for giving an arg
+% to @enumerate.
+%
+\def\alphaenumerate{\enumerate{a}}
+\def\capsenumerate{\enumerate{A}}
+\def\Ealphaenumerate{\Eenumerate}
+\def\Ecapsenumerate{\Eenumerate}
+
+% Definition of @item while inside @itemize.
+
+\def\itemizeitem{%
+\advance\itemno by 1
+{\let\par=\endgraf \smallbreak}%
+\ifhmode \errmessage{In hmode at itemizeitem}\fi
+{\parskip=0in \hskip 0pt
+\hbox to 0pt{\hss \itemcontents\hskip \itemmargin}%
+\vadjust{\penalty 1200}}%
+\flushcr}
+
+% @multitable macros
+% Amy Hendrickson, 8/18/94, 3/6/96
+%
+% @multitable ... @end multitable will make as many columns as desired.
+% Contents of each column will wrap at width given in preamble. Width
+% can be specified either with sample text given in a template line,
+% or in percent of \hsize, the current width of text on page.
+
+% Table can continue over pages but will only break between lines.
+
+% To make preamble:
+%
+% Either define widths of columns in terms of percent of \hsize:
+% @multitable @columnfractions .25 .3 .45
+% @item ...
+%
+% Numbers following @columnfractions are the percent of the total
+% current hsize to be used for each column. You may use as many
+% columns as desired.
+
+
+% Or use a template:
+% @multitable {Column 1 template} {Column 2 template} {Column 3 template}
+% @item ...
+% using the widest term desired in each column.
+%
+% For those who want to use more than one line's worth of words in
+% the preamble, break the line within one argument and it
+% will parse correctly, i.e.,
+%
+% @multitable {Column 1 template} {Column 2 template} {Column 3
+% template}
+% Not:
+% @multitable {Column 1 template} {Column 2 template}
+% {Column 3 template}
+
+% Each new table line starts with @item, each subsequent new column
+% starts with @tab. Empty columns may be produced by supplying @tab's
+% with nothing between them for as many times as empty columns are needed,
+% ie, @tab@tab@tab will produce two empty columns.
+
+% @item, @tab, @multitable or @end multitable do not need to be on their
+% own lines, but it will not hurt if they are.
+
+% Sample multitable:
+
+% @multitable {Column 1 template} {Column 2 template} {Column 3 template}
+% @item first col stuff @tab second col stuff @tab third col
+% @item
+% first col stuff
+% @tab
+% second col stuff
+% @tab
+% third col
+% @item first col stuff @tab second col stuff
+% @tab Many paragraphs of text may be used in any column.
+%
+% They will wrap at the width determined by the template.
+% @item@tab@tab This will be in third column.
+% @end multitable
+
+% Default dimensions may be reset by user.
+% @multitableparskip is vertical space between paragraphs in table.
+% @multitableparindent is paragraph indent in table.
+% @multitablecolmargin is horizontal space to be left between columns.
+% @multitablelinespace is space to leave between table items, baseline
+% to baseline.
+% 0pt means it depends on current normal line spacing.
+%
+\newskip\multitableparskip
+\newskip\multitableparindent
+\newdimen\multitablecolspace
+\newskip\multitablelinespace
+\multitableparskip=0pt
+\multitableparindent=6pt
+\multitablecolspace=12pt
+\multitablelinespace=0pt
+
+% Macros used to set up halign preamble:
+%
+\let\endsetuptable\relax
+\def\xendsetuptable{\endsetuptable}
+\let\columnfractions\relax
+\def\xcolumnfractions{\columnfractions}
+\newif\ifsetpercent
+
+% #1 is the part of the @columnfraction before the decimal point, which
+% is presumably either 0 or the empty string (but we don't check, we
+% just throw it away). #2 is the decimal part, which we use as the
+% percent of \hsize for this column.
+\def\pickupwholefraction#1.#2 {%
+ \global\advance\colcount by 1
+ \expandafter\xdef\csname col\the\colcount\endcsname{.#2\hsize}%
+ \setuptable
+}
+
+\newcount\colcount
+\def\setuptable#1{%
+ \def\firstarg{#1}%
+ \ifx\firstarg\xendsetuptable
+ \let\go = \relax
+ \else
+ \ifx\firstarg\xcolumnfractions
+ \global\setpercenttrue
+ \else
+ \ifsetpercent
+ \let\go\pickupwholefraction
+ \else
+ \global\advance\colcount by 1
+ \setbox0=\hbox{#1\unskip }% Add a normal word space as a separator;
+ % typically that is always in the input, anyway.
+ \expandafter\xdef\csname col\the\colcount\endcsname{\the\wd0}%
+ \fi
+ \fi
+ \ifx\go\pickupwholefraction
+ % Put the argument back for the \pickupwholefraction call, so
+ % we'll always have a period there to be parsed.
+ \def\go{\pickupwholefraction#1}%
+ \else
+ \let\go = \setuptable
+ \fi%
+ \fi
+ \go
+}
+
+% multitable syntax
+\def\tab{&\hskip1sp\relax} % 2/2/96
+ % tiny skip here makes sure this column space is
+ % maintained, even if it is never used.
+
+% @multitable ... @end multitable definitions:
+%
+\def\multitable{\parsearg\dotable}
+\def\dotable#1{\bgroup
+ \vskip\parskip
+ \let\item\crcr
+ \tolerance=9500
+ \hbadness=9500
+ \setmultitablespacing
+ \parskip=\multitableparskip
+ \parindent=\multitableparindent
+ \overfullrule=0pt
+ \global\colcount=0
+ \def\Emultitable{\global\setpercentfalse\cr\egroup\egroup}%
+ %
+ % To parse everything between @multitable and @item:
+ \setuptable#1 \endsetuptable
+ %
+ % \everycr will reset column counter, \colcount, at the end of
+ % each line. Every column entry will cause \colcount to advance by one.
+ % The table preamble
+ % looks at the current \colcount to find the correct column width.
+ \everycr{\noalign{%
+ %
+ % \filbreak%% keeps underfull box messages off when table breaks over pages.
+ % Maybe so, but it also creates really weird page breaks when the table
+ % breaks over pages. Wouldn't \vfil be better? Wait until the problem
+ % manifests itself, so it can be fixed for real --karl.
+ \global\colcount=0\relax}}%
+ %
+ % This preamble sets up a generic column definition, which will
+ % be used as many times as user calls for columns.
+ % \vtop will set a single line and will also let text wrap and
+ % continue for many paragraphs if desired.
+ \halign\bgroup&\global\advance\colcount by 1\relax
+ \multistrut\vtop{\hsize=\expandafter\csname col\the\colcount\endcsname
+ %
+ % In order to keep entries from bumping into each other
+ % we will add a \leftskip of \multitablecolspace to all columns after
+ % the first one.
+ %
+ % If a template has been used, we will add \multitablecolspace
+ % to the width of each template entry.
+ %
+ % If the user has set preamble in terms of percent of \hsize we will
+ % use that dimension as the width of the column, and the \leftskip
+ % will keep entries from bumping into each other. Table will start at
+ % left margin and final column will justify at right margin.
+ %
+ % Make sure we don't inherit \rightskip from the outer environment.
+ \rightskip=0pt
+ \ifnum\colcount=1
+ % The first column will be indented with the surrounding text.
+ \advance\hsize by\leftskip
+ \else
+ \ifsetpercent \else
+ % If user has not set preamble in terms of percent of \hsize
+ % we will advance \hsize by \multitablecolspace.
+ \advance\hsize by \multitablecolspace
+ \fi
+ % In either case we will make \leftskip=\multitablecolspace:
+ \leftskip=\multitablecolspace
+ \fi
+ % Ignoring space at the beginning and end avoids an occasional spurious
+ % blank line, when TeX decides to break the line at the space before the
+ % box from the multistrut, so the strut ends up on a line by itself.
+ % For example:
+ % @multitable @columnfractions .11 .89
+ % @item @code{#}
+ % @tab Legal holiday which is valid in major parts of the whole country.
+ % Is automatically provided with highlighting sequences respectively marking
+ % characters.
+ \noindent\ignorespaces##\unskip\multistrut}\cr
+}
+
+\def\setmultitablespacing{% test to see if user has set \multitablelinespace.
+% If so, do nothing. If not, give it an appropriate dimension based on
+% current baselineskip.
+\ifdim\multitablelinespace=0pt
+%% strut to put in table in case some entry doesn't have descenders,
+%% to keep lines equally spaced
+\let\multistrut = \strut
+%% Test to see if parskip is larger than space between lines of
+%% table. If not, do nothing.
+%% If so, set to same dimension as multitablelinespace.
+\else
+\gdef\multistrut{\vrule height\multitablelinespace depth\dp0
+width0pt\relax} \fi
+\ifdim\multitableparskip>\multitablelinespace
+\global\multitableparskip=\multitablelinespace
+\global\advance\multitableparskip-7pt %% to keep parskip somewhat smaller
+ %% than skip between lines in the table.
+\fi%
+\ifdim\multitableparskip=0pt
+\global\multitableparskip=\multitablelinespace
+\global\advance\multitableparskip-7pt %% to keep parskip somewhat smaller
+ %% than skip between lines in the table.
+\fi}
+
+
+\message{indexing,}
+% Index generation facilities
+
+% Define \newwrite to be identical to plain tex's \newwrite
+% except not \outer, so it can be used within \newindex.
+{\catcode`\@=11
+\gdef\newwrite{\alloc@7\write\chardef\sixt@@n}}
+
+% \newindex {foo} defines an index named foo.
+% It automatically defines \fooindex such that
+% \fooindex ...rest of line... puts an entry in the index foo.
+% It also defines \fooindfile to be the number of the output channel for
+% the file that accumulates this index. The file's extension is foo.
+% The name of an index should be no more than 2 characters long
+% for the sake of vms.
+%
+\def\newindex#1{%
+ \iflinks
+ \expandafter\newwrite \csname#1indfile\endcsname
+ \openout \csname#1indfile\endcsname \jobname.#1 % Open the file
+ \fi
+ \expandafter\xdef\csname#1index\endcsname{% % Define @#1index
+ \noexpand\doindex{#1}}
+}
+
+% @defindex foo == \newindex{foo}
+
+\def\defindex{\parsearg\newindex}
+
+% Define @defcodeindex, like @defindex except put all entries in @code.
+
+\def\newcodeindex#1{%
+ \iflinks
+ \expandafter\newwrite \csname#1indfile\endcsname
+ \openout \csname#1indfile\endcsname \jobname.#1
+ \fi
+ \expandafter\xdef\csname#1index\endcsname{%
+ \noexpand\docodeindex{#1}}
+}
+
+\def\defcodeindex{\parsearg\newcodeindex}
+
+% @synindex foo bar makes index foo feed into index bar.
+% Do this instead of @defindex foo if you don't want it as a separate index.
+% The \closeout helps reduce unnecessary open files; the limit on the
+% Acorn RISC OS is a mere 16 files.
+\def\synindex#1 #2 {%
+ \expandafter\let\expandafter\synindexfoo\expandafter=\csname#2indfile\endcsname
+ \expandafter\closeout\csname#1indfile\endcsname
+ \expandafter\let\csname#1indfile\endcsname=\synindexfoo
+ \expandafter\xdef\csname#1index\endcsname{% define \xxxindex
+ \noexpand\doindex{#2}}%
+}
+
+% @syncodeindex foo bar similar, but put all entries made for index foo
+% inside @code.
+\def\syncodeindex#1 #2 {%
+ \expandafter\let\expandafter\synindexfoo\expandafter=\csname#2indfile\endcsname
+ \expandafter\closeout\csname#1indfile\endcsname
+ \expandafter\let\csname#1indfile\endcsname=\synindexfoo
+ \expandafter\xdef\csname#1index\endcsname{% define \xxxindex
+ \noexpand\docodeindex{#2}}%
+}
+
+% Define \doindex, the driver for all \fooindex macros.
+% Argument #1 is generated by the calling \fooindex macro,
+% and it is "foo", the name of the index.
+
+% \doindex just uses \parsearg; it calls \doind for the actual work.
+% This is because \doind is more useful to call from other macros.
+
+% There is also \dosubind {index}{topic}{subtopic}
+% which makes an entry in a two-level index such as the operation index.
+
+\def\doindex#1{\edef\indexname{#1}\parsearg\singleindexer}
+\def\singleindexer #1{\doind{\indexname}{#1}}
+
+% like the previous two, but they put @code around the argument.
+\def\docodeindex#1{\edef\indexname{#1}\parsearg\singlecodeindexer}
+\def\singlecodeindexer #1{\doind{\indexname}{\code{#1}}}
+
+\def\indexdummies{%
+\def\ { }%
+% Take care of the plain tex accent commands.
+\def\"{\realbackslash "}%
+\def\`{\realbackslash `}%
+\def\'{\realbackslash '}%
+\def\^{\realbackslash ^}%
+\def\~{\realbackslash ~}%
+\def\={\realbackslash =}%
+\def\b{\realbackslash b}%
+\def\c{\realbackslash c}%
+\def\d{\realbackslash d}%
+\def\u{\realbackslash u}%
+\def\v{\realbackslash v}%
+\def\H{\realbackslash H}%
+% Take care of the plain tex special European modified letters.
+\def\oe{\realbackslash oe}%
+\def\ae{\realbackslash ae}%
+\def\aa{\realbackslash aa}%
+\def\OE{\realbackslash OE}%
+\def\AE{\realbackslash AE}%
+\def\AA{\realbackslash AA}%
+\def\o{\realbackslash o}%
+\def\O{\realbackslash O}%
+\def\l{\realbackslash l}%
+\def\L{\realbackslash L}%
+\def\ss{\realbackslash ss}%
+% Take care of texinfo commands likely to appear in an index entry.
+% (Must be a way to avoid doing expansion at all, and thus not have to
+% laboriously list every single command here.)
+\def\@{@}% will be @@ when we switch to @ as escape char.
+% Need these in case \tex is in effect and \{ is a \delimiter again.
+% But can't use \lbracecmd and \rbracecmd because texindex assumes
+% braces and backslashes are used only as delimiters.
+\let\{ = \mylbrace
+\let\} = \myrbrace
+\def\_{{\realbackslash _}}%
+\def\w{\realbackslash w }%
+\def\bf{\realbackslash bf }%
+%\def\rm{\realbackslash rm }%
+\def\sl{\realbackslash sl }%
+\def\sf{\realbackslash sf}%
+\def\tt{\realbackslash tt}%
+\def\gtr{\realbackslash gtr}%
+\def\less{\realbackslash less}%
+\def\hat{\realbackslash hat}%
+\def\TeX{\realbackslash TeX}%
+\def\dots{\realbackslash dots }%
+\def\result{\realbackslash result}%
+\def\equiv{\realbackslash equiv}%
+\def\expansion{\realbackslash expansion}%
+\def\print{\realbackslash print}%
+\def\error{\realbackslash error}%
+\def\point{\realbackslash point}%
+\def\copyright{\realbackslash copyright}%
+\def\tclose##1{\realbackslash tclose {##1}}%
+\def\code##1{\realbackslash code {##1}}%
+\def\uref##1{\realbackslash uref {##1}}%
+\def\url##1{\realbackslash url {##1}}%
+\def\env##1{\realbackslash env {##1}}%
+\def\command##1{\realbackslash command {##1}}%
+\def\option##1{\realbackslash option {##1}}%
+\def\dotless##1{\realbackslash dotless {##1}}%
+\def\samp##1{\realbackslash samp {##1}}%
+\def\,##1{\realbackslash ,{##1}}%
+\def\t##1{\realbackslash t {##1}}%
+\def\r##1{\realbackslash r {##1}}%
+\def\i##1{\realbackslash i {##1}}%
+\def\b##1{\realbackslash b {##1}}%
+\def\sc##1{\realbackslash sc {##1}}%
+\def\cite##1{\realbackslash cite {##1}}%
+\def\key##1{\realbackslash key {##1}}%
+\def\file##1{\realbackslash file {##1}}%
+\def\var##1{\realbackslash var {##1}}%
+\def\kbd##1{\realbackslash kbd {##1}}%
+\def\dfn##1{\realbackslash dfn {##1}}%
+\def\emph##1{\realbackslash emph {##1}}%
+\def\acronym##1{\realbackslash acronym {##1}}%
+%
+% Handle some cases of @value -- where the variable name does not
+% contain - or _, and the value does not contain any
+% (non-fully-expandable) commands.
+\let\value = \expandablevalue
+%
+\unsepspaces
+}
+
+% If an index command is used in an @example environment, any spaces
+% therein should become regular spaces in the raw index file, not the
+% expansion of \tie (\\leavevmode \penalty \@M \ ).
+{\obeyspaces
+ \gdef\unsepspaces{\obeyspaces\let =\space}}
+
+% \indexnofonts no-ops all font-change commands.
+% This is used when outputting the strings to sort the index by.
+\def\indexdummyfont#1{#1}
+\def\indexdummytex{TeX}
+\def\indexdummydots{...}
+
+\def\indexnofonts{%
+% Just ignore accents.
+\let\,=\indexdummyfont
+\let\"=\indexdummyfont
+\let\`=\indexdummyfont
+\let\'=\indexdummyfont
+\let\^=\indexdummyfont
+\let\~=\indexdummyfont
+\let\==\indexdummyfont
+\let\b=\indexdummyfont
+\let\c=\indexdummyfont
+\let\d=\indexdummyfont
+\let\u=\indexdummyfont
+\let\v=\indexdummyfont
+\let\H=\indexdummyfont
+\let\dotless=\indexdummyfont
+% Take care of the plain tex special European modified letters.
+\def\oe{oe}%
+\def\ae{ae}%
+\def\aa{aa}%
+\def\OE{OE}%
+\def\AE{AE}%
+\def\AA{AA}%
+\def\o{o}%
+\def\O{O}%
+\def\l{l}%
+\def\L{L}%
+\def\ss{ss}%
+\let\w=\indexdummyfont
+\let\t=\indexdummyfont
+\let\r=\indexdummyfont
+\let\i=\indexdummyfont
+\let\b=\indexdummyfont
+\let\emph=\indexdummyfont
+\let\strong=\indexdummyfont
+\let\cite=\indexdummyfont
+\let\sc=\indexdummyfont
+%Don't no-op \tt, since it isn't a user-level command
+% and is used in the definitions of the active chars like <, >, |...
+%\let\tt=\indexdummyfont
+\let\tclose=\indexdummyfont
+\let\code=\indexdummyfont
+\let\url=\indexdummyfont
+\let\uref=\indexdummyfont
+\let\env=\indexdummyfont
+\let\command=\indexdummyfont
+\let\option=\indexdummyfont
+\let\file=\indexdummyfont
+\let\samp=\indexdummyfont
+\let\kbd=\indexdummyfont
+\let\key=\indexdummyfont
+\let\var=\indexdummyfont
+\let\TeX=\indexdummytex
+\let\dots=\indexdummydots
+\def\@{@}%
+}
+
+% To define \realbackslash, we must make \ not be an escape.
+% We must first make another character (@) an escape
+% so we do not become unable to do a definition.
+
+{\catcode`\@=0 \catcode`\\=\other
+ @gdef@realbackslash{\}}
+
+\let\indexbackslash=0 %overridden during \printindex.
+\let\SETmarginindex=\relax % put index entries in margin (undocumented)?
+
+% For \ifx comparisons.
+\def\emptymacro{\empty}
+
+% Most index entries go through here, but \dosubind is the general case.
+%
+\def\doind#1#2{\dosubind{#1}{#2}\empty}
+
+% Workhorse for all \fooindexes.
+% #1 is name of index, #2 is stuff to put there, #3 is subentry --
+% \empty if called from \doind, as we usually are. The main exception
+% is with defuns, which call us directly.
+%
+\def\dosubind#1#2#3{%
+ % Put the index entry in the margin if desired.
+ \ifx\SETmarginindex\relax\else
+ \insert\margin{\hbox{\vrule height8pt depth3pt width0pt #2}}%
+ \fi
+ {%
+ \count255=\lastpenalty
+ {%
+ \indexdummies % Must do this here, since \bf, etc expand at this stage
+ \escapechar=`\\
+ {%
+ \let\folio = 0% We will expand all macros now EXCEPT \folio.
+ \def\rawbackslashxx{\indexbackslash}% \indexbackslash isn't defined now
+ % so it will be output as is; and it will print as backslash.
+ %
+ \def\thirdarg{#3}%
+ %
+ % If third arg is present, precede it with space in sort key.
+ \ifx\thirdarg\emptymacro
+ \let\subentry = \empty
+ \else
+ \def\subentry{ #3}%
+ \fi
+ %
+ % First process the index-string with all font commands turned off
+ % to get the string to sort by.
+ {\indexnofonts \xdef\indexsorttmp{#2\subentry}}%
+ %
+ % Now produce the complete index entry, with both the sort key and the
+ % original text, including any font commands.
+ \toks0 = {#2}%
+ \edef\temp{%
+ \write\csname#1indfile\endcsname{%
+ \realbackslash entry{\indexsorttmp}{\folio}{\the\toks0}}%
+ }%
+ %
+ % If third (subentry) arg is present, add it to the index string.
+ \ifx\thirdarg\emptymacro \else
+ \toks0 = {#3}%
+ \edef\temp{\temp{\the\toks0}}%
+ \fi
+ %
+ % If a skip is the last thing on the list now, preserve it
+ % by backing up by \lastskip, doing the \write, then inserting
+ % the skip again. Otherwise, the whatsit generated by the
+ % \write will make \lastskip zero. The result is that sequences
+ % like this:
+ % @end defun
+ % @tindex whatever
+ % @defun ...
+ % will have extra space inserted, because the \medbreak in the
+ % start of the @defun won't see the skip inserted by the @end of
+ % the previous defun.
+ %
+ % But don't do any of this if we're not in vertical mode. We
+ % don't want to do a \vskip and prematurely end a paragraph.
+ %
+ % Avoid page breaks due to these extra skips, too.
+ %
+ \iflinks
+ \ifvmode
+ \skip0 = \lastskip
+ \ifdim\lastskip = 0pt \else \nobreak\vskip-\lastskip \fi
+ \fi
+ %
+ \temp % do the write
+ %
+ %
+ \ifvmode \ifdim\skip0 = 0pt \else \nobreak\vskip\skip0 \fi \fi
+ \fi
+ }%
+ }%
+ \penalty\count255
+ }%
+}
+
+% The index entry written in the file actually looks like
+% \entry {sortstring}{page}{topic}
+% or
+% \entry {sortstring}{page}{topic}{subtopic}
+% The texindex program reads in these files and writes files
+% containing these kinds of lines:
+% \initial {c}
+% before the first topic whose initial is c
+% \entry {topic}{pagelist}
+% for a topic that is used without subtopics
+% \primary {topic}
+% for the beginning of a topic that is used with subtopics
+% \secondary {subtopic}{pagelist}
+% for each subtopic.
+
+% Define the user-accessible indexing commands
+% @findex, @vindex, @kindex, @cindex.
+
+\def\findex {\fnindex}
+\def\kindex {\kyindex}
+\def\cindex {\cpindex}
+\def\vindex {\vrindex}
+\def\tindex {\tpindex}
+\def\pindex {\pgindex}
+
+\def\cindexsub {\begingroup\obeylines\cindexsub}
+{\obeylines %
+\gdef\cindexsub "#1" #2^^M{\endgroup %
+\dosubind{cp}{#2}{#1}}}
+
+% Define the macros used in formatting output of the sorted index material.
+
+% @printindex causes a particular index (the ??s file) to get printed.
+% It does not print any chapter heading (usually an @unnumbered).
+%
+\def\printindex{\parsearg\doprintindex}
+\def\doprintindex#1{\begingroup
+ \dobreak \chapheadingskip{10000}%
+ %
+ \indexfonts \rm
+ \tolerance = 9500
+ \indexbreaks
+ %
+ % See if the index file exists and is nonempty.
+ % Change catcode of @ here so that if the index file contains
+ % \initial {@}
+ % as its first line, TeX doesn't complain about mismatched braces
+ % (because it thinks @} is a control sequence).
+ \catcode`\@ = 11
+ \openin 1 \jobname.#1s
+ \ifeof 1
+ % \enddoublecolumns gets confused if there is no text in the index,
+ % and it loses the chapter title and the aux file entries for the
+ % index. The easiest way to prevent this problem is to make sure
+ % there is some text.
+ (Index is nonexistent)
+ \else
+ %
+ % If the index file exists but is empty, then \openin leaves \ifeof
+ % false. We have to make TeX try to read something from the file, so
+ % it can discover if there is anything in it.
+ \read 1 to \temp
+ \ifeof 1
+ (Index is empty)
+ \else
+ % Index files are almost Texinfo source, but we use \ as the escape
+ % character. It would be better to use @, but that's too big a change
+ % to make right now.
+ \def\indexbackslash{\rawbackslashxx}%
+ \catcode`\\ = 0
+ \escapechar = `\\
+ \begindoublecolumns
+ \input \jobname.#1s
+ \enddoublecolumns
+ \fi
+ \fi
+ \closein 1
+\endgroup}
+
+% These macros are used by the sorted index file itself.
+% Change them to control the appearance of the index.
+
+\def\initial#1{{%
+ % Some minor font changes for the special characters.
+ \let\tentt=\sectt \let\tt=\sectt \let\sf=\sectt
+ %
+ % Remove any glue we may have, we'll be inserting our own.
+ \removelastskip
+ %
+ % We like breaks before the index initials, so insert a bonus.
+ \penalty -300
+ %
+ % Typeset the initial. Making this add up to a whole number of
+ % baselineskips increases the chance of the dots lining up from column
+ % to column. It still won't often be perfect, because of the stretch
+ % we need before each entry, but it's better.
+ %
+ % No shrink because it confuses \balancecolumns.
+ \vskip 1.67\baselineskip plus .5\baselineskip
+ \leftline{\secbf #1}%
+ \vskip .33\baselineskip plus .1\baselineskip
+ %
+ % Do our best not to break after the initial.
+ \nobreak
+}}
+
+% This typesets a paragraph consisting of #1, dot leaders, and then #2
+% flush to the right margin. It is used for index and table of contents
+% entries. The paragraph is indented by \leftskip.
+%
+\def\entry#1#2{\begingroup
+ %
+ % Start a new paragraph if necessary, so our assignments below can't
+ % affect previous text.
+ \par
+ %
+ % Do not fill out the last line with white space.
+ \parfillskip = 0in
+ %
+ % No extra space above this paragraph.
+ \parskip = 0in
+ %
+ % Do not prefer a separate line ending with a hyphen to fewer lines.
+ \finalhyphendemerits = 0
+ %
+ % \hangindent is only relevant when the entry text and page number
+ % don't both fit on one line. In that case, bob suggests starting the
+ % dots pretty far over on the line. Unfortunately, a large
+ % indentation looks wrong when the entry text itself is broken across
+ % lines. So we use a small indentation and put up with long leaders.
+ %
+ % \hangafter is reset to 1 (which is the value we want) at the start
+ % of each paragraph, so we need not do anything with that.
+ \hangindent = 2em
+ %
+ % When the entry text needs to be broken, just fill out the first line
+ % with blank space.
+ \rightskip = 0pt plus1fil
+ %
+ % A bit of stretch before each entry for the benefit of balancing columns.
+ \vskip 0pt plus1pt
+ %
+ % Start a ``paragraph'' for the index entry so the line breaking
+ % parameters we've set above will have an effect.
+ \noindent
+ %
+ % Insert the text of the index entry. TeX will do line-breaking on it.
+ #1%
+ % The following is kludged to not output a line of dots in the index if
+ % there are no page numbers. The next person who breaks this will be
+ % cursed by a Unix daemon.
+ \def\tempa{{\rm }}%
+ \def\tempb{#2}%
+ \edef\tempc{\tempa}%
+ \edef\tempd{\tempb}%
+ \ifx\tempc\tempd\ \else%
+ %
+ % If we must, put the page number on a line of its own, and fill out
+ % this line with blank space. (The \hfil is overwhelmed with the
+ % fill leaders glue in \indexdotfill if the page number does fit.)
+ \hfil\penalty50
+ \null\nobreak\indexdotfill % Have leaders before the page number.
+ %
+ % The `\ ' here is removed by the implicit \unskip that TeX does as
+ % part of (the primitive) \par. Without it, a spurious underfull
+ % \hbox ensues.
+ \ #2% The page number ends the paragraph.
+ \fi%
+ \par
+\endgroup}
+
+% Like \dotfill except takes at least 1 em.
+\def\indexdotfill{\cleaders
+ \hbox{$\mathsurround=0pt \mkern1.5mu ${\it .}$ \mkern1.5mu$}\hskip 1em plus 1fill}
+
+\def\primary #1{\line{#1\hfil}}
+
+\newskip\secondaryindent \secondaryindent=0.5cm
+
+\def\secondary #1#2{
+{\parfillskip=0in \parskip=0in
+\hangindent =1in \hangafter=1
+\noindent\hskip\secondaryindent\hbox{#1}\indexdotfill #2\par
+}}
+
+% Define two-column mode, which we use to typeset indexes.
+% Adapted from the TeXbook, page 416, which is to say,
+% the manmac.tex format used to print the TeXbook itself.
+\catcode`\@=11
+
+\newbox\partialpage
+\newdimen\doublecolumnhsize
+
+\def\begindoublecolumns{\begingroup % ended by \enddoublecolumns
+ % Grab any single-column material above us.
+ \output = {\global\setbox\partialpage = \vbox{%
+ %
+ % Here is a possibility not foreseen in manmac: if we accumulate a
+ % whole lot of material, we might end up calling this \output
+ % routine twice in a row (see the doublecol-lose test, which is
+ % essentially a couple of indexes with @setchapternewpage off). In
+ % that case, we must prevent the second \partialpage from
+ % simply overwriting the first, causing us to lose the page.
+ % This will preserve it until a real output routine can ship it
+ % out. Generally, \partialpage will be empty when this runs and
+ % this will be a no-op.
+ \unvbox\partialpage
+ %
+ % Unvbox the main output page.
+ \unvbox255
+ \kern-\topskip \kern\baselineskip
+ }}%
+ \eject % run that output routine to set \partialpage
+ %
+ % Use the double-column output routine for subsequent pages.
+ \output = {\doublecolumnout}%
+ %
+ % Change the page size parameters. We could do this once outside this
+ % routine, in each of @smallbook, @afourpaper, and the default 8.5x11
+ % format, but then we repeat the same computation. Repeating a couple
+ % of assignments once per index is clearly meaningless for the
+ % execution time, so we may as well do it in one place.
+ %
+ % First we halve the line length, less a little for the gutter between
+ % the columns. We compute the gutter based on the line length, so it
+ % changes automatically with the paper format. The magic constant
+ % below is chosen so that the gutter has the same value (well, +-<1pt)
+ % as it did when we hard-coded it.
+ %
+ % We put the result in a separate register, \doublecolumhsize, so we
+ % can restore it in \pagesofar, after \hsize itself has (potentially)
+ % been clobbered.
+ %
+ \doublecolumnhsize = \hsize
+ \advance\doublecolumnhsize by -.04154\hsize
+ \divide\doublecolumnhsize by 2
+ \hsize = \doublecolumnhsize
+ %
+ % Double the \vsize as well. (We don't need a separate register here,
+ % since nobody clobbers \vsize.)
+ \advance\vsize by -\ht\partialpage
+ \vsize = 2\vsize
+}
+
+% The double-column output routine for all double-column pages except
+% the last.
+%
+\def\doublecolumnout{%
+ \splittopskip=\topskip \splitmaxdepth=\maxdepth
+ % Get the available space for the double columns -- the normal
+ % (undoubled) page height minus any material left over from the
+ % previous page.
+ \dimen@ = \vsize
+ \divide\dimen@ by 2
+ %
+ % box0 will be the left-hand column, box2 the right.
+ \setbox0=\vsplit255 to\dimen@ \setbox2=\vsplit255 to\dimen@
+ \onepageout\pagesofar
+ \unvbox255
+ \penalty\outputpenalty
+}
+\def\pagesofar{%
+ % Re-output the contents of the output page -- any previous material,
+ % followed by the two boxes we just split, in box0 and box2.
+ \advance\vsize by \ht\partialpage
+ \unvbox\partialpage
+ %
+ \hsize = \doublecolumnhsize
+ \wd0=\hsize \wd2=\hsize
+ \hbox to\pagewidth{\box0\hfil\box2}%
+}
+\def\enddoublecolumns{%
+ \output = {%
+ % Split the last of the double-column material. Leave it on the
+ % current page, no automatic page break.
+ \balancecolumns
+ %
+ % If we end up splitting too much material for the current page,
+ % though, there will be another page break right after this \output
+ % invocation ends. Having called \balancecolumns once, we do not
+ % want to call it again. Therefore, reset \output to its normal
+ % definition right away. (We hope \balancecolumns will never be
+ % called on to balance too much material, but if it is, this makes
+ % the output somewhat more palatable.)
+ \global\output = {\onepageout{\pagecontents\PAGE}}%
+ }%
+ \eject
+ \endgroup % started in \begindoublecolumns
+ %
+ % \pagegoal was set to the doubled \vsize above, since we restarted
+ % the current page. We're now back to normal single-column
+ % typesetting, so reset \pagegoal to the normal \vsize (after the
+ % \endgroup where \vsize got restored).
+ \pagegoal = \vsize
+}
+\def\balancecolumns{%
+ % Called at the end of the double column material.
+ \setbox0 = \vbox{\unvbox255}% like \box255 but more efficient, see p.120.
+ \dimen@ = \ht0
+ \advance\dimen@ by \topskip
+ \advance\dimen@ by-\baselineskip
+ \divide\dimen@ by 2 % target to split to
+ %debug\message{final 2-column material height=\the\ht0, target=\the\dimen@.}%
+ \splittopskip = \topskip
+ % Loop until we get a decent breakpoint.
+ {%
+ \vbadness = 10000
+ \loop
+ \global\setbox3 = \copy0
+ \global\setbox1 = \vsplit3 to \dimen@
+ \ifdim\ht3>\dimen@
+ \global\advance\dimen@ by 1pt
+ \repeat
+ }%
+ %debug\message{split to \the\dimen@, column heights: \the\ht1, \the\ht3.}%
+ \setbox0=\vbox to\dimen@{\unvbox1}%
+ \setbox2=\vbox to\dimen@{\unvbox3}%
+ %
+ \pagesofar
+}
+\catcode`\@ = \other
+
+
+\message{sectioning,}
+% Define chapters, sections, etc.
+
+\newcount\chapno
+\newcount\secno \secno=0
+\newcount\subsecno \subsecno=0
+\newcount\subsubsecno \subsubsecno=0
+
+% This counter is funny since it counts through charcodes of letters A, B, ...
+\newcount\appendixno \appendixno = `\@
+\def\appendixletter{\char\the\appendixno}
+
+% Each @chapter defines this as the name of the chapter.
+% page headings and footings can use it. @section does likewise.
+\def\thischapter{}
+\def\thissection{}
+
+\newcount\absseclevel % used to calculate proper heading level
+\newcount\secbase\secbase=0 % @raise/lowersections modify this count
+
+% @raisesections: treat @section as chapter, @subsection as section, etc.
+\def\raisesections{\global\advance\secbase by -1}
+\let\up=\raisesections % original BFox name
+
+% @lowersections: treat @chapter as section, @section as subsection, etc.
+\def\lowersections{\global\advance\secbase by 1}
+\let\down=\lowersections % original BFox name
+
+% Choose a numbered-heading macro
+% #1 is heading level if unmodified by @raisesections or @lowersections
+% #2 is text for heading
+\def\numhead#1#2{\absseclevel=\secbase\advance\absseclevel by #1
+\ifcase\absseclevel
+ \chapterzzz{#2}
+\or
+ \seczzz{#2}
+\or
+ \numberedsubseczzz{#2}
+\or
+ \numberedsubsubseczzz{#2}
+\else
+ \ifnum \absseclevel<0
+ \chapterzzz{#2}
+ \else
+ \numberedsubsubseczzz{#2}
+ \fi
+\fi
+}
+
+% like \numhead, but chooses appendix heading levels
+\def\apphead#1#2{\absseclevel=\secbase\advance\absseclevel by #1
+\ifcase\absseclevel
+ \appendixzzz{#2}
+\or
+ \appendixsectionzzz{#2}
+\or
+ \appendixsubseczzz{#2}
+\or
+ \appendixsubsubseczzz{#2}
+\else
+ \ifnum \absseclevel<0
+ \appendixzzz{#2}
+ \else
+ \appendixsubsubseczzz{#2}
+ \fi
+\fi
+}
+
+% like \numhead, but chooses numberless heading levels
+\def\unnmhead#1#2{\absseclevel=\secbase\advance\absseclevel by #1
+\ifcase\absseclevel
+ \unnumberedzzz{#2}
+\or
+ \unnumberedseczzz{#2}
+\or
+ \unnumberedsubseczzz{#2}
+\or
+ \unnumberedsubsubseczzz{#2}
+\else
+ \ifnum \absseclevel<0
+ \unnumberedzzz{#2}
+ \else
+ \unnumberedsubsubseczzz{#2}
+ \fi
+\fi
+}
+
+% @chapter, @appendix, @unnumbered.
+\def\thischaptername{No Chapter Title}
+\outer\def\chapter{\parsearg\chapteryyy}
+\def\chapteryyy #1{\numhead0{#1}} % normally numhead0 calls chapterzzz
+\def\chapterzzz #1{%
+\secno=0 \subsecno=0 \subsubsecno=0
+\global\advance \chapno by 1 \message{\putwordChapter\space \the\chapno}%
+\chapmacro {#1}{\the\chapno}%
+\gdef\thissection{#1}%
+\gdef\thischaptername{#1}%
+% We don't substitute the actual chapter name into \thischapter
+% because we don't want its macros evaluated now.
+\xdef\thischapter{\putwordChapter{} \the\chapno: \noexpand\thischaptername}%
+\toks0 = {#1}%
+\edef\temp{\noexpand\writetocentry{\realbackslash chapentry{\the\toks0}%
+ {\the\chapno}}}%
+\temp
+\donoderef
+\global\let\section = \numberedsec
+\global\let\subsection = \numberedsubsec
+\global\let\subsubsection = \numberedsubsubsec
+}
+
+\outer\def\appendix{\parsearg\appendixyyy}
+\def\appendixyyy #1{\apphead0{#1}} % normally apphead0 calls appendixzzz
+\def\appendixzzz #1{%
+\secno=0 \subsecno=0 \subsubsecno=0
+\global\advance \appendixno by 1
+\message{\putwordAppendix\space \appendixletter}%
+\chapmacro {#1}{\putwordAppendix{} \appendixletter}%
+\gdef\thissection{#1}%
+\gdef\thischaptername{#1}%
+\xdef\thischapter{\putwordAppendix{} \appendixletter: \noexpand\thischaptername}%
+\toks0 = {#1}%
+\edef\temp{\noexpand\writetocentry{\realbackslash chapentry{\the\toks0}%
+ {\putwordAppendix{} \appendixletter}}}%
+\temp
+\appendixnoderef
+\global\let\section = \appendixsec
+\global\let\subsection = \appendixsubsec
+\global\let\subsubsection = \appendixsubsubsec
+}
+
+% @centerchap is like @unnumbered, but the heading is centered.
+\outer\def\centerchap{\parsearg\centerchapyyy}
+\def\centerchapyyy #1{{\let\unnumbchapmacro=\centerchapmacro \unnumberedyyy{#1}}}
+
+% @top is like @unnumbered.
+\outer\def\top{\parsearg\unnumberedyyy}
+
+\outer\def\unnumbered{\parsearg\unnumberedyyy}
+\def\unnumberedyyy #1{\unnmhead0{#1}} % normally unnmhead0 calls unnumberedzzz
+\def\unnumberedzzz #1{%
+\secno=0 \subsecno=0 \subsubsecno=0
+%
+% This used to be simply \message{#1}, but TeX fully expands the
+% argument to \message. Therefore, if #1 contained @-commands, TeX
+% expanded them. For example, in `@unnumbered The @cite{Book}', TeX
+% expanded @cite (which turns out to cause errors because \cite is meant
+% to be executed, not expanded).
+%
+% Anyway, we don't want the fully-expanded definition of @cite to appear
+% as a result of the \message, we just want `@cite' itself. We use
+% \the<toks register> to achieve this: TeX expands \the<toks> only once,
+% simply yielding the contents of <toks register>. (We also do this for
+% the toc entries.)
+\toks0 = {#1}\message{(\the\toks0)}%
+%
+\unnumbchapmacro {#1}%
+\gdef\thischapter{#1}\gdef\thissection{#1}%
+\toks0 = {#1}%
+\edef\temp{\noexpand\writetocentry{\realbackslash unnumbchapentry{\the\toks0}}}%
+\temp
+\unnumbnoderef
+\global\let\section = \unnumberedsec
+\global\let\subsection = \unnumberedsubsec
+\global\let\subsubsection = \unnumberedsubsubsec
+}
+
+% Sections.
+\outer\def\numberedsec{\parsearg\secyyy}
+\def\secyyy #1{\numhead1{#1}} % normally calls seczzz
+\def\seczzz #1{%
+\subsecno=0 \subsubsecno=0 \global\advance \secno by 1 %
+\gdef\thissection{#1}\secheading {#1}{\the\chapno}{\the\secno}%
+\toks0 = {#1}%
+\edef\temp{\noexpand\writetocentry{\realbackslash secentry{\the\toks0}%
+ {\the\chapno}{\the\secno}}}%
+\temp
+\donoderef
+\nobreak
+}
+
+\outer\def\appendixsection{\parsearg\appendixsecyyy}
+\outer\def\appendixsec{\parsearg\appendixsecyyy}
+\def\appendixsecyyy #1{\apphead1{#1}} % normally calls appendixsectionzzz
+\def\appendixsectionzzz #1{%
+\subsecno=0 \subsubsecno=0 \global\advance \secno by 1 %
+\gdef\thissection{#1}\secheading {#1}{\appendixletter}{\the\secno}%
+\toks0 = {#1}%
+\edef\temp{\noexpand\writetocentry{\realbackslash secentry{\the\toks0}%
+ {\appendixletter}{\the\secno}}}%
+\temp
+\appendixnoderef
+\nobreak
+}
+
+\outer\def\unnumberedsec{\parsearg\unnumberedsecyyy}
+\def\unnumberedsecyyy #1{\unnmhead1{#1}} % normally calls unnumberedseczzz
+\def\unnumberedseczzz #1{%
+\plainsecheading {#1}\gdef\thissection{#1}%
+\toks0 = {#1}%
+\edef\temp{\noexpand\writetocentry{\realbackslash unnumbsecentry{\the\toks0}}}%
+\temp
+\unnumbnoderef
+\nobreak
+}
+
+% Subsections.
+\outer\def\numberedsubsec{\parsearg\numberedsubsecyyy}
+\def\numberedsubsecyyy #1{\numhead2{#1}} % normally calls numberedsubseczzz
+\def\numberedsubseczzz #1{%
+\gdef\thissection{#1}\subsubsecno=0 \global\advance \subsecno by 1 %
+\subsecheading {#1}{\the\chapno}{\the\secno}{\the\subsecno}%
+\toks0 = {#1}%
+\edef\temp{\noexpand\writetocentry{\realbackslash subsecentry{\the\toks0}%
+ {\the\chapno}{\the\secno}{\the\subsecno}}}%
+\temp
+\donoderef
+\nobreak
+}
+
+\outer\def\appendixsubsec{\parsearg\appendixsubsecyyy}
+\def\appendixsubsecyyy #1{\apphead2{#1}} % normally calls appendixsubseczzz
+\def\appendixsubseczzz #1{%
+\gdef\thissection{#1}\subsubsecno=0 \global\advance \subsecno by 1 %
+\subsecheading {#1}{\appendixletter}{\the\secno}{\the\subsecno}%
+\toks0 = {#1}%
+\edef\temp{\noexpand\writetocentry{\realbackslash subsecentry{\the\toks0}%
+ {\appendixletter}{\the\secno}{\the\subsecno}}}%
+\temp
+\appendixnoderef
+\nobreak
+}
+
+\outer\def\unnumberedsubsec{\parsearg\unnumberedsubsecyyy}
+\def\unnumberedsubsecyyy #1{\unnmhead2{#1}} %normally calls unnumberedsubseczzz
+\def\unnumberedsubseczzz #1{%
+\plainsubsecheading {#1}\gdef\thissection{#1}%
+\toks0 = {#1}%
+\edef\temp{\noexpand\writetocentry{\realbackslash unnumbsubsecentry%
+ {\the\toks0}}}%
+\temp
+\unnumbnoderef
+\nobreak
+}
+
+% Subsubsections.
+\outer\def\numberedsubsubsec{\parsearg\numberedsubsubsecyyy}
+\def\numberedsubsubsecyyy #1{\numhead3{#1}} % normally numberedsubsubseczzz
+\def\numberedsubsubseczzz #1{%
+\gdef\thissection{#1}\global\advance \subsubsecno by 1 %
+\subsubsecheading {#1}
+ {\the\chapno}{\the\secno}{\the\subsecno}{\the\subsubsecno}%
+\toks0 = {#1}%
+\edef\temp{\noexpand\writetocentry{\realbackslash subsubsecentry{\the\toks0}%
+ {\the\chapno}{\the\secno}{\the\subsecno}{\the\subsubsecno}}}%
+\temp
+\donoderef
+\nobreak
+}
+
+\outer\def\appendixsubsubsec{\parsearg\appendixsubsubsecyyy}
+\def\appendixsubsubsecyyy #1{\apphead3{#1}} % normally appendixsubsubseczzz
+\def\appendixsubsubseczzz #1{%
+\gdef\thissection{#1}\global\advance \subsubsecno by 1 %
+\subsubsecheading {#1}
+ {\appendixletter}{\the\secno}{\the\subsecno}{\the\subsubsecno}%
+\toks0 = {#1}%
+\edef\temp{\noexpand\writetocentry{\realbackslash subsubsecentry{\the\toks0}%
+ {\appendixletter}{\the\secno}{\the\subsecno}{\the\subsubsecno}}}%
+\temp
+\appendixnoderef
+\nobreak
+}
+
+\outer\def\unnumberedsubsubsec{\parsearg\unnumberedsubsubsecyyy}
+\def\unnumberedsubsubsecyyy #1{\unnmhead3{#1}} %normally unnumberedsubsubseczzz
+\def\unnumberedsubsubseczzz #1{%
+\plainsubsubsecheading {#1}\gdef\thissection{#1}%
+\toks0 = {#1}%
+\edef\temp{\noexpand\writetocentry{\realbackslash unnumbsubsubsecentry%
+ {\the\toks0}}}%
+\temp
+\unnumbnoderef
+\nobreak
+}
+
+% These are variants which are not "outer", so they can appear in @ifinfo.
+% Actually, they should now be obsolete; ordinary section commands should work.
+\def\infotop{\parsearg\unnumberedzzz}
+\def\infounnumbered{\parsearg\unnumberedzzz}
+\def\infounnumberedsec{\parsearg\unnumberedseczzz}
+\def\infounnumberedsubsec{\parsearg\unnumberedsubseczzz}
+\def\infounnumberedsubsubsec{\parsearg\unnumberedsubsubseczzz}
+
+\def\infoappendix{\parsearg\appendixzzz}
+\def\infoappendixsec{\parsearg\appendixseczzz}
+\def\infoappendixsubsec{\parsearg\appendixsubseczzz}
+\def\infoappendixsubsubsec{\parsearg\appendixsubsubseczzz}
+
+\def\infochapter{\parsearg\chapterzzz}
+\def\infosection{\parsearg\sectionzzz}
+\def\infosubsection{\parsearg\subsectionzzz}
+\def\infosubsubsection{\parsearg\subsubsectionzzz}
+
+% These macros control what the section commands do, according
+% to what kind of chapter we are in (ordinary, appendix, or unnumbered).
+% Define them by default for a numbered chapter.
+\global\let\section = \numberedsec
+\global\let\subsection = \numberedsubsec
+\global\let\subsubsection = \numberedsubsubsec
+
+% Define @majorheading, @heading and @subheading
+
+% NOTE on use of \vbox for chapter headings, section headings, and such:
+% 1) We use \vbox rather than the earlier \line to permit
+% overlong headings to fold.
+% 2) \hyphenpenalty is set to 10000 because hyphenation in a
+% heading is obnoxious; this forbids it.
+% 3) Likewise, headings look best if no \parindent is used, and
+% if justification is not attempted. Hence \raggedright.
+
+
+\def\majorheading{\parsearg\majorheadingzzz}
+\def\majorheadingzzz #1{%
+{\advance\chapheadingskip by 10pt \chapbreak }%
+{\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000
+ \parindent=0pt\raggedright
+ \rm #1\hfill}}\bigskip \par\penalty 200}
+
+\def\chapheading{\parsearg\chapheadingzzz}
+\def\chapheadingzzz #1{\chapbreak %
+{\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000
+ \parindent=0pt\raggedright
+ \rm #1\hfill}}\bigskip \par\penalty 200}
+
+% @heading, @subheading, @subsubheading.
+\def\heading{\parsearg\plainsecheading}
+\def\subheading{\parsearg\plainsubsecheading}
+\def\subsubheading{\parsearg\plainsubsubsecheading}
+
+% These macros generate a chapter, section, etc. heading only
+% (including whitespace, linebreaking, etc. around it),
+% given all the information in convenient, parsed form.
+
+%%% Args are the skip and penalty (usually negative)
+\def\dobreak#1#2{\par\ifdim\lastskip<#1\removelastskip\penalty#2\vskip#1\fi}
+
+\def\setchapterstyle #1 {\csname CHAPF#1\endcsname}
+
+%%% Define plain chapter starts, and page on/off switching for it
+% Parameter controlling skip before chapter headings (if needed)
+
+\newskip\chapheadingskip
+
+\def\chapbreak{\dobreak \chapheadingskip {-4000}}
+\def\chappager{\par\vfill\supereject}
+\def\chapoddpage{\chappager \ifodd\pageno \else \hbox to 0pt{} \chappager\fi}
+
+\def\setchapternewpage #1 {\csname CHAPPAG#1\endcsname}
+
+\def\CHAPPAGoff{%
+\global\let\contentsalignmacro = \chappager
+\global\let\pchapsepmacro=\chapbreak
+\global\let\pagealignmacro=\chappager}
+
+\def\CHAPPAGon{%
+\global\let\contentsalignmacro = \chappager
+\global\let\pchapsepmacro=\chappager
+\global\let\pagealignmacro=\chappager
+\global\def\HEADINGSon{\HEADINGSsingle}}
+
+\def\CHAPPAGodd{
+\global\let\contentsalignmacro = \chapoddpage
+\global\let\pchapsepmacro=\chapoddpage
+\global\let\pagealignmacro=\chapoddpage
+\global\def\HEADINGSon{\HEADINGSdouble}}
+
+\CHAPPAGon
+
+\def\CHAPFplain{
+\global\let\chapmacro=\chfplain
+\global\let\unnumbchapmacro=\unnchfplain
+\global\let\centerchapmacro=\centerchfplain}
+
+% Plain chapter opening.
+% #1 is the text, #2 the chapter number or empty if unnumbered.
+\def\chfplain#1#2{%
+ \pchapsepmacro
+ {%
+ \chapfonts \rm
+ \def\chapnum{#2}%
+ \setbox0 = \hbox{#2\ifx\chapnum\empty\else\enspace\fi}%
+ \vbox{\hyphenpenalty=10000 \tolerance=5000 \parindent=0pt \raggedright
+ \hangindent = \wd0 \centerparametersmaybe
+ \unhbox0 #1\par}%
+ }%
+ \nobreak\bigskip % no page break after a chapter title
+ \nobreak
+}
+
+% Plain opening for unnumbered.
+\def\unnchfplain#1{\chfplain{#1}{}}
+
+% @centerchap -- centered and unnumbered.
+\let\centerparametersmaybe = \relax
+\def\centerchfplain#1{{%
+ \def\centerparametersmaybe{%
+ \advance\rightskip by 3\rightskip
+ \leftskip = \rightskip
+ \parfillskip = 0pt
+ }%
+ \chfplain{#1}{}%
+}}
+
+\CHAPFplain % The default
+
+\def\unnchfopen #1{%
+\chapoddpage {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000
+ \parindent=0pt\raggedright
+ \rm #1\hfill}}\bigskip \par\nobreak
+}
+
+\def\chfopen #1#2{\chapoddpage {\chapfonts
+\vbox to 3in{\vfil \hbox to\hsize{\hfil #2} \hbox to\hsize{\hfil #1} \vfil}}%
+\par\penalty 5000 %
+}
+
+\def\centerchfopen #1{%
+\chapoddpage {\chapfonts \vbox{\hyphenpenalty=10000\tolerance=5000
+ \parindent=0pt
+ \hfill {\rm #1}\hfill}}\bigskip \par\nobreak
+}
+
+\def\CHAPFopen{
+\global\let\chapmacro=\chfopen
+\global\let\unnumbchapmacro=\unnchfopen
+\global\let\centerchapmacro=\centerchfopen}
+
+
+% Section titles.
+\newskip\secheadingskip
+\def\secheadingbreak{\dobreak \secheadingskip {-1000}}
+\def\secheading#1#2#3{\sectionheading{sec}{#2.#3}{#1}}
+\def\plainsecheading#1{\sectionheading{sec}{}{#1}}
+
+% Subsection titles.
+\newskip \subsecheadingskip
+\def\subsecheadingbreak{\dobreak \subsecheadingskip {-500}}
+\def\subsecheading#1#2#3#4{\sectionheading{subsec}{#2.#3.#4}{#1}}
+\def\plainsubsecheading#1{\sectionheading{subsec}{}{#1}}
+
+% Subsubsection titles.
+\let\subsubsecheadingskip = \subsecheadingskip
+\let\subsubsecheadingbreak = \subsecheadingbreak
+\def\subsubsecheading#1#2#3#4#5{\sectionheading{subsubsec}{#2.#3.#4.#5}{#1}}
+\def\plainsubsubsecheading#1{\sectionheading{subsubsec}{}{#1}}
+
+
+% Print any size section title.
+%
+% #1 is the section type (sec/subsec/subsubsec), #2 is the section
+% number (maybe empty), #3 the text.
+\def\sectionheading#1#2#3{%
+ {%
+ \expandafter\advance\csname #1headingskip\endcsname by \parskip
+ \csname #1headingbreak\endcsname
+ }%
+ {%
+ % Switch to the right set of fonts.
+ \csname #1fonts\endcsname \rm
+ %
+ % Only insert the separating space if we have a section number.
+ \def\secnum{#2}%
+ \setbox0 = \hbox{#2\ifx\secnum\empty\else\enspace\fi}%
+ %
+ \vbox{\hyphenpenalty=10000 \tolerance=5000 \parindent=0pt \raggedright
+ \hangindent = \wd0 % zero if no section number
+ \unhbox0 #3}%
+ }%
+ \ifdim\parskip<10pt \nobreak\kern10pt\nobreak\kern-\parskip\fi \nobreak
+}
+
+
+\message{toc,}
+\newwrite\tocfile
+
+% Write an entry to the toc file, opening it if necessary.
+% Called from @chapter, etc. We supply {\folio} at the end of the
+% argument, which will end up as the last argument to the \...entry macro.
+%
+% We open the .toc file here instead of at @setfilename or any other
+% given time so that @contents can be put in the document anywhere.
+%
+\newif\iftocfileopened
+\def\writetocentry#1{%
+ \iftocfileopened\else
+ \immediate\openout\tocfile = \jobname.toc
+ \global\tocfileopenedtrue
+ \fi
+ \iflinks \write\tocfile{#1{\folio}}\fi
+}
+
+\newskip\contentsrightmargin \contentsrightmargin=1in
+\newcount\savepageno
+\newcount\lastnegativepageno \lastnegativepageno = -1
+
+% Finish up the main text and prepare to read what we've written
+% to \tocfile.
+%
+\def\startcontents#1{%
+ % If @setchapternewpage on, and @headings double, the contents should
+ % start on an odd page, unlike chapters. Thus, we maintain
+ % \contentsalignmacro in parallel with \pagealignmacro.
+ % From: Torbjorn Granlund <tege@matematik.su.se>
+ \contentsalignmacro
+ \immediate\closeout\tocfile
+ %
+ % Don't need to put `Contents' or `Short Contents' in the headline.
+ % It is abundantly clear what they are.
+ \unnumbchapmacro{#1}\def\thischapter{}%
+ \savepageno = \pageno
+ \begingroup % Set up to handle contents files properly.
+ \catcode`\\=0 \catcode`\{=1 \catcode`\}=2 \catcode`\@=11
+ % We can't do this, because then an actual ^ in a section
+ % title fails, e.g., @chapter ^ -- exponentiation. --karl, 9jul97.
+ %\catcode`\^=7 % to see ^^e4 as \"a etc. juha@piuha.ydi.vtt.fi
+ \raggedbottom % Worry more about breakpoints than the bottom.
+ \advance\hsize by -\contentsrightmargin % Don't use the full line length.
+ %
+ % Roman numerals for page numbers.
+ \ifnum \pageno>0 \pageno = \lastnegativepageno \fi
+}
+
+
+% Normal (long) toc.
+\def\contents{%
+ \startcontents{\putwordTableofContents}%
+ \openin 1 \jobname.toc
+ \ifeof 1 \else
+ \closein 1
+ \input \jobname.toc
+ \fi
+ \vfill \eject
+ \endgroup
+ \lastnegativepageno = \pageno
+ \pageno = \savepageno
+}
+
+% And just the chapters.
+\def\summarycontents{%
+ \startcontents{\putwordShortContents}%
+ %
+ \let\chapentry = \shortchapentry
+ \let\unnumbchapentry = \shortunnumberedentry
+ % We want a true roman here for the page numbers.
+ \secfonts
+ \let\rm=\shortcontrm \let\bf=\shortcontbf \let\sl=\shortcontsl
+ \rm
+ \hyphenpenalty = 10000
+ \advance\baselineskip by 1pt % Open it up a little.
+ \def\secentry ##1##2##3##4{}
+ \def\unnumbsecentry ##1##2{}
+ \def\subsecentry ##1##2##3##4##5{}
+ \def\unnumbsubsecentry ##1##2{}
+ \def\subsubsecentry ##1##2##3##4##5##6{}
+ \def\unnumbsubsubsecentry ##1##2{}
+ \openin 1 \jobname.toc
+ \ifeof 1 \else
+ \closein 1
+ \input \jobname.toc
+ \fi
+ \vfill \eject
+ \endgroup
+ \lastnegativepageno = \pageno
+ \pageno = \savepageno
+}
+\let\shortcontents = \summarycontents
+
+% These macros generate individual entries in the table of contents.
+% The first argument is the chapter or section name.
+% The last argument is the page number.
+% The arguments in between are the chapter number, section number, ...
+
+% Chapter-level things, for both the long and short contents.
+\def\chapentry#1#2#3{\dochapentry{#2\labelspace#1}{#3}}
+
+% See comments in \dochapentry re vbox and related settings
+\def\shortchapentry#1#2#3{%
+ \tocentry{\shortchaplabel{#2}\labelspace #1}{\doshortpageno{#3}}%
+}
+
+% Typeset the label for a chapter or appendix for the short contents.
+% The arg is, e.g. `Appendix A' for an appendix, or `3' for a chapter.
+% We could simplify the code here by writing out an \appendixentry
+% command in the toc file for appendices, instead of using \chapentry
+% for both, but it doesn't seem worth it.
+\setbox0 = \hbox{\shortcontrm \putwordAppendix }
+\newdimen\shortappendixwidth \shortappendixwidth = \wd0
+
+\def\shortchaplabel#1{%
+ % We typeset #1 in a box of constant width, regardless of the text of
+ % #1, so the chapter titles will come out aligned.
+ \setbox0 = \hbox{#1}%
+ \dimen0 = \ifdim\wd0 > \shortappendixwidth \shortappendixwidth \else 0pt \fi
+ %
+ % This space should be plenty, since a single number is .5em, and the
+ % widest letter (M) is 1em, at least in the Computer Modern fonts.
+ % (This space doesn't include the extra space that gets added after
+ % the label; that gets put in by \shortchapentry above.)
+ \advance\dimen0 by 1.1em
+ \hbox to \dimen0{#1\hfil}%
+}
+
+\def\unnumbchapentry#1#2{\dochapentry{#1}{#2}}
+\def\shortunnumberedentry#1#2{\tocentry{#1}{\doshortpageno{#2}}}
+
+% Sections.
+\def\secentry#1#2#3#4{\dosecentry{#2.#3\labelspace#1}{#4}}
+\def\unnumbsecentry#1#2{\dosecentry{#1}{#2}}
+
+% Subsections.
+\def\subsecentry#1#2#3#4#5{\dosubsecentry{#2.#3.#4\labelspace#1}{#5}}
+\def\unnumbsubsecentry#1#2{\dosubsecentry{#1}{#2}}
+
+% And subsubsections.
+\def\subsubsecentry#1#2#3#4#5#6{%
+ \dosubsubsecentry{#2.#3.#4.#5\labelspace#1}{#6}}
+\def\unnumbsubsubsecentry#1#2{\dosubsubsecentry{#1}{#2}}
+
+% This parameter controls the indentation of the various levels.
+\newdimen\tocindent \tocindent = 3pc
+
+% Now for the actual typesetting. In all these, #1 is the text and #2 is the
+% page number.
+%
+% If the toc has to be broken over pages, we want it to be at chapters
+% if at all possible; hence the \penalty.
+\def\dochapentry#1#2{%
+ \penalty-300 \vskip1\baselineskip plus.33\baselineskip minus.25\baselineskip
+ \begingroup
+ \chapentryfonts
+ \tocentry{#1}{\dopageno{#2}}%
+ \endgroup
+ \nobreak\vskip .25\baselineskip plus.1\baselineskip
+}
+
+\def\dosecentry#1#2{\begingroup
+ \secentryfonts \leftskip=\tocindent
+ \tocentry{#1}{\dopageno{#2}}%
+\endgroup}
+
+\def\dosubsecentry#1#2{\begingroup
+ \subsecentryfonts \leftskip=2\tocindent
+ \tocentry{#1}{\dopageno{#2}}%
+\endgroup}
+
+\def\dosubsubsecentry#1#2{\begingroup
+ \subsubsecentryfonts \leftskip=3\tocindent
+ \tocentry{#1}{\dopageno{#2}}%
+\endgroup}
+
+% Final typesetting of a toc entry; we use the same \entry macro as for
+% the index entries, but we want to suppress hyphenation here. (We
+% can't do that in the \entry macro, since index entries might consist
+% of hyphenated-identifiers-that-do-not-fit-on-a-line-and-nothing-else.)
+\def\tocentry#1#2{\begingroup
+ \vskip 0pt plus1pt % allow a little stretch for the sake of nice page breaks
+ % Do not use \turnoffactive in these arguments. Since the toc is
+ % typeset in cmr, so characters such as _ would come out wrong; we
+ % have to do the usual translation tricks.
+ \entry{#1}{#2}%
+\endgroup}
+
+% Space between chapter (or whatever) number and the title.
+\def\labelspace{\hskip1em \relax}
+
+\def\dopageno#1{{\rm #1}}
+\def\doshortpageno#1{{\rm #1}}
+
+\def\chapentryfonts{\secfonts \rm}
+\def\secentryfonts{\textfonts}
+\let\subsecentryfonts = \textfonts
+\let\subsubsecentryfonts = \textfonts
+
+
+\message{environments,}
+
+% Since these characters are used in examples, it should be an even number of
+% \tt widths. Each \tt character is 1en, so two makes it 1em.
+% Furthermore, these definitions must come after we define our fonts.
+\newbox\dblarrowbox \newbox\longdblarrowbox
+\newbox\pushcharbox \newbox\bullbox
+\newbox\equivbox \newbox\errorbox
+
+%{\tentt
+%\global\setbox\dblarrowbox = \hbox to 1em{\hfil$\Rightarrow$\hfil}
+%\global\setbox\longdblarrowbox = \hbox to 1em{\hfil$\mapsto$\hfil}
+%\global\setbox\pushcharbox = \hbox to 1em{\hfil$\dashv$\hfil}
+%\global\setbox\equivbox = \hbox to 1em{\hfil$\ptexequiv$\hfil}
+% Adapted from the manmac format (p.420 of TeXbook)
+%\global\setbox\bullbox = \hbox to 1em{\kern.15em\vrule height .75ex width .85ex
+% depth .1ex\hfil}
+%}
+
+% @point{}, @result{}, @expansion{}, @print{}, @equiv{}.
+\def\point{$\star$}
+\def\result{\leavevmode\raise.15ex\hbox to 1em{\hfil$\Rightarrow$\hfil}}
+\def\expansion{\leavevmode\raise.1ex\hbox to 1em{\hfil$\mapsto$\hfil}}
+\def\print{\leavevmode\lower.1ex\hbox to 1em{\hfil$\dashv$\hfil}}
+\def\equiv{\leavevmode\lower.1ex\hbox to 1em{\hfil$\ptexequiv$\hfil}}
+
+% Adapted from the TeXbook's \boxit.
+{\tentt \global\dimen0 = 3em}% Width of the box.
+\dimen2 = .55pt % Thickness of rules
+% The text. (`r' is open on the right, `e' somewhat less so on the left.)
+\setbox0 = \hbox{\kern-.75pt \tensf error\kern-1.5pt}
+
+\global\setbox\errorbox=\hbox to \dimen0{\hfil
+ \hsize = \dimen0 \advance\hsize by -5.8pt % Space to left+right.
+ \advance\hsize by -2\dimen2 % Rules.
+ \vbox{
+ \hrule height\dimen2
+ \hbox{\vrule width\dimen2 \kern3pt % Space to left of text.
+ \vtop{\kern2.4pt \box0 \kern2.4pt}% Space above/below.
+ \kern3pt\vrule width\dimen2}% Space to right.
+ \hrule height\dimen2}
+ \hfil}
+
+% The @error{} command.
+\def\error{\leavevmode\lower.7ex\copy\errorbox}
+
+% @tex ... @end tex escapes into raw Tex temporarily.
+% One exception: @ is still an escape character, so that @end tex works.
+% But \@ or @@ will get a plain tex @ character.
+
+\def\tex{\begingroup
+ \catcode `\\=0 \catcode `\{=1 \catcode `\}=2
+ \catcode `\$=3 \catcode `\&=4 \catcode `\#=6
+ \catcode `\^=7 \catcode `\_=8 \catcode `\~=13 \let~=\tie
+ \catcode `\%=14
+ \catcode 43=12 % plus
+ \catcode`\"=12
+ \catcode`\==12
+ \catcode`\|=12
+ \catcode`\<=12
+ \catcode`\>=12
+ \escapechar=`\\
+ %
+ \let\b=\ptexb
+ \let\bullet=\ptexbullet
+ \let\c=\ptexc
+ \let\,=\ptexcomma
+ \let\.=\ptexdot
+ \let\dots=\ptexdots
+ \let\equiv=\ptexequiv
+ \let\!=\ptexexclam
+ \let\i=\ptexi
+ \let\{=\ptexlbrace
+ \let\+=\tabalign
+ \let\}=\ptexrbrace
+ \let\*=\ptexstar
+ \let\t=\ptext
+ %
+ \def\endldots{\mathinner{\ldots\ldots\ldots\ldots}}%
+ \def\enddots{\relax\ifmmode\endldots\else$\mathsurround=0pt \endldots\,$\fi}%
+ \def\@{@}%
+\let\Etex=\endgroup}
+
+% Define @lisp ... @endlisp.
+% @lisp does a \begingroup so it can rebind things,
+% including the definition of @endlisp (which normally is erroneous).
+
+% Amount to narrow the margins by for @lisp.
+\newskip\lispnarrowing \lispnarrowing=0.4in
+
+% This is the definition that ^^M gets inside @lisp, @example, and other
+% such environments. \null is better than a space, since it doesn't
+% have any width.
+\def\lisppar{\null\endgraf}
+
+% Make each space character in the input produce a normal interword
+% space in the output. Don't allow a line break at this space, as this
+% is used only in environments like @example, where each line of input
+% should produce a line of output anyway.
+%
+{\obeyspaces %
+\gdef\sepspaces{\obeyspaces\let =\tie}}
+
+% Define \obeyedspace to be our active space, whatever it is. This is
+% for use in \parsearg.
+{\sepspaces%
+\global\let\obeyedspace= }
+
+% This space is always present above and below environments.
+\newskip\envskipamount \envskipamount = 0pt
+
+% Make spacing and below environment symmetrical. We use \parskip here
+% to help in doing that, since in @example-like environments \parskip
+% is reset to zero; thus the \afterenvbreak inserts no space -- but the
+% start of the next paragraph will insert \parskip
+%
+\def\aboveenvbreak{{\advance\envskipamount by \parskip
+\endgraf \ifdim\lastskip<\envskipamount
+\removelastskip \penalty-50 \vskip\envskipamount \fi}}
+
+\let\afterenvbreak = \aboveenvbreak
+
+% \nonarrowing is a flag. If "set", @lisp etc don't narrow margins.
+\let\nonarrowing=\relax
+
+% @cartouche ... @end cartouche: draw rectangle w/rounded corners around
+% environment contents.
+\font\circle=lcircle10
+\newdimen\circthick
+\newdimen\cartouter\newdimen\cartinner
+\newskip\normbskip\newskip\normpskip\newskip\normlskip
+\circthick=\fontdimen8\circle
+%
+\def\ctl{{\circle\char'013\hskip -6pt}}% 6pt from pl file: 1/2charwidth
+\def\ctr{{\hskip 6pt\circle\char'010}}
+\def\cbl{{\circle\char'012\hskip -6pt}}
+\def\cbr{{\hskip 6pt\circle\char'011}}
+\def\carttop{\hbox to \cartouter{\hskip\lskip
+ \ctl\leaders\hrule height\circthick\hfil\ctr
+ \hskip\rskip}}
+\def\cartbot{\hbox to \cartouter{\hskip\lskip
+ \cbl\leaders\hrule height\circthick\hfil\cbr
+ \hskip\rskip}}
+%
+\newskip\lskip\newskip\rskip
+
+\long\def\cartouche{%
+\begingroup
+ \lskip=\leftskip \rskip=\rightskip
+ \leftskip=0pt\rightskip=0pt %we want these *outside*.
+ \cartinner=\hsize \advance\cartinner by-\lskip
+ \advance\cartinner by-\rskip
+ \cartouter=\hsize
+ \advance\cartouter by 18.4pt % allow for 3pt kerns on either
+% side, and for 6pt waste from
+% each corner char, and rule thickness
+ \normbskip=\baselineskip \normpskip=\parskip \normlskip=\lineskip
+ % Flag to tell @lisp, etc., not to narrow margin.
+ \let\nonarrowing=\comment
+ \vbox\bgroup
+ \baselineskip=0pt\parskip=0pt\lineskip=0pt
+ \carttop
+ \hbox\bgroup
+ \hskip\lskip
+ \vrule\kern3pt
+ \vbox\bgroup
+ \hsize=\cartinner
+ \kern3pt
+ \begingroup
+ \baselineskip=\normbskip
+ \lineskip=\normlskip
+ \parskip=\normpskip
+ \vskip -\parskip
+\def\Ecartouche{%
+ \endgroup
+ \kern3pt
+ \egroup
+ \kern3pt\vrule
+ \hskip\rskip
+ \egroup
+ \cartbot
+ \egroup
+\endgroup
+}}
+
+
+% This macro is called at the beginning of all the @example variants,
+% inside a group.
+\def\nonfillstart{%
+ \aboveenvbreak
+ \inENV % This group ends at the end of the body
+ \hfuzz = 12pt % Don't be fussy
+ \sepspaces % Make spaces be word-separators rather than space tokens.
+ \singlespace
+ \let\par = \lisppar % don't ignore blank lines
+ \obeylines % each line of input is a line of output
+ \parskip = 0pt
+ \parindent = 0pt
+ \emergencystretch = 0pt % don't try to avoid overfull boxes
+ % @cartouche defines \nonarrowing to inhibit narrowing
+ % at next level down.
+ \ifx\nonarrowing\relax
+ \advance \leftskip by \lispnarrowing
+ \exdentamount=\lispnarrowing
+ \let\exdent=\nofillexdent
+ \let\nonarrowing=\relax
+ \fi
+}
+
+% Define the \E... control sequence only if we are inside the particular
+% environment, so the error checking in \end will work.
+%
+% To end an @example-like environment, we first end the paragraph (via
+% \afterenvbreak's vertical glue), and then the group. That way we keep
+% the zero \parskip that the environments set -- \parskip glue will be
+% inserted at the beginning of the next paragraph in the document, after
+% the environment.
+%
+\def\nonfillfinish{\afterenvbreak\endgroup}
+
+% @lisp: indented, narrowed, typewriter font.
+\def\lisp{\begingroup
+ \nonfillstart
+ \let\Elisp = \nonfillfinish
+ \tt
+ \let\kbdfont = \kbdexamplefont % Allow @kbd to do something special.
+ \gobble % eat return
+}
+
+% @example: Same as @lisp.
+\def\example{\begingroup \def\Eexample{\nonfillfinish\endgroup}\lisp}
+
+% @small... is usually equivalent to the non-small (@smallbook
+% redefines). We must call \example (or whatever) last in the
+% definition, since it reads the return following the @example (or
+% whatever) command.
+%
+% This actually allows (for example) @end display inside an
+% @smalldisplay. Too bad, but makeinfo will catch the error anyway.
+%
+\def\smalldisplay{\begingroup\def\Esmalldisplay{\nonfillfinish\endgroup}\display}
+\def\smallexample{\begingroup\def\Esmallexample{\nonfillfinish\endgroup}\lisp}
+\def\smallformat{\begingroup\def\Esmallformat{\nonfillfinish\endgroup}\format}
+\def\smalllisp{\begingroup\def\Esmalllisp{\nonfillfinish\endgroup}\lisp}
+
+% Real @smallexample and @smalllisp (when @smallbook): use smaller fonts.
+% Originally contributed by Pavel@xerox.
+\def\smalllispx{\begingroup
+ \def\Esmalllisp{\nonfillfinish\endgroup}%
+ \def\Esmallexample{\nonfillfinish\endgroup}%
+ \indexfonts
+ \lisp
+}
+
+% @display: same as @lisp except keep current font.
+%
+\def\display{\begingroup
+ \nonfillstart
+ \let\Edisplay = \nonfillfinish
+ \gobble
+}
+
+% @smalldisplay (when @smallbook): @display plus smaller fonts.
+%
+\def\smalldisplayx{\begingroup
+ \def\Esmalldisplay{\nonfillfinish\endgroup}%
+ \indexfonts \rm
+ \display
+}
+
+% @format: same as @display except don't narrow margins.
+%
+\def\format{\begingroup
+ \let\nonarrowing = t
+ \nonfillstart
+ \let\Eformat = \nonfillfinish
+ \gobble
+}
+
+% @smallformat (when @smallbook): @format plus smaller fonts.
+%
+\def\smallformatx{\begingroup
+ \def\Esmallformat{\nonfillfinish\endgroup}%
+ \indexfonts \rm
+ \format
+}
+
+% @flushleft (same as @format).
+%
+\def\flushleft{\begingroup \def\Eflushleft{\nonfillfinish\endgroup}\format}
+
+% @flushright.
+%
+\def\flushright{\begingroup
+ \let\nonarrowing = t
+ \nonfillstart
+ \let\Eflushright = \nonfillfinish
+ \advance\leftskip by 0pt plus 1fill
+ \gobble
+}
+
+% @quotation does normal linebreaking (hence we can't use \nonfillstart)
+% and narrows the margins.
+%
+\def\quotation{%
+ \begingroup\inENV %This group ends at the end of the @quotation body
+ {\parskip=0pt \aboveenvbreak}% because \aboveenvbreak inserts \parskip
+ \singlespace
+ \parindent=0pt
+ % We have retained a nonzero parskip for the environment, since we're
+ % doing normal filling. So to avoid extra space below the environment...
+ \def\Equotation{\parskip = 0pt \nonfillfinish}%
+ %
+ % @cartouche defines \nonarrowing to inhibit narrowing at next level down.
+ \ifx\nonarrowing\relax
+ \advance\leftskip by \lispnarrowing
+ \advance\rightskip by \lispnarrowing
+ \exdentamount = \lispnarrowing
+ \let\nonarrowing = \relax
+ \fi
+}
+
+
+\message{defuns,}
+% Define formatter for defuns
+% First, allow user to change definition object font (\df) internally
+\def\setdeffont #1 {\csname DEF#1\endcsname}
+
+\newskip\defbodyindent \defbodyindent=.4in
+\newskip\defargsindent \defargsindent=50pt
+\newskip\deftypemargin \deftypemargin=12pt
+\newskip\deflastargmargin \deflastargmargin=18pt
+
+\newcount\parencount
+% define \functionparens, which makes ( and ) and & do special things.
+% \functionparens affects the group it is contained in.
+\def\activeparens{%
+\catcode`\(=\active \catcode`\)=\active \catcode`\&=\active
+\catcode`\[=\active \catcode`\]=\active}
+
+% Make control sequences which act like normal parenthesis chars.
+\let\lparen = ( \let\rparen = )
+
+{\activeparens % Now, smart parens don't turn on until &foo (see \amprm)
+
+% Be sure that we always have a definition for `(', etc. For example,
+% if the fn name has parens in it, \boldbrax will not be in effect yet,
+% so TeX would otherwise complain about undefined control sequence.
+\global\let(=\lparen \global\let)=\rparen
+\global\let[=\lbrack \global\let]=\rbrack
+
+\gdef\functionparens{\boldbrax\let&=\amprm\parencount=0 }
+\gdef\boldbrax{\let(=\opnr\let)=\clnr\let[=\lbrb\let]=\rbrb}
+% This is used to turn on special parens
+% but make & act ordinary (given that it's active).
+\gdef\boldbraxnoamp{\let(=\opnr\let)=\clnr\let[=\lbrb\let]=\rbrb\let&=\ampnr}
+
+% Definitions of (, ) and & used in args for functions.
+% This is the definition of ( outside of all parentheses.
+\gdef\oprm#1 {{\rm\char`\(}#1 \bf \let(=\opnested
+ \global\advance\parencount by 1
+}
+%
+% This is the definition of ( when already inside a level of parens.
+\gdef\opnested{\char`\(\global\advance\parencount by 1 }
+%
+\gdef\clrm{% Print a paren in roman if it is taking us back to depth of 0.
+ % also in that case restore the outer-level definition of (.
+ \ifnum \parencount=1 {\rm \char `\)}\sl \let(=\oprm \else \char `\) \fi
+ \global\advance \parencount by -1 }
+% If we encounter &foo, then turn on ()-hacking afterwards
+\gdef\amprm#1 {{\rm\}\let(=\oprm \let)=\clrm\ }
+%
+\gdef\normalparens{\boldbrax\let&=\ampnr}
+} % End of definition inside \activeparens
+%% These parens (in \boldbrax) actually are a little bolder than the
+%% contained text. This is especially needed for [ and ]
+\def\opnr{{\sf\char`\(}\global\advance\parencount by 1 }
+\def\clnr{{\sf\char`\)}\global\advance\parencount by -1 }
+\def\ampnr{\&}
+\def\lbrb{{\bf\char`\[}}
+\def\rbrb{{\bf\char`\]}}
+
+% First, defname, which formats the header line itself.
+% #1 should be the function name.
+% #2 should be the type of definition, such as "Function".
+
+\def\defname #1#2{%
+% Get the values of \leftskip and \rightskip as they were
+% outside the @def...
+\dimen2=\leftskip
+\advance\dimen2 by -\defbodyindent
+\noindent
+\setbox0=\hbox{\hskip \deflastargmargin{\rm #2}\hskip \deftypemargin}%
+\dimen0=\hsize \advance \dimen0 by -\wd0 % compute size for first line
+\dimen1=\hsize \advance \dimen1 by -\defargsindent %size for continuations
+\parshape 2 0in \dimen0 \defargsindent \dimen1
+% Now output arg 2 ("Function" or some such)
+% ending at \deftypemargin from the right margin,
+% but stuck inside a box of width 0 so it does not interfere with linebreaking
+{% Adjust \hsize to exclude the ambient margins,
+% so that \rightline will obey them.
+\advance \hsize by -\dimen2
+\rlap{\rightline{{\rm #2}\hskip -1.25pc }}}%
+% Make all lines underfull and no complaints:
+\tolerance=10000 \hbadness=10000
+\advance\leftskip by -\defbodyindent
+\exdentamount=\defbodyindent
+{\df #1}\enskip % Generate function name
+}
+
+% Actually process the body of a definition
+% #1 should be the terminating control sequence, such as \Edefun.
+% #2 should be the "another name" control sequence, such as \defunx.
+% #3 should be the control sequence that actually processes the header,
+% such as \defunheader.
+
+\def\defparsebody #1#2#3{\begingroup\inENV% Environment for definitionbody
+\medbreak %
+% Define the end token that this defining construct specifies
+% so that it will exit this group.
+\def#1{\endgraf\endgroup\medbreak}%
+\def#2{\begingroup\obeylines\activeparens\spacesplit#3}%
+\parindent=0in
+\advance\leftskip by \defbodyindent
+\exdentamount=\defbodyindent
+\begingroup %
+\catcode 61=\active % 61 is `='
+\obeylines\activeparens\spacesplit#3}
+
+% #1 is the \E... control sequence to end the definition (which we define).
+% #2 is the \...x control sequence for consecutive fns (which we define).
+% #3 is the control sequence to call to resume processing.
+% #4, delimited by the space, is the class name.
+%
+\def\defmethparsebody#1#2#3#4 {\begingroup\inENV %
+\medbreak %
+% Define the end token that this defining construct specifies
+% so that it will exit this group.
+\def#1{\endgraf\endgroup\medbreak}%
+\def#2##1 {\begingroup\obeylines\activeparens\spacesplit{#3{##1}}}%
+\parindent=0in
+\advance\leftskip by \defbodyindent
+\exdentamount=\defbodyindent
+\begingroup\obeylines\activeparens\spacesplit{#3{#4}}}
+
+% @deftypemethod has an extra argument that nothing else does. Sigh.
+% #1 is the \E... control sequence to end the definition (which we define).
+% #2 is the \...x control sequence for consecutive fns (which we define).
+% #3 is the control sequence to call to resume processing.
+% #4, delimited by the space, is the class name.
+% #5 is the method's return type.
+%
+\def\deftypemethparsebody#1#2#3#4 #5 {\begingroup\inENV %
+\medbreak %
+% Define the end token that this defining construct specifies
+% so that it will exit this group.
+\def#1{\endgraf\endgroup\medbreak}%
+\def#2##1 ##2 {\begingroup\obeylines\activeparens\spacesplit{#3{##1}{##2}}}%
+\parindent=0in
+\advance\leftskip by \defbodyindent
+\exdentamount=\defbodyindent
+\begingroup\obeylines\activeparens\spacesplit{#3{#4}{#5}}}
+
+\def\defopparsebody #1#2#3#4#5 {\begingroup\inENV %
+\medbreak %
+% Define the end token that this defining construct specifies
+% so that it will exit this group.
+\def#1{\endgraf\endgroup\medbreak}%
+\def#2##1 ##2 {\def#4{##1}%
+\begingroup\obeylines\activeparens\spacesplit{#3{##2}}}%
+\parindent=0in
+\advance\leftskip by \defbodyindent
+\exdentamount=\defbodyindent
+\begingroup\obeylines\activeparens\spacesplit{#3{#5}}}
+
+% These parsing functions are similar to the preceding ones
+% except that they do not make parens into active characters.
+% These are used for "variables" since they have no arguments.
+
+\def\defvarparsebody #1#2#3{\begingroup\inENV% Environment for definitionbody
+\medbreak %
+% Define the end token that this defining construct specifies
+% so that it will exit this group.
+\def#1{\endgraf\endgroup\medbreak}%
+\def#2{\begingroup\obeylines\spacesplit#3}%
+\parindent=0in
+\advance\leftskip by \defbodyindent
+\exdentamount=\defbodyindent
+\begingroup %
+\catcode 61=\active %
+\obeylines\spacesplit#3}
+
+% This is used for \def{tp,vr}parsebody. It could probably be used for
+% some of the others, too, with some judicious conditionals.
+%
+\def\parsebodycommon#1#2#3{%
+ \begingroup\inENV %
+ \medbreak %
+ % Define the end token that this defining construct specifies
+ % so that it will exit this group.
+ \def#1{\endgraf\endgroup\medbreak}%
+ \def#2##1 {\begingroup\obeylines\spacesplit{#3{##1}}}%
+ \parindent=0in
+ \advance\leftskip by \defbodyindent
+ \exdentamount=\defbodyindent
+ \begingroup\obeylines
+}
+
+\def\defvrparsebody#1#2#3#4 {%
+ \parsebodycommon{#1}{#2}{#3}%
+ \spacesplit{#3{#4}}%
+}
+
+% This loses on `@deftp {Data Type} {struct termios}' -- it thinks the
+% type is just `struct', because we lose the braces in `{struct
+% termios}' when \spacesplit reads its undelimited argument. Sigh.
+% \let\deftpparsebody=\defvrparsebody
+%
+% So, to get around this, we put \empty in with the type name. That
+% way, TeX won't find exactly `{...}' as an undelimited argument, and
+% won't strip off the braces.
+%
+\def\deftpparsebody #1#2#3#4 {%
+ \parsebodycommon{#1}{#2}{#3}%
+ \spacesplit{\parsetpheaderline{#3{#4}}}\empty
+}
+
+% Fine, but then we have to eventually remove the \empty *and* the
+% braces (if any). That's what this does.
+%
+\def\removeemptybraces\empty#1\relax{#1}
+
+% After \spacesplit has done its work, this is called -- #1 is the final
+% thing to call, #2 the type name (which starts with \empty), and #3
+% (which might be empty) the arguments.
+%
+\def\parsetpheaderline#1#2#3{%
+ #1{\removeemptybraces#2\relax}{#3}%
+}%
+
+\def\defopvarparsebody #1#2#3#4#5 {\begingroup\inENV %
+\medbreak %
+% Define the end token that this defining construct specifies
+% so that it will exit this group.
+\def#1{\endgraf\endgroup\medbreak}%
+\def#2##1 ##2 {\def#4{##1}%
+\begingroup\obeylines\spacesplit{#3{##2}}}%
+\parindent=0in
+\advance\leftskip by \defbodyindent
+\exdentamount=\defbodyindent
+\begingroup\obeylines\spacesplit{#3{#5}}}
+
+% Split up #2 at the first space token.
+% call #1 with two arguments:
+% the first is all of #2 before the space token,
+% the second is all of #2 after that space token.
+% If #2 contains no space token, all of it is passed as the first arg
+% and the second is passed as empty.
+
+{\obeylines
+\gdef\spacesplit#1#2^^M{\endgroup\spacesplitfoo{#1}#2 \relax\spacesplitfoo}%
+\long\gdef\spacesplitfoo#1#2 #3#4\spacesplitfoo{%
+\ifx\relax #3%
+#1{#2}{}\else #1{#2}{#3#4}\fi}}
+
+% So much for the things common to all kinds of definitions.
+
+% Define @defun.
+
+% First, define the processing that is wanted for arguments of \defun
+% Use this to expand the args and terminate the paragraph they make up
+
+\def\defunargs #1{\functionparens \sl
+% Expand, preventing hyphenation at `-' chars.
+% Note that groups don't affect changes in \hyphenchar.
+\hyphenchar\tensl=0
+#1%
+\hyphenchar\tensl=45
+\ifnum\parencount=0 \else \errmessage{Unbalanced parentheses in @def}\fi%
+\interlinepenalty=10000
+\advance\rightskip by 0pt plus 1fil
+\endgraf\nobreak\vskip -\parskip\nobreak
+}
+
+\def\deftypefunargs #1{%
+% Expand, preventing hyphenation at `-' chars.
+% Note that groups don't affect changes in \hyphenchar.
+% Use \boldbraxnoamp, not \functionparens, so that & is not special.
+\boldbraxnoamp
+\tclose{#1}% avoid \code because of side effects on active chars
+\interlinepenalty=10000
+\advance\rightskip by 0pt plus 1fil
+\endgraf\nobreak\vskip -\parskip\nobreak
+}
+
+% Do complete processing of one @defun or @defunx line already parsed.
+
+% @deffn Command forward-char nchars
+
+\def\deffn{\defmethparsebody\Edeffn\deffnx\deffnheader}
+
+\def\deffnheader #1#2#3{\doind {fn}{\code{#2}}%
+\begingroup\defname {#2}{#1}\defunargs{#3}\endgroup %
+\catcode 61=\other % Turn off change made in \defparsebody
+}
+
+% @defun == @deffn Function
+
+\def\defun{\defparsebody\Edefun\defunx\defunheader}
+
+\def\defunheader #1#2{\doind {fn}{\code{#1}}% Make entry in function index
+\begingroup\defname {#1}{Function}%
+\defunargs {#2}\endgroup %
+\catcode 61=\other % Turn off change made in \defparsebody
+}
+
+% @deftypefun int foobar (int @var{foo}, float @var{bar})
+
+\def\deftypefun{\defparsebody\Edeftypefun\deftypefunx\deftypefunheader}
+
+% #1 is the data type. #2 is the name and args.
+\def\deftypefunheader #1#2{\deftypefunheaderx{#1}#2 \relax}
+% #1 is the data type, #2 the name, #3 the args.
+\def\deftypefunheaderx #1#2 #3\relax{%
+\doind {fn}{\code{#2}}% Make entry in function index
+\begingroup\defname {\defheaderxcond#1\relax$$$#2}{Function}%
+\deftypefunargs {#3}\endgroup %
+\catcode 61=\other % Turn off change made in \defparsebody
+}
+
+% @deftypefn {Library Function} int foobar (int @var{foo}, float @var{bar})
+
+\def\deftypefn{\defmethparsebody\Edeftypefn\deftypefnx\deftypefnheader}
+
+% \defheaderxcond#1\relax$$$
+% puts #1 in @code, followed by a space, but does nothing if #1 is null.
+\def\defheaderxcond#1#2$$${\ifx#1\relax\else\code{#1#2} \fi}
+
+% #1 is the classification. #2 is the data type. #3 is the name and args.
+\def\deftypefnheader #1#2#3{\deftypefnheaderx{#1}{#2}#3 \relax}
+% #1 is the classification, #2 the data type, #3 the name, #4 the args.
+\def\deftypefnheaderx #1#2#3 #4\relax{%
+\doind {fn}{\code{#3}}% Make entry in function index
+\begingroup
+\normalparens % notably, turn off `&' magic, which prevents
+% at least some C++ text from working
+\defname {\defheaderxcond#2\relax$$$#3}{#1}%
+\deftypefunargs {#4}\endgroup %
+\catcode 61=\other % Turn off change made in \defparsebody
+}
+
+% @defmac == @deffn Macro
+
+\def\defmac{\defparsebody\Edefmac\defmacx\defmacheader}
+
+\def\defmacheader #1#2{\doind {fn}{\code{#1}}% Make entry in function index
+\begingroup\defname {#1}{Macro}%
+\defunargs {#2}\endgroup %
+\catcode 61=\other % Turn off change made in \defparsebody
+}
+
+% @defspec == @deffn Special Form
+
+\def\defspec{\defparsebody\Edefspec\defspecx\defspecheader}
+
+\def\defspecheader #1#2{\doind {fn}{\code{#1}}% Make entry in function index
+\begingroup\defname {#1}{Special Form}%
+\defunargs {#2}\endgroup %
+\catcode 61=\other % Turn off change made in \defparsebody
+}
+
+% This definition is run if you use @defunx
+% anywhere other than immediately after a @defun or @defunx.
+
+\def\deffnx #1 {\errmessage{@deffnx in invalid context}}
+\def\defunx #1 {\errmessage{@defunx in invalid context}}
+\def\defmacx #1 {\errmessage{@defmacx in invalid context}}
+\def\defspecx #1 {\errmessage{@defspecx in invalid context}}
+\def\deftypefnx #1 {\errmessage{@deftypefnx in invalid context}}
+\def\deftypemethodx #1 {\errmessage{@deftypemethodx in invalid context}}
+\def\deftypefunx #1 {\errmessage{@deftypefunx in invalid context}}
+
+% @defmethod, and so on
+
+% @defop CATEGORY CLASS OPERATION ARG...
+
+\def\defop #1 {\def\defoptype{#1}%
+\defopparsebody\Edefop\defopx\defopheader\defoptype}
+
+\def\defopheader #1#2#3{%
+\dosubind {fn}{\code{#2}}{\putwordon\ #1}% Make entry in function index
+\begingroup\defname {#2}{\defoptype{} on #1}%
+\defunargs {#3}\endgroup %
+}
+
+% @deftypemethod CLASS RETURN-TYPE METHOD ARG...
+%
+\def\deftypemethod{%
+ \deftypemethparsebody\Edeftypemethod\deftypemethodx\deftypemethodheader}
+%
+% #1 is the class name, #2 the data type, #3 the method name, #4 the args.
+\def\deftypemethodheader#1#2#3#4{%
+ \dosubind{fn}{\code{#3}}{\putwordon\ \code{#1}}% entry in function index
+ \begingroup
+ \defname{\defheaderxcond#2\relax$$$#3}{\putwordMethodon\ \code{#1}}%
+ \deftypefunargs{#4}%
+ \endgroup
+}
+
+% @defmethod == @defop Method
+%
+\def\defmethod{\defmethparsebody\Edefmethod\defmethodx\defmethodheader}
+%
+% #1 is the class name, #2 the method name, #3 the args.
+\def\defmethodheader#1#2#3{%
+ \dosubind{fn}{\code{#2}}{\putwordon\ \code{#1}}% entry in function index
+ \begingroup
+ \defname{#2}{\putwordMethodon\ \code{#1}}%
+ \defunargs{#3}%
+ \endgroup
+}
+
+% @defcv {Class Option} foo-class foo-flag
+
+\def\defcv #1 {\def\defcvtype{#1}%
+\defopvarparsebody\Edefcv\defcvx\defcvarheader\defcvtype}
+
+\def\defcvarheader #1#2#3{%
+\dosubind {vr}{\code{#2}}{of #1}% Make entry in var index
+\begingroup\defname {#2}{\defcvtype{} of #1}%
+\defvarargs {#3}\endgroup %
+}
+
+% @defivar == @defcv {Instance Variable}
+
+\def\defivar{\defvrparsebody\Edefivar\defivarx\defivarheader}
+
+\def\defivarheader #1#2#3{%
+\dosubind {vr}{\code{#2}}{of #1}% Make entry in var index
+\begingroup\defname {#2}{Instance Variable of #1}%
+\defvarargs {#3}\endgroup %
+}
+
+% These definitions are run if you use @defmethodx, etc.,
+% anywhere other than immediately after a @defmethod, etc.
+
+\def\defopx #1 {\errmessage{@defopx in invalid context}}
+\def\defmethodx #1 {\errmessage{@defmethodx in invalid context}}
+\def\defcvx #1 {\errmessage{@defcvx in invalid context}}
+\def\defivarx #1 {\errmessage{@defivarx in invalid context}}
+
+% Now @defvar
+
+% First, define the processing that is wanted for arguments of @defvar.
+% This is actually simple: just print them in roman.
+% This must expand the args and terminate the paragraph they make up
+\def\defvarargs #1{\normalparens #1%
+\interlinepenalty=10000
+\endgraf\nobreak\vskip -\parskip\nobreak}
+
+% @defvr Counter foo-count
+
+\def\defvr{\defvrparsebody\Edefvr\defvrx\defvrheader}
+
+\def\defvrheader #1#2#3{\doind {vr}{\code{#2}}%
+\begingroup\defname {#2}{#1}\defvarargs{#3}\endgroup}
+
+% @defvar == @defvr Variable
+
+\def\defvar{\defvarparsebody\Edefvar\defvarx\defvarheader}
+
+\def\defvarheader #1#2{\doind {vr}{\code{#1}}% Make entry in var index
+\begingroup\defname {#1}{Variable}%
+\defvarargs {#2}\endgroup %
+}
+
+% @defopt == @defvr {User Option}
+
+\def\defopt{\defvarparsebody\Edefopt\defoptx\defoptheader}
+
+\def\defoptheader #1#2{\doind {vr}{\code{#1}}% Make entry in var index
+\begingroup\defname {#1}{User Option}%
+\defvarargs {#2}\endgroup %
+}
+
+% @deftypevar int foobar
+
+\def\deftypevar{\defvarparsebody\Edeftypevar\deftypevarx\deftypevarheader}
+
+% #1 is the data type. #2 is the name, perhaps followed by text that
+% is actually part of the data type, which should not be put into the index.
+\def\deftypevarheader #1#2{%
+\dovarind#2 \relax% Make entry in variables index
+\begingroup\defname {\defheaderxcond#1\relax$$$#2}{Variable}%
+\interlinepenalty=10000
+\endgraf\nobreak\vskip -\parskip\nobreak
+\endgroup}
+\def\dovarind#1 #2\relax{\doind{vr}{\code{#1}}}
+
+% @deftypevr {Global Flag} int enable
+
+\def\deftypevr{\defvrparsebody\Edeftypevr\deftypevrx\deftypevrheader}
+
+\def\deftypevrheader #1#2#3{\dovarind#3 \relax%
+\begingroup\defname {\defheaderxcond#2\relax$$$#3}{#1}
+\interlinepenalty=10000
+\endgraf\nobreak\vskip -\parskip\nobreak
+\endgroup}
+
+% This definition is run if you use @defvarx
+% anywhere other than immediately after a @defvar or @defvarx.
+
+\def\defvrx #1 {\errmessage{@defvrx in invalid context}}
+\def\defvarx #1 {\errmessage{@defvarx in invalid context}}
+\def\defoptx #1 {\errmessage{@defoptx in invalid context}}
+\def\deftypevarx #1 {\errmessage{@deftypevarx in invalid context}}
+\def\deftypevrx #1 {\errmessage{@deftypevrx in invalid context}}
+
+% Now define @deftp
+% Args are printed in bold, a slight difference from @defvar.
+
+\def\deftpargs #1{\bf \defvarargs{#1}}
+
+% @deftp Class window height width ...
+
+\def\deftp{\deftpparsebody\Edeftp\deftpx\deftpheader}
+
+\def\deftpheader #1#2#3{\doind {tp}{\code{#2}}%
+\begingroup\defname {#2}{#1}\deftpargs{#3}\endgroup}
+
+% This definition is run if you use @deftpx, etc
+% anywhere other than immediately after a @deftp, etc.
+
+\def\deftpx #1 {\errmessage{@deftpx in invalid context}}
+
+
+\message{macros,}
+% @macro.
+
+% To do this right we need a feature of e-TeX, \scantokens,
+% which we arrange to emulate with a temporary file in ordinary TeX.
+\ifx\eTeXversion\undefined
+ \newwrite\macscribble
+ \def\scanmacro#1{%
+ \begingroup \newlinechar`\^^M
+ \immediate\openout\macscribble=\jobname.tmp
+ \immediate\write\macscribble{#1}%
+ \immediate\closeout\macscribble
+ \let\xeatspaces\eatspaces
+ \input \jobname.tmp
+ \endgroup
+}
+\else
+\def\scanmacro#1{%
+\begingroup \newlinechar`\^^M
+\let\xeatspaces\eatspaces\scantokens{#1}\endgroup}
+\fi
+
+\newcount\paramno % Count of parameters
+\newtoks\macname % Macro name
+\newif\ifrecursive % Is it recursive?
+
+% Utility routines.
+% Thisdoes \let #1 = #2, except with \csnames.
+\def\cslet#1#2{%
+\expandafter\expandafter
+\expandafter\let
+\expandafter\expandafter
+\csname#1\endcsname
+\csname#2\endcsname}
+
+% Trim leading and trailing spaces off a string.
+% Concepts from aro-bend problem 15 (see CTAN).
+{\catcode`\@=11
+\gdef\eatspaces #1{\expandafter\trim@\expandafter{#1 }}
+\gdef\trim@ #1{\trim@@ @#1 @ #1 @ @@}
+\gdef\trim@@ #1@ #2@ #3@@{\trim@@@\empty #2 @}
+\def\unbrace#1{#1}
+\unbrace{\gdef\trim@@@ #1 } #2@{#1}
+}
+
+% Trim a single trailing ^^M off a string.
+{\catcode`\^^M=12\catcode`\Q=3%
+\gdef\eatcr #1{\eatcra #1Q^^MQ}%
+\gdef\eatcra#1^^MQ{\eatcrb#1Q}%
+\gdef\eatcrb#1Q#2Q{#1}%
+}
+
+% Macro bodies are absorbed as an argument in a context where
+% all characters are catcode 10, 11 or 12, except \ which is active
+% (as in normal texinfo). It is necessary to change the definition of \.
+
+% It's necessary to have hard CRs when the macro is executed. This is
+% done by making ^^M (\endlinechar) catcode 12 when reading the macro
+% body, and then making it the \newlinechar in \scanmacro.
+
+\def\macrobodyctxt{%
+ \catcode`\~=12
+ \catcode`\^=12
+ \catcode`\_=12
+ \catcode`\|=12
+ \catcode`\<=12
+ \catcode`\>=12
+ \catcode`\+=12
+ \catcode`\{=12
+ \catcode`\}=12
+ \catcode`\@=12
+ \catcode`\^^M=12
+ \usembodybackslash}
+
+\def\macroargctxt{%
+ \catcode`\~=12
+ \catcode`\^=12
+ \catcode`\_=12
+ \catcode`\|=12
+ \catcode`\<=12
+ \catcode`\>=12
+ \catcode`\+=12
+ \catcode`\@=12
+ \catcode`\\=12}
+
+% \mbodybackslash is the definition of \ in @macro bodies.
+% It maps \foo\ => \csname macarg.foo\endcsname => #N
+% where N is the macro parameter number.
+% We define \csname macarg.\endcsname to be \realbackslash, so
+% \\ in macro replacement text gets you a backslash.
+
+{\catcode`@=0 @catcode`@\=@active
+ @gdef@usembodybackslash{@let\=@mbodybackslash}
+ @gdef@mbodybackslash#1\{@csname macarg.#1@endcsname}
+}
+\expandafter\def\csname macarg.\endcsname{\realbackslash}
+
+\def\macro{\recursivefalse\parsearg\macroxxx}
+\def\rmacro{\recursivetrue\parsearg\macroxxx}
+
+\def\macroxxx#1{%
+ \getargs{#1}% now \macname is the macname and \argl the arglist
+ \ifx\argl\empty % no arguments
+ \paramno=0%
+ \else
+ \expandafter\parsemargdef \argl;%
+ \fi
+ \expandafter\ifx \csname macsave.\the\macname\endcsname \relax
+ \cslet{macsave.\the\macname}{\the\macname}%
+ \else
+ \message{Warning: redefining \the\macname}%
+ \fi
+ \begingroup \macrobodyctxt
+ \ifrecursive \expandafter\parsermacbody
+ \else \expandafter\parsemacbody
+ \fi}
+
+\def\unmacro{\parsearg\unmacroxxx}
+\def\unmacroxxx#1{%
+ \expandafter\ifx \csname macsave.\the\macname\endcsname \relax
+ \errmessage{Macro \the\macname\ not defined.}%
+ \else
+ \cslet{#1}{macsave.#1}%
+ \expandafter\let \csname macsave.\the\macname\endcsname \undefined
+ \fi
+}
+
+% This makes use of the obscure feature that if the last token of a
+% <parameter list> is #, then the preceding argument is delimited by
+% an opening brace, and that opening brace is not consumed.
+\def\getargs#1{\getargsxxx#1{}}
+\def\getargsxxx#1#{\getmacname #1 \relax\getmacargs}
+\def\getmacname #1 #2\relax{\macname={#1}}
+\def\getmacargs#1{\def\argl{#1}}
+
+% Parse the optional {params} list. Set up \paramno and \paramlist
+% so \defmacro knows what to do. Define \macarg.blah for each blah
+% in the params list, to be ##N where N is the position in that list.
+% That gets used by \mbodybackslash (above).
+
+% We need to get `macro parameter char #' into several definitions.
+% The technique used is stolen from LaTeX: let \hash be something
+% unexpandable, insert that wherever you need a #, and then redefine
+% it to # just before using the token list produced.
+%
+% The same technique is used to protect \eatspaces till just before
+% the macro is used.
+
+\def\parsemargdef#1;{\paramno=0\def\paramlist{}%
+ \let\hash\relax\let\xeatspaces\relax\parsemargdefxxx#1,;,}
+\def\parsemargdefxxx#1,{%
+ \if#1;\let\next=\relax
+ \else \let\next=\parsemargdefxxx
+ \advance\paramno by 1%
+ \expandafter\edef\csname macarg.\eatspaces{#1}\endcsname
+ {\xeatspaces{\hash\the\paramno}}%
+ \edef\paramlist{\paramlist\hash\the\paramno,}%
+ \fi\next}
+
+% These two commands read recursive and nonrecursive macro bodies.
+% (They're different since rec and nonrec macros end differently.)
+
+\long\def\parsemacbody#1@end macro%
+{\xdef\temp{\eatcr{#1}}\endgroup\defmacro}%
+\long\def\parsermacbody#1@end rmacro%
+{\xdef\temp{\eatcr{#1}}\endgroup\defmacro}%
+
+% This defines the macro itself. There are six cases: recursive and
+% nonrecursive macros of zero, one, and many arguments.
+% Much magic with \expandafter here.
+% \xdef is used so that macro definitions will survive the file
+% they're defined in; @include reads the file inside a group.
+\def\defmacro{%
+ \let\hash=##% convert placeholders to macro parameter chars
+ \ifrecursive
+ \ifcase\paramno
+ % 0
+ \expandafter\xdef\csname\the\macname\endcsname{%
+ \noexpand\scanmacro{\temp}}%
+ \or % 1
+ \expandafter\xdef\csname\the\macname\endcsname{%
+ \bgroup\noexpand\macroargctxt
+ \noexpand\braceorline\csname\the\macname xxx\endcsname}%
+ \expandafter\xdef\csname\the\macname xxx\endcsname##1{%
+ \egroup\noexpand\scanmacro{\temp}}%
+ \else % many
+ \expandafter\xdef\csname\the\macname\endcsname{%
+ \bgroup\noexpand\macroargctxt
+ \noexpand\csname\the\macname xx\endcsname}
+ \expandafter\xdef\csname\the\macname xx\endcsname##1{%
+ \csname\the\macname xxx\endcsname ##1,}%
+ \expandafter\expandafter
+ \expandafter\xdef
+ \expandafter\expandafter
+ \csname\the\macname xxx\endcsname
+ \paramlist{\egroup\noexpand\scanmacro{\temp}}%
+ \fi
+ \else
+ \ifcase\paramno
+ % 0
+ \expandafter\xdef\csname\the\macname\endcsname{%
+ \noexpand\norecurse{\the\macname}%
+ \noexpand\scanmacro{\temp}\egroup}%
+ \or % 1
+ \expandafter\xdef\csname\the\macname\endcsname{%
+ \bgroup\noexpand\macroargctxt
+ \noexpand\braceorline\csname\the\macname xxx\endcsname}%
+ \expandafter\xdef\csname\the\macname xxx\endcsname##1{%
+ \egroup
+ \noexpand\norecurse{\the\macname}%
+ \noexpand\scanmacro{\temp}\egroup}%
+ \else % many
+ \expandafter\xdef\csname\the\macname\endcsname{%
+ \bgroup\noexpand\macroargctxt
+ \noexpand\csname\the\macname xx\endcsname}
+ \expandafter\xdef\csname\the\macname xx\endcsname##1{%
+ \csname\the\macname xxx\endcsname ##1,}%
+ \expandafter\expandafter
+ \expandafter\xdef
+ \expandafter\expandafter
+ \csname\the\macname xxx\endcsname
+ \paramlist{%
+ \egroup
+ \noexpand\norecurse{\the\macname}%
+ \noexpand\scanmacro{\temp}\egroup}%
+ \fi
+ \fi}
+
+\def\norecurse#1{\bgroup\cslet{#1}{macsave.#1}}
+
+% \braceorline decides whether the next nonwhitespace character is a
+% {. If so it reads up to the closing }, if not, it reads the whole
+% line. Whatever was read is then fed to the next control sequence
+% as an argument (by \parsebrace or \parsearg)
+\def\braceorline#1{\let\next=#1\futurelet\nchar\braceorlinexxx}
+\def\braceorlinexxx{%
+ \ifx\nchar\bgroup\else
+ \expandafter\parsearg
+ \fi \next}
+
+
+\message{cross references,}
+\newwrite\auxfile
+
+\newif\ifhavexrefs % True if xref values are known.
+\newif\ifwarnedxrefs % True if we warned once that they aren't known.
+
+% @inforef is relatively simple.
+\def\inforef #1{\inforefzzz #1,,,,**}
+\def\inforefzzz #1,#2,#3,#4**{\putwordSee{} \putwordInfo{} \putwordfile{} \file{\ignorespaces #3{}},
+ node \samp{\ignorespaces#1{}}}
+
+% @node's job is to define \lastnode.
+\def\node{\ENVcheck\parsearg\nodezzz}
+\def\nodezzz#1{\nodexxx [#1,]}
+\def\nodexxx[#1,#2]{\gdef\lastnode{#1}}
+\let\nwnode=\node
+\let\lastnode=\relax
+
+% The sectioning commands (@chapter, etc.) call these.
+\def\donoderef{%
+ \ifx\lastnode\relax\else
+ \expandafter\expandafter\expandafter\setref{\lastnode}%
+ {Ysectionnumberandtype}%
+ \global\let\lastnode=\relax
+ \fi
+}
+\def\unnumbnoderef{%
+ \ifx\lastnode\relax\else
+ \expandafter\expandafter\expandafter\setref{\lastnode}{Ynothing}%
+ \global\let\lastnode=\relax
+ \fi
+}
+\def\appendixnoderef{%
+ \ifx\lastnode\relax\else
+ \expandafter\expandafter\expandafter\setref{\lastnode}%
+ {Yappendixletterandtype}%
+ \global\let\lastnode=\relax
+ \fi
+}
+
+
+% @anchor{NAME} -- define xref target at arbitrary point.
+%
+\def\anchor#1{\setref{#1}{Ynothing}}
+
+
+% \setref{NAME}{SNT} defines a cross-reference point NAME, namely
+% NAME-title, NAME-pg, and NAME-SNT. Called from \foonoderef. We have
+% to set \indexdummies so commands such as @code in a section title
+% aren't expanded. It would be nicer not to expand the titles in the
+% first place, but there's so many layers that that is hard to do.
+%
+\def\setref#1#2{{%
+ \indexdummies
+ \dosetq{#1-title}{Ytitle}%
+ \dosetq{#1-pg}{Ypagenumber}%
+ \dosetq{#1-snt}{#2}
+}}
+
+% @xref, @pxref, and @ref generate cross-references. For \xrefX, #1 is
+% the node name, #2 the name of the Info cross-reference, #3 the printed
+% node name, #4 the name of the Info file, #5 the name of the printed
+% manual. All but the node name can be omitted.
+%
+\def\pxref#1{\putwordsee{} \xrefX[#1,,,,,,,]}
+\def\xref#1{\putwordSee{} \xrefX[#1,,,,,,,]}
+\def\ref#1{\xrefX[#1,,,,,,,]}
+\def\xrefX[#1,#2,#3,#4,#5,#6]{\begingroup
+ \def\printedmanual{\ignorespaces #5}%
+ \def\printednodename{\ignorespaces #3}%
+ \setbox1=\hbox{\printedmanual}%
+ \setbox0=\hbox{\printednodename}%
+ \ifdim \wd0 = 0pt
+ % No printed node name was explicitly given.
+ \expandafter\ifx\csname SETxref-automatic-section-title\endcsname\relax
+ % Use the node name inside the square brackets.
+ \def\printednodename{\ignorespaces #1}%
+ \else
+ % Use the actual chapter/section title appear inside
+ % the square brackets. Use the real section title if we have it.
+ \ifdim \wd1 > 0pt
+ % It is in another manual, so we don't have it.
+ \def\printednodename{\ignorespaces #1}%
+ \else
+ \ifhavexrefs
+ % We know the real title if we have the xref values.
+ \def\printednodename{\refx{#1-title}{}}%
+ \else
+ % Otherwise just copy the Info node name.
+ \def\printednodename{\ignorespaces #1}%
+ \fi%
+ \fi
+ \fi
+ \fi
+ %
+ % If we use \unhbox0 and \unhbox1 to print the node names, TeX does not
+ % insert empty discretionaries after hyphens, which means that it will
+ % not find a line break at a hyphen in a node names. Since some manuals
+ % are best written with fairly long node names, containing hyphens, this
+ % is a loss. Therefore, we give the text of the node name again, so it
+ % is as if TeX is seeing it for the first time.
+ \ifdim \wd1 > 0pt
+ \putwordsection{} ``\printednodename'' in \cite{\printedmanual}%
+ \else
+ % _ (for example) has to be the character _ for the purposes of the
+ % control sequence corresponding to the node, but it has to expand
+ % into the usual \leavevmode...\vrule stuff for purposes of
+ % printing. So we \turnoffactive for the \refx-snt, back on for the
+ % printing, back off for the \refx-pg.
+ {\normalturnoffactive
+ % Only output a following space if the -snt ref is nonempty; for
+ % @unnumbered and @anchor, it won't be.
+ \setbox2 = \hbox{\ignorespaces \refx{#1-snt}{}}%
+ \ifdim \wd2 > 0pt \refx{#1-snt}\space\fi
+ }%
+ % [mynode],
+ [\printednodename],\space
+ % page 3
+ \turnoffactive \putwordpage\tie\refx{#1-pg}{}%
+ \fi
+\endgroup}
+
+% \dosetq is the interface for calls from other macros
+
+% Use \normalturnoffactive so that punctuation chars such as underscore
+% and backslash work in node names. (\turnoffactive doesn't do \.)
+\def\dosetq#1#2{%
+ {\let\folio=0
+ \normalturnoffactive
+ \edef\next{\write\auxfile{\internalsetq{#1}{#2}}}%
+ \iflinks
+ \next
+ \fi
+ }%
+}
+
+% \internalsetq {foo}{page} expands into
+% CHARACTERS 'xrdef {foo}{...expansion of \Ypage...}
+% When the aux file is read, ' is the escape character
+
+\def\internalsetq #1#2{'xrdef {#1}{\csname #2\endcsname}}
+
+% Things to be expanded by \internalsetq
+
+\def\Ypagenumber{\folio}
+
+\def\Ytitle{\thissection}
+
+\def\Ynothing{}
+
+\def\Ysectionnumberandtype{%
+\ifnum\secno=0 \putwordChapter\xreftie\the\chapno %
+\else \ifnum \subsecno=0 \putwordSection\xreftie\the\chapno.\the\secno %
+\else \ifnum \subsubsecno=0 %
+\putwordSection\xreftie\the\chapno.\the\secno.\the\subsecno %
+\else %
+\putwordSection\xreftie\the\chapno.\the\secno.\the\subsecno.\the\subsubsecno %
+\fi \fi \fi }
+
+\def\Yappendixletterandtype{%
+\ifnum\secno=0 \putwordAppendix\xreftie'char\the\appendixno{}%
+\else \ifnum \subsecno=0 \putwordSection\xreftie'char\the\appendixno.\the\secno %
+\else \ifnum \subsubsecno=0 %
+\putwordSection\xreftie'char\the\appendixno.\the\secno.\the\subsecno %
+\else %
+\putwordSection\xreftie'char\the\appendixno.\the\secno.\the\subsecno.\the\subsubsecno %
+\fi \fi \fi }
+
+\gdef\xreftie{'tie}
+
+% Use TeX 3.0's \inputlineno to get the line number, for better error
+% messages, but if we're using an old version of TeX, don't do anything.
+%
+\ifx\inputlineno\thisisundefined
+ \let\linenumber = \empty % Non-3.0.
+\else
+ \def\linenumber{\the\inputlineno:\space}
+\fi
+
+% Define \refx{NAME}{SUFFIX} to reference a cross-reference string named NAME.
+% If its value is nonempty, SUFFIX is output afterward.
+
+\def\refx#1#2{%
+ \expandafter\ifx\csname X#1\endcsname\relax
+ % If not defined, say something at least.
+ \angleleft un\-de\-fined\angleright
+ \iflinks
+ \ifhavexrefs
+ \message{\linenumber Undefined cross reference `#1'.}%
+ \else
+ \ifwarnedxrefs\else
+ \global\warnedxrefstrue
+ \message{Cross reference values unknown; you must run TeX again.}%
+ \fi
+ \fi
+ \fi
+ \else
+ % It's defined, so just use it.
+ \csname X#1\endcsname
+ \fi
+ #2% Output the suffix in any case.
+}
+
+% This is the macro invoked by entries in the aux file.
+%
+\def\xrdef#1{\begingroup
+ % Reenable \ as an escape while reading the second argument.
+ \catcode`\\ = 0
+ \afterassignment\endgroup
+ \expandafter\gdef\csname X#1\endcsname
+}
+
+% Read the last existing aux file, if any. No error if none exists.
+\def\readauxfile{\begingroup
+ \catcode`\^^@=\other
+ \catcode`\^^A=\other
+ \catcode`\^^B=\other
+ \catcode`\^^C=\other
+ \catcode`\^^D=\other
+ \catcode`\^^E=\other
+ \catcode`\^^F=\other
+ \catcode`\^^G=\other
+ \catcode`\^^H=\other
+ \catcode`\^^K=\other
+ \catcode`\^^L=\other
+ \catcode`\^^N=\other
+ \catcode`\^^P=\other
+ \catcode`\^^Q=\other
+ \catcode`\^^R=\other
+ \catcode`\^^S=\other
+ \catcode`\^^T=\other
+ \catcode`\^^U=\other
+ \catcode`\^^V=\other
+ \catcode`\^^W=\other
+ \catcode`\^^X=\other
+ \catcode`\^^Z=\other
+ \catcode`\^^[=\other
+ \catcode`\^^\=\other
+ \catcode`\^^]=\other
+ \catcode`\^^^=\other
+ \catcode`\^^_=\other
+ \catcode`\@=\other
+ \catcode`\^=\other
+ % It was suggested to define this as 7, which would allow ^^e4 etc.
+ % in xref tags, i.e., node names. But since ^^e4 notation isn't
+ % supported in the main text, it doesn't seem desirable. Furthermore,
+ % that is not enough: for node names that actually contain a ^
+ % character, we would end up writing a line like this: 'xrdef {'hat
+ % b-title}{'hat b} and \xrdef does a \csname...\endcsname on the first
+ % argument, and \hat is not an expandable control sequence. It could
+ % all be worked out, but why? Either we support ^^ or we don't.
+ %
+ % The other change necessary for this was to define \auxhat:
+ % \def\auxhat{\def^{'hat }}% extra space so ok if followed by letter
+ % and then to call \auxhat in \setq.
+ %
+ \catcode`\~=\other
+ \catcode`\[=\other
+ \catcode`\]=\other
+ \catcode`\"=\other
+ \catcode`\_=\other
+ \catcode`\|=\other
+ \catcode`\<=\other
+ \catcode`\>=\other
+ \catcode`\$=\other
+ \catcode`\#=\other
+ \catcode`\&=\other
+ \catcode`+=\other % avoid \+ for paranoia even though we've turned it off
+ % Make the characters 128-255 be printing characters
+ {%
+ \count 1=128
+ \def\loop{%
+ \catcode\count 1=\other
+ \advance\count 1 by 1
+ \ifnum \count 1<256 \loop \fi
+ }%
+ }%
+ % The aux file uses ' as the escape (for now).
+ % Turn off \ as an escape so we do not lose on
+ % entries which were dumped with control sequences in their names.
+ % For example, 'xrdef {$\leq $-fun}{page ...} made by @defun ^^
+ % Reference to such entries still does not work the way one would wish,
+ % but at least they do not bomb out when the aux file is read in.
+ \catcode`\{=1
+ \catcode`\}=2
+ \catcode`\%=\other
+ \catcode`\'=0
+ \catcode`\\=\other
+ %
+ \openin 1 \jobname.aux
+ \ifeof 1 \else
+ \closein 1
+ \input \jobname.aux
+ \global\havexrefstrue
+ \global\warnedobstrue
+ \fi
+ % Open the new aux file. TeX will close it automatically at exit.
+ \openout\auxfile=\jobname.aux
+\endgroup}
+
+
+% Footnotes.
+
+\newcount \footnoteno
+
+% The trailing space in the following definition for supereject is
+% vital for proper filling; pages come out unaligned when you do a
+% pagealignmacro call if that space before the closing brace is
+% removed. (Generally, numeric constants should always be followed by a
+% space to prevent strange expansion errors.)
+\def\supereject{\par\penalty -20000\footnoteno =0 }
+
+% @footnotestyle is meaningful for info output only.
+\let\footnotestyle=\comment
+
+\let\ptexfootnote=\footnote
+
+{\catcode `\@=11
+%
+% Auto-number footnotes. Otherwise like plain.
+\gdef\footnote{%
+ \global\advance\footnoteno by \@ne
+ \edef\thisfootno{$^{\the\footnoteno}$}%
+ %
+ % In case the footnote comes at the end of a sentence, preserve the
+ % extra spacing after we do the footnote number.
+ \let\@sf\empty
+ \ifhmode\edef\@sf{\spacefactor\the\spacefactor}\/\fi
+ %
+ % Remove inadvertent blank space before typesetting the footnote number.
+ \unskip
+ \thisfootno\@sf
+ \footnotezzz
+}%
+
+% Don't bother with the trickery in plain.tex to not require the
+% footnote text as a parameter. Our footnotes don't need to be so general.
+%
+% Oh yes, they do; otherwise, @ifset and anything else that uses
+% \parseargline fail inside footnotes because the tokens are fixed when
+% the footnote is read. --karl, 16nov96.
+%
+\long\gdef\footnotezzz{\insert\footins\bgroup
+ % We want to typeset this text as a normal paragraph, even if the
+ % footnote reference occurs in (for example) a display environment.
+ % So reset some parameters.
+ \interlinepenalty\interfootnotelinepenalty
+ \splittopskip\ht\strutbox % top baseline for broken footnotes
+ \splitmaxdepth\dp\strutbox
+ \floatingpenalty\@MM
+ \leftskip\z@skip
+ \rightskip\z@skip
+ \spaceskip\z@skip
+ \xspaceskip\z@skip
+ \parindent\defaultparindent
+ %
+ % Hang the footnote text off the number.
+ \hang
+ \textindent{\thisfootno}%
+ %
+ % Don't crash into the line above the footnote text. Since this
+ % expands into a box, it must come within the paragraph, lest it
+ % provide a place where TeX can split the footnote.
+ \footstrut
+ \futurelet\next\fo@t
+}
+\def\fo@t{\ifcat\bgroup\noexpand\next \let\next\f@@t
+ \else\let\next\f@t\fi \next}
+\def\f@@t{\bgroup\aftergroup\@foot\let\next}
+\def\f@t#1{#1\@foot}
+\def\@foot{\strut\egroup}
+
+}%end \catcode `\@=11
+
+% Set the baselineskip to #1, and the lineskip and strut size
+% correspondingly. There is no deep meaning behind these magic numbers
+% used as factors; they just match (closely enough) what Knuth defined.
+%
+\def\lineskipfactor{.08333}
+\def\strutheightpercent{.70833}
+\def\strutdepthpercent {.29167}
+%
+\def\setleading#1{%
+ \normalbaselineskip = #1\relax
+ \normallineskip = \lineskipfactor\normalbaselineskip
+ \normalbaselines
+ \setbox\strutbox =\hbox{%
+ \vrule width0pt height\strutheightpercent\baselineskip
+ depth \strutdepthpercent \baselineskip
+ }%
+}
+
+% @| inserts a changebar to the left of the current line. It should
+% surround any changed text. This approach does *not* work if the
+% change spans more than two lines of output. To handle that, we would
+% have adopt a much more difficult approach (putting marks into the main
+% vertical list for the beginning and end of each change).
+%
+\def\|{%
+ % \vadjust can only be used in horizontal mode.
+ \leavevmode
+ %
+ % Append this vertical mode material after the current line in the output.
+ \vadjust{%
+ % We want to insert a rule with the height and depth of the current
+ % leading; that is exactly what \strutbox is supposed to record.
+ \vskip-\baselineskip
+ %
+ % \vadjust-items are inserted at the left edge of the type. So
+ % the \llap here moves out into the left-hand margin.
+ \llap{%
+ %
+ % For a thicker or thinner bar, change the `1pt'.
+ \vrule height\baselineskip width1pt
+ %
+ % This is the space between the bar and the text.
+ \hskip 12pt
+ }%
+ }%
+}
+
+% For a final copy, take out the rectangles
+% that mark overfull boxes (in case you have decided
+% that the text looks ok even though it passes the margin).
+%
+\def\finalout{\overfullrule=0pt}
+
+% @image. We use the macros from epsf.tex to support this.
+% If epsf.tex is not installed and @image is used, we complain.
+%
+% Check for and read epsf.tex up front. If we read it only at @image
+% time, we might be inside a group, and then its definitions would get
+% undone and the next image would fail.
+\openin 1 = epsf.tex
+\ifeof 1 \else
+ \closein 1
+ % Do not bother showing banner with post-v2.7 epsf.tex (available in
+ % doc/epsf.tex until it shows up on ctan).
+ \def\epsfannounce{\toks0 = }%
+ \input epsf.tex
+\fi
+%
+\newif\ifwarnednoepsf
+\newhelp\noepsfhelp{epsf.tex must be installed for images to
+ work. It is also included in the Texinfo distribution, or you can get
+ it from ftp://ftp.tug.org/tex/epsf.tex.}
+%
+% Only complain once about lack of epsf.tex.
+\def\image#1{%
+ \ifx\epsfbox\undefined
+ \ifwarnednoepsf \else
+ \errhelp = \noepsfhelp
+ \errmessage{epsf.tex not found, images will be ignored}%
+ \global\warnednoepsftrue
+ \fi
+ \else
+ \imagexxx #1,,,\finish
+ \fi
+}
+%
+% Arguments to @image:
+% #1 is (mandatory) image filename; we tack on .eps extension.
+% #2 is (optional) width, #3 is (optional) height.
+% #4 is just the usual extra ignored arg for parsing this stuff.
+\def\imagexxx#1,#2,#3,#4\finish{%
+ % \epsfbox itself resets \epsf?size at each figure.
+ \setbox0 = \hbox{\ignorespaces #2}\ifdim\wd0 > 0pt \epsfxsize=#2\relax \fi
+ \setbox0 = \hbox{\ignorespaces #3}\ifdim\wd0 > 0pt \epsfysize=#3\relax \fi
+ % If the image is by itself, center it.
+ \ifvmode
+ \nobreak\medskip
+ \nobreak
+ \centerline{\epsfbox{#1.eps}}%
+ \bigbreak
+ \else
+ \epsfbox{#1.eps}%
+ \fi
+}
+
+
+\message{paper sizes,}
+% And other related parameters.
+
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+\chapheadingskip = 15pt plus 4pt minus 2pt
+\secheadingskip = 12pt plus 3pt minus 2pt
+\subsecheadingskip = 9pt plus 2pt minus 2pt
+
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+% Following George Bush, just get rid of widows and orphans.
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+\clubpenalty=10000
+
+% Use TeX 3.0's \emergencystretch to help line breaking, but if we're
+% using an old version of TeX, don't do anything. We want the amount of
+% stretch added to depend on the line length, hence the dependence on
+% \hsize. This makes it come to about 9pt for the 8.5x11 format. We
+% call this whenever the paper size is set.
+%
+\def\setemergencystretch{%
+ \ifx\emergencystretch\thisisundefined
+ % Allow us to assign to \emergencystretch anyway.
+ \def\emergencystretch{\dimen0}%
+ \else
+ \emergencystretch = \hsize
+ \divide\emergencystretch by 45
+ \fi
+}
+
+% Parameters in order: 1) textheight; 2) textwidth; 3) voffset;
+% 4) hoffset; 5) binding offset; 6) topskip. Then whoever calls us can
+% set \parskip and call \setleading for \baselineskip.
+%
+\def\internalpagesizes#1#2#3#4#5#6{%
+ \voffset = #3\relax
+ \topskip = #6\relax
+ \splittopskip = \topskip
+ %
+ \vsize = #1\relax
+ \advance\vsize by \topskip
+ \outervsize = \vsize
+ \advance\outervsize by 2\topandbottommargin
+ \pageheight = \vsize
+ %
+ \hsize = #2\relax
+ \outerhsize = \hsize
+ \advance\outerhsize by 0.5in
+ \pagewidth = \hsize
+ %
+ \normaloffset = #4\relax
+ \bindingoffset = #5\relax
+ %
+ \parindent = \defaultparindent
+ \setemergencystretch
+}
+
+% @letterpaper (the default).
+\def\letterpaper{{\globaldefs = 1
+ \parskip = 3pt plus 2pt minus 1pt
+ \setleading{13.2pt}%
+ %
+ % If page is nothing but text, make it come out even.
+ \internalpagesizes{46\baselineskip}{6in}{\voffset}{.25in}{\bindingoffset}{36pt}%
+}}
+
+% Use @smallbook to reset parameters for 7x9.5 (or so) format.
+\def\smallbook{{\globaldefs = 1
+ \parskip = 2pt plus 1pt
+ \setleading{12pt}%
+ %
+ \internalpagesizes{7.5in}{5.in}{\voffset}{.25in}{\bindingoffset}{16pt}%
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+ \contentsrightmargin = 0pt
+ \deftypemargin = 0pt
+ \defbodyindent = .5cm
+ %
+ \let\smalldisplay = \smalldisplayx
+ \let\smallexample = \smalllispx
+ \let\smallformat = \smallformatx
+ \let\smalllisp = \smalllispx
+}}
+
+% Use @afourpaper to print on European A4 paper.
+\def\afourpaper{{\globaldefs = 1
+ \setleading{12pt}%
+ \parskip = 3pt plus 2pt minus 1pt
+ %
+ \internalpagesizes{53\baselineskip}{160mm}{\voffset}{4mm}{\bindingoffset}{44pt}%
+ %
+ \tolerance = 700
+ \hfuzz = 1pt
+}}
+
+% A specific text layout, 24x15cm overall, intended for A4 paper. Top margin
+% 29mm, hence bottom margin 28mm, nominal side margin 3cm.
+\def\afourlatex{{\globaldefs = 1
+ \setleading{13.6pt}%
+ %
+ \afourpaper
+ \internalpagesizes{237mm}{150mm}{3.6mm}{3.6mm}{3mm}{7mm}%
+ %
+ \globaldefs = 0
+}}
+
+% Use @afourwide to print on European A4 paper in wide format.
+\def\afourwide{%
+ \afourpaper
+ \internalpagesizes{9.5in}{6.5in}{\hoffset}{\normaloffset}{\bindingoffset}{7mm}%
+ %
+ \globaldefs = 0
+}
+
+% @pagesizes TEXTHEIGHT[,TEXTWIDTH]
+% Perhaps we should allow setting the margins, \topskip, \parskip,
+% and/or leading, also. Or perhaps we should compute them somehow.
+%
+\def\pagesizes{\parsearg\pagesizesxxx}
+\def\pagesizesxxx#1{\pagesizesyyy #1,,\finish}
+\def\pagesizesyyy#1,#2,#3\finish{{%
+ \setbox0 = \hbox{\ignorespaces #2}\ifdim\wd0 > 0pt \hsize=#2\relax \fi
+ \globaldefs = 1
+ %
+ \parskip = 3pt plus 2pt minus 1pt
+ \setleading{13.2pt}%
+ %
+ \internalpagesizes{#1}{\hsize}{\voffset}{\normaloffset}{\bindingoffset}{44pt}%
+}}
+
+% Set default to letter.
+%
+\letterpaper
+
+\message{and turning on texinfo input format.}
+
+% Define macros to output various characters with catcode for normal text.
+\catcode`\"=\other
+\catcode`\~=\other
+\catcode`\^=\other
+\catcode`\_=\other
+\catcode`\|=\other
+\catcode`\<=\other
+\catcode`\>=\other
+\catcode`\+=\other
+\def\normaldoublequote{"}
+\def\normaltilde{~}
+\def\normalcaret{^}
+\def\normalunderscore{_}
+\def\normalverticalbar{|}
+\def\normalless{<}
+\def\normalgreater{>}
+\def\normalplus{+}
+
+% This macro is used to make a character print one way in ttfont
+% where it can probably just be output, and another way in other fonts,
+% where something hairier probably needs to be done.
+%
+% #1 is what to print if we are indeed using \tt; #2 is what to print
+% otherwise. Since all the Computer Modern typewriter fonts have zero
+% interword stretch (and shrink), and it is reasonable to expect all
+% typewriter fonts to have this, we can check that font parameter.
+%
+\def\ifusingtt#1#2{\ifdim \fontdimen3\the\font=0pt #1\else #2\fi}
+
+% Turn off all special characters except @
+% (and those which the user can use as if they were ordinary).
+% Most of these we simply print from the \tt font, but for some, we can
+% use math or other variants that look better in normal text.
+
+\catcode`\"=\active
+\def\activedoublequote{{\tt\char34}}
+\let"=\activedoublequote
+\catcode`\~=\active
+\def~{{\tt\char126}}
+\chardef\hat=`\^
+\catcode`\^=\active
+\def^{{\tt \hat}}
+
+\catcode`\_=\active
+\def_{\ifusingtt\normalunderscore\_}
+% Subroutine for the previous macro.
+\def\_{\leavevmode \kern.06em \vbox{\hrule width.3em height.1ex}}
+
+\catcode`\|=\active
+\def|{{\tt\char124}}
+\chardef \less=`\<
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+\def<{{\tt \less}}
+\chardef \gtr=`\>
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+\def>{{\tt \gtr}}
+\catcode`\+=\active
+\def+{{\tt \char 43}}
+%\catcode 27=\active
+%\def^^[{$\diamondsuit$}
+
+% Set up an active definition for =, but don't enable it most of the time.
+{\catcode`\==\active
+\global\def={{\tt \char 61}}}
+
+\catcode`+=\active
+\catcode`\_=\active
+
+% If a .fmt file is being used, characters that might appear in a file
+% name cannot be active until we have parsed the command line.
+% So turn them off again, and have \everyjob (or @setfilename) turn them on.
+% \otherifyactive is called near the end of this file.
+\def\otherifyactive{\catcode`+=\other \catcode`\_=\other}
+
+\catcode`\@=0
+
+% \rawbackslashxx output one backslash character in current font
+\global\chardef\rawbackslashxx=`\\
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+%@gdef@rawbackslashxx{\}}
+
+% \rawbackslash redefines \ as input to do \rawbackslashxx.
+{\catcode`\\=\active
+@gdef@rawbackslash{@let\=@rawbackslashxx }}
+
+% \normalbackslash outputs one backslash in fixed width font.
+\def\normalbackslash{{\tt\rawbackslashxx}}
+
+% Say @foo, not \foo, in error messages.
+\escapechar=`\@
+
+% \catcode 17=0 % Define control-q
+\catcode`\\=\active
+
+% Used sometimes to turn off (effectively) the active characters
+% even after parsing them.
+@def@turnoffactive{@let"=@normaldoublequote
+@let\=@realbackslash
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+@let^=@normalcaret
+@let_=@normalunderscore
+@let|=@normalverticalbar
+@let<=@normalless
+@let>=@normalgreater
+@let+=@normalplus}
+
+@def@normalturnoffactive{@let"=@normaldoublequote
+@let\=@normalbackslash
+@let~=@normaltilde
+@let^=@normalcaret
+@let_=@normalunderscore
+@let|=@normalverticalbar
+@let<=@normalless
+@let>=@normalgreater
+@let+=@normalplus}
+
+% Make _ and + \other characters, temporarily.
+% This is canceled by @fixbackslash.
+@otherifyactive
+
+% If a .fmt file is being used, we don't want the `\input texinfo' to show up.
+% That is what \eatinput is for; after that, the `\' should revert to printing
+% a backslash.
+%
+@gdef@eatinput input texinfo{@fixbackslash}
+@global@let\ = @eatinput
+
+% On the other hand, perhaps the file did not have a `\input texinfo'. Then
+% the first `\{ in the file would cause an error. This macro tries to fix
+% that, assuming it is called before the first `\' could plausibly occur.
+% Also back turn on active characters that might appear in the input
+% file name, in case not using a pre-dumped format.
+%
+@gdef@fixbackslash{@ifx\@eatinput @let\ = @normalbackslash @fi
+ @catcode`+=@active @catcode`@_=@active}
+
+% These look ok in all fonts, so just make them not special. The @rm below
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+@catcode`@$=@other @catcode`@%=@other @catcode`@&=@other @catcode`@#=@other
+
+@textfonts
+@rm
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+@c Local variables:
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+@c page-delimiter: "^\\\\message"
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+@c time-stamp-format: "%:y-%02m-%02d"
+@c time-stamp-end: "}"
+@c End:
+++ /dev/null
-<!DOCTYPE Book PUBLIC "-//Davenport//DTD DocBook V3.0//EN">
-
-<book>
-<title>GiNaC MAJOR_VERSION.MINOR_VERSION Tutorial</title>
-<bookinfo>
-<subtitle>An open framework for symbolic computation within the C++ programming language</subtitle>
-<bookbiblio>
-<authorgroup>
- <collab>
- <collabname>The GiNaC Group</collabname>
- </collab>
- <author>
- <firstname>Christian</firstname><surname>Bauer</surname>
- <affiliation>
- <address><email>Christian.Bauer@Uni-Mainz.DE</email></address>
- </affiliation>
- </author>
- <author>
- <firstname>Alexander</firstname><surname>Frink</surname>
- <affiliation>
- <address><email>Alexander.Frink@Uni-Mainz.DE</email></address>
- </affiliation>
- </author>
- <author>
- <firstname>Richard</firstname><othername>B.</othername><surname>Kreckel</surname>
- <affiliation>
- <address><email>Richard.Kreckel@Uni-Mainz.DE</email></address>
- </affiliation>
- </author>
-</authorgroup>
-</bookbiblio>
-</bookinfo>
-
-<preface>
-<title>Introduction</title>
-
-<para>The motivation behind GiNaC derives from the observation that
-most present day computer algebra systems (CAS) are linguistically and
-semantically impoverished. It is an attempt to overcome the current
-situation by extending a well established and standardized computer
-language (C++) by some fundamental symbolic capabilities, thus
-allowing for integrated systems that embed symbolic manipulations
-together with more established areas of computer science (like
-computation-intense numeric applications, graphical interfaces, etc.)
-under one roof.</para>
-
-<para>This tutorial is intended for the novice user who is new to
-GiNaC but already has some background in C++ programming. However,
-since a hand made documentation like this one is difficult to keep in
-sync with the development the actual documentation is inside the
-sources in the form of comments. That documentation may be parsed by
-one of the many Javadoc-like documentation systems. If you fail at
-generating it you may access it directly at URL <ulink
-url="http://www.ginac.de/reference/"><literal>http://www.ginac.de/reference/</literal></ulink>.
-It is an invaluable resource not only for the advanced user who wishes
-to extend the system (or chase bugs) but for everybody who wants to
-comprehend the inner workings of GiNaC. This little tutorial on the
-other hand only covers the basic things that are unlikely to change in
-the near future. </para>
-
-<sect1><title>License</title>
-
-<para>The GiNaC framework for symbolic computation within the C++
-programming language is Copyright (C) 1999 Johannes Gutenberg
-Universität Mainz, Germany.</para>
-
-<para>This program is free software; you can redistribute it and/or
-modify it under the terms of the GNU General Public License as
-published by the Free Software Foundation; either version 2 of the
-License, or (at your option) any later version.</para>
-
-<para>This program is distributed in the hope that it will be useful, but
-WITHOUT ANY WARRANTY; without even the implied warranty of
-MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
-General Public License for more details.</para>
-
-<para>You should have received a copy of the GNU General Public License
-along with this program; see the file COPYING. If not, write to the
-Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
-MA 02111-1307, USA.</para>
-
-</preface>
-
-<chapter>
-<title>A Tour of GiNaC</title>
-
-<para>This quick tour of GiNaC wants to rise your interest in in the
-subsequent chapters by showing off a bit. Please excuse us if it
-leaves many open questions.</para>
-
-<sect1><title>How to use it from within C++</title> <para>The GiNaC
-open framework for symbolic computation within the C++ programming
-language does not try to define a language of it's own as conventional
-CAS do. Instead, it extends the capabilities of C++ by symbolic
-manipulations. Here is how to generate and print a simple (and
-pointless) bivariate polynomial with some large coefficients:
-<example>
-<title>My first GiNaC program (a bivariate polynomial)</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-int main()
-{
- symbol x("x"), y("y");
- ex poly;
-
- for (int i=0; i<3; ++i)
- poly += factorial(i+16)*pow(x,i)*pow(y,2-i);
-
- cout << poly << endl;
- return 0;
-}
-</programlisting>
-<para>Assuming the file is called <literal>hello.cc</literal>, on
-our system we can compile and run it like this:</para>
-<screen>
-<prompt>$</prompt> c++ hello.cc -o hello -lcln -lginac
-<prompt>$</prompt> ./hello
-355687428096000*x*y+20922789888000*y^2+6402373705728000*x^2
-</screen>
-</example>
-</para>
-
-<para>Next, there is a more meaningful C++ program that calls a
-function which generates Hermite polynomials in a specified free
-variable.
-<example>
-<title>My second GiNaC program (Hermite polynomials)</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-ex HermitePoly(symbol x, int deg)
-{
- ex HKer=exp(-pow(x,2));
- // uses the identity H_n(x) == (-1)^n exp(x^2) (d/dx)^n exp(-x^2)
- return normal(pow(-1,deg) * diff(HKer, x, deg) / HKer);
-}
-
-int main()
-{
- symbol z("z");
-
- for (int i=0; i<6; ++i)
- cout << "H_" << i << "(z) == " << HermitePoly(z,i) << endl;
-
- return 0;
-}
-</programlisting>
-<para>When run, this will type out</para>
-<screen>
-H_0(z) == 1
-H_1(z) == 2*z
-H_2(z) == 4*z^2-2
-H_3(z) == -12*z+8*z^3
-H_4(z) == -48*z^2+16*z^4+12
-H_5(z) == 120*z-160*z^3+32*z^5
-</screen>
-</example>
-This method of generating the coefficients is of course far from
-optimal for production purposes.</para>
-
-<para>In order to show some more examples of what GiNaC can do we
-will now use <literal>ginsh</literal>, a simple GiNaC interactive
-shell that provides a convenient window into GiNaC's capabilities.
-</para></sect1>
-
-<sect1><title>What it can do for you</title>
-
-<para>After invoking <literal>ginsh</literal> one can test and
-experiment with GiNaC's features much like in other Computer Algebra
-Systems except that it does not provide programming constructs like
-loops or conditionals. For a concise description of the
-<literal>ginsh</literal> syntax we refer to its accompanied man-page.
-Suffice to say that assignments and comparisons in
-<literal>ginsh</literal> are written as they are in C,
-i.e. <literal>=</literal> assigns and <literal>==</literal>
-compares.</para>
-
-<para>It can manipulate arbitrary precision integers in a very fast
-way. Rational numbers are automatically converted to fractions of
-coprime integers:
-<screen>
-> x=3^150;
-369988485035126972924700782451696644186473100389722973815184405301748249
-> y=3^149;
-123329495011708990974900260817232214728824366796574324605061468433916083
-> x/y;
-3
-> y/x;
-1/3
-</screen>
-</para>
-
-<para>All numbers occuring in GiNaC's expressions can be converted
-into floating point numbers with the <literal>evalf</literal> method,
-to arbitrary accuracy:
-<screen>
-> evalf(1/7);
-0.14285714285714285714
-> Digits=150;
-150
-> evalf(1/7);
-0.1428571428571428571428571428571428571428571428571428571428571428571428
-5714285714285714285714285714285714285
-</screen>
-</para>
-
-<para>Exact numbers other than rationals that can be manipulated in
-GiNaC include predefined constants like Archimedes' Pi. They can both
-be used in symbolic manipulations (as an exact number) as well as in
-numeric expressions (as an inexact number):
-<screen>
-> a=Pi^2+x;
-x+Pi^2
-> evalf(a);
-x+9.869604401089358619L0
-> x=2;
-2
-> evalf(a);
-11.869604401089358619L0
-</screen>
-</para>
-
-<para>Built-in functions evaluate immediately to exact numbers if
-this is possible. Conversions that can be safely performed are done
-immediately; conversions that are not generally valid are not done:
-<screen>
-> cos(42*Pi);
-1
-> cos(acos(x));
-x
-> acos(cos(x));
-acos(cos(x))
-</screen>
-(Note that converting the last input to <literal>x</literal> would
-allow one to conclude that <literal>42*Pi</literal> is equal to
-<literal>0</literal>.)</para>
-
-<para>Linear equation systems can be solved along with basic linear
-algebra manipulations over symbolic expressions. In C++ GiNaC offers
-a matrix class for this purpose but we can see what it can do using
-<literal>ginsh</literal>'s notation of double brackets to type them
-in:
-<screen>
-> lsolve(a+x*y==z,x);
-y^(-1)*(z-a);
-lsolve([3*x+5*y == 7, -2*x+10*y == -5], [x, y]);
-[x==19/8,y==-1/40]
-> M = [[ [[1, 3]], [[-3, 2]] ]];
-[[ [[1,3]], [[-3,2]] ]]
-> determinant(M);
-11
-> charpoly(M,lambda);
-lambda^2-3*lambda+11
-</screen>
-</para>
-
-<para>Multivariate polynomials and rational functions may be expanded,
-collected and normalized (i.e. converted to a ratio of two coprime
-polynomials):
-<screen>
-> a = x^4 + 2*x^2*y^2 + 4*x^3*y + 12*x*y^3 - 3*y^4;
--3*y^4+x^4+12*x*y^3+2*x^2*y^2+4*x^3*y
-> b = x^2 + 4*x*y - y^2;
--y^2+x^2+4*x*y
-> expand(a*b);
-3*y^6+x^6-24*x*y^5+43*x^2*y^4+16*x^3*y^3+17*x^4*y^2+8*x^5*y
-> collect(a*b,x);
-3*y^6+48*x*y^4+2*x^2*y^2+x^4*(-y^2+x^2+4*x*y)+4*x^3*y*(-y^2+x^2+4*x*y)
-> normal(a/b);
-3*y^2+x^2
-</screen>
-</para>
-
-<para>You can differentiate functions and expand them as Taylor or
-Laurent series (the third argument of series is the evaluation point,
-the fourth defines the order):
-<screen>
-> diff(tan(x),x);
-tan(x)^2+1
-> series(sin(x),x,0,4);
-x-1/6*x^3+Order(x^4)
-> series(1/tan(x),x,0,4);
-x^(-1)-1/3*x+Order(x^2)
-</screen>
-</para>
-
-<para>If you ever wanted to convert units in C or C++ and found this
-is cumbersome, here is the solution. Symbolic types can always be
-used as tags for different types of objects. Converting from wrong
-units to the metric system is therefore easy:
-<screen>
-> in=.0254*m;
-0.0254*m
-> lb=.45359237*kg;
-0.45359237*kg
-> 200*lb/in^2;
-140613.91592783185568*kg*m^(-2)
-</screen>
-</para>
-
-</sect1>
-
-</chapter>
-
-
-<chapter>
-<title>Installation</title>
-
-<para>GiNaC's installation follows the spirit of most GNU software. It is
-easily installed on your system by three steps: configuration, build,
-installation.</para>
-
-<sect1><title id="CLN-main">Prerequistes</title>
-
-<para>In order to install GiNaC on your system, some prerequistes need
-to be met. First of all, you need to have a C++-compiler adhering to
-the ANSI-standard <citation>ISO/IEC 14882:1998(E)</citation>. We used
-<literal>GCC</literal> for development so if you have a different
-compiler you are on your own. For the configuration to succeed you
-need a Posix compliant shell installed in <literal>/bin/sh</literal>,
-GNU <literal>bash</literal> is fine. Perl is needed by the built
-process as well, since some of the source files are automatically
-generated by Perl scripts. Last but not least, Bruno Haible's library
-<literal>CLN</literal> is extensively used and needs to be installed
-on your system. Please get it from <ulink
-url="ftp://ftp.santafe.edu/pub/gnu/"><literal>ftp://ftp.santafe.edu/pub/gnu/</literal></ulink>
-or from <ulink
-url="ftp://ftp.ilog.fr/pub/Users/haible/gnu/"><literal>ftp://ftp.ilog.fr/pub/Users/haible/gnu/</literal></ulink>
-(it is covered by GPL) and install it prior to trying to install
-GiNaC. The configure script checks if it can find it and if it cannot
-it will refuse to continue.</para></sect1>
-
-<sect1><title>Configuration</title>
-
-<para>To configure GiNaC means to prepare the source distribution for
-building. It is done via a shell script called
-<literal>configure</literal> that is shipped with the sources.
-(Actually, this script is by itself created with GNU Autoconf from the
-files <literal>configure.in</literal> and
-<literal>aclocal.m4</literal>.) Since a configure script generated by
-GNU Autoconf never prompts, all customization must be done either via
-command line parameters or environment variables. It accepts a list
-of parameters, the complete set of which can be listed by calling it
-with the <literal>--help</literal> option. The most important ones
-will be shortly described in what follows:
-<itemizedlist>
- <listitem>
- <para><literal>--disable-shared</literal>: When given, this option
- switches off the build of a shared library, i.e. a
- <literal>.so</literal>-file. This may be convenient when developing
- because it considerably speeds up compilation.</para>
- </listitem>
- <listitem>
- <para><literal>--prefix=</literal><emphasis>PREFIX</emphasis>: The
- directory where the compiled library and headers are installed. It
- defaults to <literal>/usr/local</literal> which means that the
- library is installed in the directory
- <literal>/usr/local/lib</literal> and the header files in
- <literal>/usr/local/include/GiNaC</literal> and the documentation
- (like this one) into <literal>/usr/local/share/doc/GiNaC</literal>.</para>
- </listitem>
- <listitem>
- <para><literal>--libdir=</literal><emphasis>LIBDIR</emphasis>: Use
- this option in case you want to have the library installed in some
- other directory than
- <emphasis>PREFIX</emphasis><literal>/lib/</literal>.</para>
- </listitem>
- <listitem>
- <para><literal>--includedir=</literal><emphasis>INCLUDEDIR</emphasis>:
- Use this option in case you want to have the header files
- installed in some other directory than
- <emphasis>PREFIX</emphasis><literal>/include/ginac/</literal>. For
- instance, if you specify
- <literal>--includedir=/usr/include</literal> you will end up with
- the header files sitting in the directory
- <literal>/usr/include/ginac/</literal>. Note that the subdirectory
- <literal>GiNaC</literal> is enforced by this process in order to
- keep the header files separated from others. This avoids some
- clashes and allows for an easier deinstallation of GiNaC. This ought
- to be considered A Good Thing (tm).</para>
- </listitem>
- <listitem>
- <para><literal>--datadir=</literal><emphasis>DATADIR</emphasis>:
- This option may be given in case you want to have the documentation
- installed in some other directory than
- <emphasis>PREFIX</emphasis><literal>/share/doc/GiNaC/</literal>.
- </listitem>
-</itemizedlist>
-</para>
-
-<para>In addition, you may specify some environment variables.
-<literal>CXX</literal> holds the path and the name of the C++ compiler
-in case you want to override the default in your path. (The
-<literal>configure</literal> script searches your path for
-<literal>c++</literal>, <literal>g++</literal>,
-<literal>gcc</literal>, <literal>CC</literal>, <literal>cxx</literal>
-and <literal>cc++</literal> in that order.) It may be very useful to
-define some compiler flags with the <literal>CXXFLAGS</literal>
-environment variable, like optimization, debugging information and
-warning levels. If ommitted, it defaults to <literal>-g
--O2</literal>.</para>
-
-<para>The whole process is illustrated in the following two
-examples. (Substitute <literal>setenv VARIABLE value</literal> for
-<literal>export VARIABLE=value</literal> if the Berkeley C shell is
-your login shell.)
-
-<example><title>Sample sessions of how to call the
-configure-script</title> <para>Simple configuration for a site-wide
-GiNaC library assuming everything is in default paths:</para>
-<screen>
-<prompt>$</prompt> export CXXFLAGS="-Wall -O2"
-<prompt>$</prompt> ./configure
-</screen>
-<para>Configuration for a private static GiNaC library with several
-components sitting in custom places (site-wide <literal>GCC</literal>
-and private <literal>CLN</literal>), the compiler pursueded to be
-picky and full assertions switched on:</para>
-<screen>
-<prompt>$</prompt> export CXX=/usr/local/gnu/bin/c++
-<prompt>$</prompt> export CPPFLAGS="${CPPFLAGS} -I${HOME}/include"
-<prompt>$</prompt> export CXXFLAGS="${CXXFLAGS} -DDO_GINAC_ASSERT -ggdb -Wall -ansi -pedantic -O2"
-<prompt>$</prompt> export LDFLAGS="${LDFLAGS} -L${HOME}/lib"
-<prompt>$</prompt> ./configure --disable-shared --prefix=${HOME}
-</screen>
-</example>
-</para>
-
-</sect1>
-
-<sect1><title>Building GiNaC</title>
-
-<para>After proper configuration you should just build the whole
-library by typing <literal>make</literal> at the command
-prompt and go for a cup of coffee.</para>
-
-<para>Just to make sure GiNaC works properly you may run a simple test
-suite by typing <literal>make check</literal>. This will compile some
-sample programs, run them and compare the output to reference output.
-Each of the checks should return a message <literal>passed</literal>
-together with the CPU time used for that particular test. If it does
-not, something went wrong. This is mostly intended to be a QA-check
-if something was broken during the development, but not a sanity check
-of your system. Another intent is to allow people to fiddle around
-with optimization. If <literal>CLN</literal> was installed all right
-this step is unlikely to return any errors.</para>
-
-</sect1>
-
-<sect1><title>Installation</title>
-
-<para>To install GiNaC on your system, simply type <literal>make
-install</literal>. As described in the section about configuration
-the files will be installed in the following directories (the
-directories will be created if they don't already exist):
-<itemizedlist>
- <listitem>
- <para><literal>libginac.a</literal> will go into
- <emphasis>PREFIX</emphasis><literal>/lib/</literal> (or
- <emphasis>LIBDIR</emphasis>) which defaults to
- <literal>/usr/local/lib/</literal>. So will
- <literal>libginac.so</literal> if the the configure script was
- given the option <literal>--enable-shared</literal>. In that
- case, the proper symlinks will be established as well (by running
- <literal>ldconfig</literal>).</para>
- </listitem>
- <listitem>
- <para>All the header files will be installed into
- <emphasis>PREFIX</emphasis><literal>/include/ginac/</literal> (or
- <emphasis>INCLUDEDIR</emphasis><literal>/ginac/</literal>, if
- specified).</para>
- </listitem>
- <listitem>
- <para>All documentation (HTML, Postscript and DVI) will be stuffed
- into
- <emphasis>PREFIX</emphasis><literal>/share/doc/GiNaC/</literal>
- (or <emphasis>DATADIR</emphasis><literal>/doc/GiNaC/</literal>, if
- specified).</para>
- </listitem>
-</itemizedlist>
-</para>
-
-<para>Just for the record we will list some other useful make targets:
-<literal>make clean</literal> deletes all files generated by
-<literal>make</literal>, i.e. all the object files. In addition
-<literal>make distclean</literal> removes all files generated by
-configuration. And finally <literal>make uninstall</literal> removes
-the installed library and header files<footnoteref
-linkend="warnuninstall-1">.
-
- <footnote id="warnuninstall-1"><para>Uninstallation does not work
- after you have called <literal>make distclean</literal> since the
- <literal>Makefile</literal> is itself generated by the configuration
- from <literal>Makefile.in</literal> and hence deleted by
- <literal>make distclean</literal>. There are two obvious ways out
- of this dilemma. First, you can run the configuration again with
- the same <emphasis>PREFIX</emphasis> thus creating a
- <literal>Makefile</literal> with a working
- <literal>uninstall</literal> target. Second, you can do it by hand
- since you now know where all the files went during
- installation.</para></footnote>
-</para>
-
-</sect1>
-</chapter>
-
-
-<chapter>
-<title>Basic Concepts</title>
-
-<para>This chapter will describe the different fundamental objects
-that can be handled with GiNaC. But before doing so, it is worthwhile
-introducing you to the more commonly used class of expressions,
-representing a flexible meta-class for storing all mathematical
-objects.</para>
-
-<sect1><title>Expressions</title>
-
-<para>The most common class of objects a user deals with is the
-expression <literal>ex</literal>, representing a mathematical object
-like a variable, number, function, sum, product, etc... Expressions
-may be put together to form new expressions, passed as arguments to
-functions, and so on. Here is a little collection of valid
-expressions:
-<example><title>Examples of expressions</title>
-<programlisting>
- ex MyEx1 = 5; // simple number
- ex MyEx2 = x + 2*y; // polynomial in x and y
- ex MyEx3 = (x + 1)/(x - 1); // rational expression
- ex MyEx4 = sin(x + 2*y) + 3*z + 41; // containing a function
- ex MyEx5 = MyEx4 + 1; // similar to above
-</programlisting>
-</example>
-Before describing the more fundamental objects that form the building
-blocks of expressions we'll have a quick look under the hood by
-describing how expressions are internally managed.</para>
-
-<sect2><title>Digression: Expressions are reference counted</title>
-
-<para>An expression is extremely light-weight since internally it
-works like a handle to the actual representation and really holds
-nothing more than a pointer to some other object. What this means in
-practice is that whenever you create two <literal>ex</literal> and set
-the second equal to the first no copying process is involved. Instead,
-the copying takes place as soon as you try to change the second.
-Consider the simple sequence of code:
-<example><title>Simple copy-on-write semantics</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-int main()
-{
- symbol x("x"), y("y"), z("z");
- ex e1, e2;
-
- e1 = sin(x + 2*y) + 3*z + 41;
- e2 = e1; // e2 points to same object as e1
- cout << e2 << endl; // prints sin(x+2*y)+3*z+41
- e2 += 1; // e2 is copied into a new object
- cout << e2 << endl; // prints sin(x+2*y)+3*z+42
- // ...
-}
-</programlisting>
-</example>
-The line <literal>e2 = e1;</literal> creates a second expression
-pointing to the object held already by <literal>e1</literal>. The
-time involved for this operation is therefore constant, no matter how
-large <literal>e1</literal> was. Actual copying, however, must take
-place in the line <literal>e2 += 1</literal> because
-<literal>e1</literal> and <literal>e2</literal> are not handles for
-the same object any more. This concept is called
-<emphasis>copy-on-write semantics</emphasis>. It increases
-performance considerably whenever one object occurs multiple times and
-represents a simple garbage collection scheme because when an
-<literal>ex</literal> runs out of scope its destructor checks whether
-other expressions handle the object it points to too and deletes the
-object from memory if that turns out not to be the case. A slightly
-less trivial example of differentiation using the chain-rule should
-make clear how powerful this can be. <example><title>Advanced
-copy-on-write semantics</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-int main()
-{
- symbol x("x"), y("y");
-
- ex e1 = x + 3*y;
- ex e2 = pow(e1, 3);
- ex e3 = diff(sin(e2), x); // first derivative of sin(e2) by x
- cout << e1 << endl // prints x+3*y
- << e2 << endl // prints (x+3*y)^3
- << e3 << endl; // prints 3*(x+3*y)^2*cos((x+3*y)^3)
- // ...
-}
-</programlisting>
-</example>
-Here, <literal>e1</literal> will actually be referenced three times
-while <literal>e2</literal> will be referenced two times. When the
-power of an expression is built, that expression needs not be
-copied. Likewise, since the derivative of a power of an expression can
-be easily expressed in terms of that expression, no copying of
-<literal>e1</literal> is involved when <literal>e3</literal> is
-constructed. So, when <literal>e3</literal> is constructed it will
-print as <literal>3*(x+3*y)^2*cos((x+3*y)^3)</literal> but the
-argument of <literal>cos()</literal> only holds a reference to
-<literal>e2</literal> and the factor in front is just
-<literal>3*e1^2</literal>.
-</para>
-
-<para>As a user of GiNaC, you cannot see this mechanism of
-copy-on-write semantics. When you insert an expression into a second
-expression, the result behaves exactly as if the contents of the first
-expression were inserted. But it may be useful to remember that this
-is not what happens. Knowing this will enable you to write much more
-efficient code. If you still have an uncertain feeling with
-copy-on-write semantics, we recommend you have a look at the
-<emphasis>C++-FAQ lite</emphasis> by Marshall Cline. Chapter 16
-covers this issue and presents an implementation which is pretty close
-to the one in GiNaC. You can find it on the Web at <ulink
-url="http://www.cerfnet.com/~mpcline/c++-faq-lite/"><literal>http://www.cerfnet.com/~mpcline/c++-faq-lite/</literal></ulink>.</para>
-
-<para>So much for expressions. But what exactly are these expressions
-handles of? This will be answered in the following sections.</para>
-</sect2>
-</sect1>
-
-<sect1><title>The Class Hierarchy</title>
-
-<para>GiNaC's class hierarchy consists of several classes representing
-mathematical objects, all of which (except for <literal>ex</literal>
-and some helpers) are internally derived from one abstract base class
-called <literal>basic</literal>. You do not have to deal with objects
-of class <literal>basic</literal>, instead you'll be dealing with
-symbols and functions of symbols. You'll soon learn in this chapter
-how many of the functions on symbols are really classes. This is
-because simple symbolic arithmetic is not supported by languages like
-C++ so in a certain way GiNaC has to implement its own arithmetic.</para>
-
-<para>To give an idea about what kinds of symbolic composits may be
-built we have a look at the most important classes in the class
-hierarchy. The dashed line symbolizes a "points to" or "handles"
-relationship while the solid lines stand for "inherits from"
-relationships.
-<figure id="classhier-id" float="1">
-<title>The GiNaC class hierarchy</title>
- <graphic align="center" fileref="classhierarchy.graext" format="GRAEXT"></graphic>
-</figure>
-Some of the classes shown here (the ones sitting in white boxes) are
-abstract base classes that are of no interest at all for the user.
-They are used internally in order to avoid code duplication if
-two or more classes derived from them share certain features. An
-example would be <literal>expairseq</literal>, which is a container
-for a sequence of pairs each consisting of one expression and a number
-(<literal>numeric</literal>). What <emphasis>is</emphasis> visible to
-the user are the derived classes <literal>add</literal> and
-<literal>mul</literal>, representing sums of terms and products,
-respectively. We'll come back later to some more details about these
-two classes and motivate the use of pairs in sums and products here.</para>
-
-<sect2><title>Digression: Internal representation of products and sums</title>
-
-<para>Although it should be completely transparent for the user of
-GiNaC a short discussion of this topic helps to understand the sources
-and also explain performance to a large degree. Consider the symbolic
-expression
-<emphasis>2*d<superscript>3</superscript>*(4*a+5*b-3)</emphasis>,
-which could naively be represented by a tree of linear containers for
-addition and multiplication, one container for exponentiation with
-base and exponent and some atomic leaves of symbols and numbers in
-this fashion:
-<figure id="repres-naive-id" float="1">
-<title>Naive internal representation-tree for <emphasis>2*d<superscript>3</superscript>*(4*a+5*b-3)</emphasis></title>
- <graphic align="center" fileref="rep_naive.graext" format="GRAEXT"></graphic>
-</figure>
-However, doing so results in a rather deeply nested tree which will
-quickly become inefficient to manipulate. If we represent the sum
-instead as a sequence of terms, each having a purely numeric
-multiplicative coefficient and the multiplication as a sequence of
-terms, each having a numeric exponent, the tree becomes much more
-flat.
-<figure id="repres-pair-id" float="1">
-<title>Pair-wise internal representation-tree for <emphasis>2*d<superscript>3</superscript>*(4*a+5*b-3)</emphasis></title>
- <graphic align="center" fileref="rep_pair.graext" format="GRAEXT"></graphic>
-</figure>
-The number <literal>3</literal> above the symbol <literal>d</literal>
-shows that <literal>mul</literal> objects are treated similarly where
-the coefficients are interpreted as <emphasis>exponents</emphasis>
-now. Addition of sums of terms or multiplication of products with
-numerical exponents can be coded to be very efficient with such a
-pair-representation. Internally, this handling is done by many CAS in
-this way. It typically speeds up manipulations by an order of
-magnitude. The overall multiplicative factor <literal>2</literal> and
-the additive term <literal>-3</literal> look somewhat cumbersome in
-this representation, however, since they are still carrying a trivial
-exponent and multiplicative factor <literal>1</literal> respectively.
-Within GiNaC, this is avoided by adding a field that carries overall
-numeric coefficient.
-<figure id="repres-real-id" float="1">
-<title>Realistic picture of GiNaC's representation-tree for <emphasis>2*d<superscript>3</superscript>*(4*a+5*b-3)</emphasis></title>
- <graphic align="center" fileref="rep_real.graext" format="GRAEXT"></graphic>
-</figure>
-This also allows for a better handling of numeric radicals, since
-<literal>sqrt(2)</literal> can now be carried along calculations. Now
-it should be clear, why both classes <literal>add</literal> and
-<literal>mul</literal> are derived from the same abstract class: the
-data representation is the same, only the semantics differs. In the
-class hierarchy, methods for polynomial expansion and such are
-reimplemented for <literal>add</literal> and <literal>mul</literal>,
-but the data structure is inherited from
-<literal>expairseq</literal>.</para>
-
-</sect1>
-
-<sect1><title>Symbols</title>
-
-<para>Symbols are for symbolic manipulation what atoms are for
-chemistry. You can declare objects of class <literal>symbol</literal>
-as any other object simply by saying <literal>symbol x,y;</literal>.
-There is, however, a catch in here having to do with the fact that C++
-is a compiled language. The information about the symbol's name is
-thrown away by the compiler but at a later stage you may want to print
-expressions holding your symbols. In order to avoid confusion GiNaC's
-symbols are able to know their own name. This is accomplished by
-declaring its name for output at construction time in the fashion
-<literal>symbol x("x");</literal>. If you declare a symbol using the
-default constructor (i.e. without string-argument) the system will
-deal out a unique name. That name may not be suitable for printing
-but for internal routines when no output is desired it is often
-enough. We'll come across examples of such symbols later in this
-tutorial.</para>
-
-<para>This implies that the stings passed to symbols at construction
-time may not be used for comparing two of them. It is perfectly
-legitimate to write <literal>symbol x("x"),y("x");</literal> but it is
-likely to lead into trouble. Here, <literal>x</literal> and
-<literal>y</literal> are different symbols and statements like
-<literal>x-y</literal> will not be simplified to zero although the
-output <literal>x-x</literal> looks funny. Such output may also occur
-when there are two different symbols in two scopes, for instance when
-you call a function that declares a symbol with a name already
-existent in a symbol in the calling function. Again, comparing them
-(using <literal>operator==</literal> for instance) will always reveal
-their difference. Watch out, please.</para>
-
-<para>Although symbols can be assigned expressions for internal
-reasons, you should not do it (and we are not going to tell you how it
-is done). If you want to replace a symbol with something else in an
-expression, you can use the expression's <literal>.subs()</literal>
-method.</para>
-
-</sect1>
-
-<sect1><title>Numbers</title>
-
-<para>For storing numerical things, GiNaC uses Bruno Haible's library
-<literal>CLN</literal>. The classes therein serve as foundation
-classes for GiNaC. <literal>CLN</literal> stands for Class Library
-for Numbers or alternatively for Common Lisp Numbers. In order to
-find out more about <literal>CLN</literal>'s internals the reader is
-refered to the documentation of that library. Suffice to say that it
-is by itself build on top of another library, the GNU Multiple
-Precision library <literal>GMP</literal>, which is an extremely fast
-library for arbitrary long integers and rationals as well as arbitrary
-precision floating point numbers. It is very commonly used by several
-popular cryptographic applications. <literal>CLN</literal> extends
-<literal>GMP</literal> by several useful things: First, it introduces
-the complex number field over either reals (i.e. floating point
-numbers with arbitrary precision) or rationals. Second, it
-automatically converts rationals to integers if the denominator is
-unity and complex numbers to real numbers if the imaginary part
-vanishes and also correctly treats algebraic functions. Third it
-provides good implementations of state-of-the-art algorithms for all
-trigonometric and hyperbolic functions as well as for calculation of
-some useful constants.</para>
-
-<para>The user can construct an object of class
-<literal>numeric</literal> in several ways. The following example
-shows the four most important constructors: construction from
-C-integer, construction of fractions from two integers, construction
-from C-float and construction from a string.
-<example><title>Construction of numbers</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-int main()
-{
- numeric two(2); // exact integer 2
- numeric r(2,3); // exact fraction 2/3
- numeric e(2.71828); // floating point number
- numeric p("3.1415926535897932385"); // floating point number
-
- cout << two*p << endl; // floating point 6.283...
- // ...
-}
-</programlisting>
-</example>
-Note that all those constructors are <emphasis>explicit</emphasis>
-which means you are not allowed to write <literal>numeric
-two=2;</literal>. This is because the basic objects to be handled by
-GiNaC are the expressions <literal>ex</literal> and we want to keep
-things simple and wish objects like <literal>pow(x,2)</literal> to be
-handled the same way as <literal>pow(x,a)</literal>, which means that
-we need to allow a general <literal>ex</literal> as base and exponent.
-Therefore there is an implicit constructor from C-integers directly to
-expressions handling numerics at work in most of our examples. This
-design really becomes convenient when one declares own functions
-having more than one parameter but it forbids using implicit
-constructors because that would lead to ambiguities. </para>
-
-<para>It may be tempting to construct numbers writing <literal>numeric
-r(3/2)</literal>. This would, however, call C's built-in operator
-<literal>/</literal> for integers first and result in a numeric
-holding a plain integer 1. <emphasis>Never use
-</emphasis><literal>/</literal><emphasis> on integers!</emphasis> Use
-the constructor from two integers instead, as shown in the example
-above. Writing <literal>numeric(1)/2</literal> may look funny but
-works also. </para>
-
-<para>We have seen now the distinction between exact numbers and
-floating point numbers. Clearly, the user should never have to worry
-about dynamically created exact numbers, since their "exactness"
-always determines how they ought to be handled. The situation is
-different for floating point numbers. Their accuracy is handled by
-one <emphasis>global</emphasis> variable, called
-<literal>Digits</literal>. (For those readers who know about Maple:
-it behaves very much like Maple's <literal>Digits</literal>). All
-objects of class numeric that are constructed from then on will be
-stored with a precision matching that number of decimal digits:
-<example><title>Controlling the precision of floating point numbers</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-void foo()
-{
- numeric three(3.0), one(1.0);
- numeric x = one/three;
-
- cout << "in " << Digits << " digits:" << endl;
- cout << x << endl;
- cout << Pi.evalf() << endl;
-}
-
-int main()
-{
- foo();
- Digits = 60;
- foo();
- return 0;
-}
-</programlisting>
-</example>
-The above example prints the following output to screen:
-<screen>
-in 17 digits:
-0.333333333333333333
-3.14159265358979324
-in 60 digits:
-0.333333333333333333333333333333333333333333333333333333333333333333
-3.14159265358979323846264338327950288419716939937510582097494459231
-</screen>
-</para>
-
-<para>It should be clear that objects of class
-<literal>numeric</literal> should be used for constructing numbers or
-for doing arithmetic with them. The objects one deals with most of
-the time are the polymorphic expressions <literal>ex</literal>.</para>
-
-<sect2><title>Tests on numbers</title>
-
-<para>Once you have declared some numbers, assigned them to
-expressions and done some arithmetic with them it is frequently
-desired to retrieve some kind of information from them like asking
-whether that number is integer, rational, real or complex. For those
-cases GiNaC provides several useful methods. (Internally, they fall
-back to invocations of certain CLN functions.)</para>
-
-<para>As an example, let's construct some rational number, multiply it
-with some multiple of its denominator and check what comes out:
-<example><title>Sample test on objects of type numeric</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-// some very important constants:
-const numeric twentyone(21);
-const numeric ten(10);
-const numeric fife(5);
-
-int main()
-{
- numeric answer = twentyone;
-
- answer /= five;
- cout << answer.is_integer() << endl; // false, it's 21/5
- answer *= ten;
- cout << answer.is_integer() << endl; // true, it's 42 now!
- // ...
-}
-</programlisting>
-</example>
-
-Note that the variable <literal>answer</literal> is constructed here
-as an integer by <literal>numeric</literal>'s copy constructor but in
-an intermediate step it holds a rational number represented as integer
-numerator and integer denominator. When multiplied by 10, the
-denominator becomes unity and the result is automatically converted to
-a pure integer again. Internally, the underlying
-<literal>CLN</literal> is responsible for this behaviour and we refer
-the reader to <literal>CLN</literal>'s documentation. Suffice to say
-that the same behaviour applies to complex numbers as well as return
-values of certain functions. Complex numbers are automatically
-converted to real numbers if the imaginary part becomes zero. The
-full set of tests that can be applied is listed in the following
-table.
-
-<informaltable colsep="0" frame="topbot" pgwide="1">
-<tgroup cols="2">
-<colspec colnum="1" colwidth="1*">
-<colspec colnum="2" colwidth="2*">
-<thead>
- <row>
- <entry>Method</entry>
- <entry>Returns true if...</entry>
- </row>
-</thead>
-<tbody>
- <row>
- <entry><literal>.is_zero()</literal></entry>
- <entry>object is equal to zero</entry>
- </row>
- <row>
- <entry><literal>.is_positive()</literal></entry>
- <entry>object is not complex and greater than 0</entry>
- </row>
- <row>
- <entry><literal>.is_integer()</literal></entry>
- <entry>object is a (non-complex) integer</entry>
- </row>
- <row>
- <entry><literal>.is_pos_integer()</literal></entry>
- <entry>object is an integer and greater than 0</entry>
- </row>
- <row>
- <entry><literal>.is_nonneg_integer()</literal></entry>
- <entry>object is an integer and greater equal 0</entry>
- </row>
- <row>
- <entry><literal>.is_even()</literal></entry>
- <entry>object is an even integer</entry>
- </row>
- <row>
- <entry><literal>.is_odd()</literal></entry>
- <entry>object is an odd integer</entry>
- </row>
- <row>
- <entry><literal>.is_prime()</literal></entry>
- <entry>object is a prime integer (probabilistic primality test)</entry>
- </row>
- <row>
- <entry><literal>.is_rational()</literal></entry>
- <entry>object is an exact rational number (integers are rational, too, as are complex extensions like <literal>2/3+7/2*I</literal>)</entry>
- </row>
- <row>
- <entry><literal>.is_real()</literal></entry>
- <entry>object is a real integer, rational or float (i.e. is not complex)</entry>
- </row>
-</tbody>
-</tgroup>
-</informaltable>
-</para>
-
-</sect2>
-
-</sect1>
-
-
-<sect1><title>Constants</title>
-
-<para>Constants behave pretty much like symbols except that that they return
-some specific number when the method <literal>.evalf()</literal> is called.
-</para>
-
-<para>The predefined known constants are:
-<informaltable colsep="0" frame="topbot" pgwide="1">
-<tgroup cols="3">
-<colspec colnum="1" colwidth="1*">
-<colspec colnum="2" colwidth="2*">
-<colspec colnum="3" colwidth="4*">
-<thead>
- <row>
- <entry>Name</entry>
- <entry>Common Name</entry>
- <entry>Numerical Value (35 digits)</entry>
- </row>
-</thead>
-<tbody>
- <row>
- <entry><literal>Pi</literal></entry>
- <entry>Archimedes' constant</entry>
- <entry>3.14159265358979323846264338327950288</entry>
- </row><row>
- <entry><literal>Catalan</literal></entry>
- <entry>Catalan's constant</entry>
- <entry>0.91596559417721901505460351493238411</entry>
- </row><row>
- <entry><literal>EulerGamma</literal></entry>
- <entry>Euler's (or Euler-Mascheroni) constant</entry>
- <entry>0.57721566490153286060651209008240243</entry>
- </row>
-</tbody>
-</tgroup>
-</informaltable>
-</para>
-
-</sect1>
-
-<sect1><title>Fundamental operations: The <literal>power</literal>, <literal>add</literal> and <literal>mul</literal> classes</title>
-
-<para>Simple polynomial expressions are written down in GiNaC pretty
-much like in other CAS. The necessary operators <literal>+</literal>,
-<literal>-</literal>, <literal>*</literal> and <literal>/</literal>
-have been overloaded to achieve this goal. When you run the following
-program, the constructor for an object of type <literal>mul</literal>
-is automatically called to hold the product of <literal>a</literal>
-and <literal>b</literal> and then the constructor for an object of
-type <literal>add</literal> is called to hold the sum of that
-<literal>mul</literal> object and the number one:
-<example><title>Construction of <literal>add</literal> and <literal>mul</literal> objects</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-int main()
-{
- symbol a("a"), b("b");
- ex MyTerm = 1+a*b;
- // ...
-}
-</programlisting>
-</example></para>
-
-<para>For exponentiation, you have already seen the somewhat clumsy
-(though C-ish) statement <literal>pow(x,2);</literal> to represent
-<literal>x</literal> squared. This direct construction is necessary
-since we cannot safely overload the constructor <literal>^</literal>
-in <literal>C++</literal> to construct a <literal>power</literal>
-object. If we did, it would have several counterintuitive effects:
-<itemizedlist>
- <listitem>
- <para>Due to <literal>C</literal>'s operator precedence,
- <literal>2*x^2</literal> would be parsed as <literal>(2*x)^2</literal>.
- </listitem>
- <listitem>
- <para>Due to the binding of the operator <literal>^</literal>,
- <literal>x^a^b</literal> would result in <literal>(x^a)^b</literal>.
- This would be confusing since most (though not all) other CAS
- interpret this as <literal>x^(a^b)</literal>.
- </listitem>
- <listitem>
- <para>Also, expressions involving integer exponents are very
- frequently used, which makes it even more dangerous to overload
- <literal>^</literal> since it is then hard to distinguish between the
- semantics as exponentiation and the one for exclusive or. (It would
- be embarassing to return <literal>1</literal> where one has requested
- <literal>2^3</literal>.)</para>
- </listitem>
-</itemizedlist>
-All effects are contrary to mathematical notation and differ from the
-way most other CAS handle exponentiation, therefore overloading
-<literal>^</literal> is ruled out for GiNaC's C++ part. The situation
-is different in <literal>ginsh</literal>, there the
-exponentiation-<literal>^</literal> exists. (Also note, that the
-other frequently used exponentiation operator <literal>**</literal>
-does not exist at all in <literal>C++</literal>).</para>
-
-<para>To be somewhat more precise, objects of the three classes
-described here, are all containers for other expressions. An object
-of class <literal>power</literal> is best viewed as a container with
-two slots, one for the basis, one for the exponent. All valid GiNaC
-expressions can be inserted. However, basic transformations like
-simplifying <literal>pow(pow(x,2),3)</literal> to
-<literal>x^6</literal> automatically are only performed when
-this is mathematically possible. If we replace the outer exponent
-three in the example by some symbols <literal>a</literal>, the
-simplification is not safe and will not be performed, since
-<literal>a</literal> might be <literal>1/2</literal> and
-<literal>x</literal> negative.</para>
-
-<para>Objects of type <literal>add</literal> and
-<literal>mul</literal> are containers with an arbitrary number of
-slots for expressions to be inserted. Again, simple and safe
-simplifications are carried out like transforming
-<literal>3*x+4-x</literal> to <literal>2*x+4</literal>.</para>
-
-<para>The general rule is that when you construct such objects, GiNaC
-automatically creates them in canonical form, which might differ from
-the form you typed in your program. This allows for rapid comparison
-of expressions, since after all <literal>a-a</literal> is simply zero.
-Note, that the canonical form is not necessarily lexicographical
-ordering or in any way easily guessable. It is only guaranteed that
-constructing the same expression twice, either implicitly or
-explicitly, results in the same canonical form.</para>
-
-</sect1>
-
-<sect1><title>Built-in Functions</title>
-
-<para>There are quite a number of useful functions built into GiNaC.
-They are all objects of class <literal>function</literal>. They
-accept one or more expressions as arguments and return one expression.
-If the arguments are not numerical, the evaluation of the functions
-may be halted, as it does in the next example:
-<example><title>Evaluation of built-in functions</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-int main()
-{
- symbol x("x"), y("y");
-
- ex foo = x+y/2;
- cout << "gamma(" << foo << ") -> " << gamma(foo) << endl;
- ex bar = foo.subs(y==1);
- cout << "gamma(" << bar << ") -> " << gamma(bar) << endl;
- ex foobar= bar.subs(x==7);
- cout << "gamma(" << foobar << ") -> " << gamma(foobar) << endl;
- // ...
-}
-</programlisting>
-<para>This program will type out two times a function and then an
-expression that may be really useful:
-<screen>
-gamma(x+(1/2)*y) -> gamma(x+(1/2)*y)
-gamma(x+1/2) -> gamma(x+1/2)
-gamma(15/2) -> (135135/128)*Pi^(1/2)
-</screen></para>
-</example>
-Most of these functions can be differentiated, series expanded so on.
-Read the next chapter in order to learn more about this..</para>
-
-</sect1>
-
-</chapter>
-
-
-<chapter>
-<title>Important Algorithms</title>
-
-<para>In this chapter the most important algorithms provided by GiNaC
-will be described. Some of them are implemented as functions on
-expressions, others are implemented as methods provided by expression
-objects. If they are methods, there exists a wrapper function around
-it, so you can alternatively call it in a functional way as shown in
-the simple example:
-<example><title>Methods vs. wrapper functions</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-int main()
-{
- ex x = numeric(1.0);
-
- cout << "As method: " << sin(x).evalf() << endl;
- cout << "As function: " << evalf(sin(x)) << endl;
- // ...
-}
-</programlisting>
-</example>
-The general rule is that wherever methods accept one or more
-parameters (<emphasis>arg1</emphasis>, <emphasis>arg2</emphasis>, ...)
-the order of arguments the function wrapper accepts is the same but
-preceded by the object to act on (<emphasis>object</emphasis>,
-<emphasis>arg1</emphasis>, <emphasis>arg2</emphasis>, ...). This
-approach is the most natural one in an OO model but it may lead to
-confusion for MapleV users because where they would type
-<literal>A:=x+1; subs(x=2,A);</literal> GiNaC would require
-<literal>A=x+1; subs(A,x==2);</literal> (after proper declaration of A
-and x). On the other hand, since MapleV returns 3 on
-<literal>A:=x^2+3; coeff(A,x,0);</literal> (GiNaC:
-<literal>A=pow(x,2)+3; coeff(A,x,0);</literal>) it is clear that
-MapleV is not trying to be consistent here. Also, users of MuPAD will
-in most cases feel more comfortable with GiNaC's convention. All
-function wrappers are always implemented as simple inline functions
-which just call the corresponding method and are only provided for
-users uncomfortable with OO who are dead set to avoid method
-invocations. Generally, a chain of function wrappers is much harder
-to read than a chain of methods and should therefore be avoided if
-possible. On the other hand, not everything in GiNaC is a method on
-class <literal>ex</literal> and sometimes calling a function cannot be
-avoided.
-</para>
-
-<sect1><title>Polynomial Expansion</title>
-
-<para>A polynomial in one or more variables has many equivalent
-representations. Some useful ones serve a specific purpose. Consider
-for example the trivariate polynomial <literal>4*x*y + x*z + 20*y^2 +
-21*y*z + 4*z^2</literal>. It is equivalent to the factorized
-polynomial <literal>(x + 5*y + 4*z)*(4*y + z)</literal>. Other
-representations are the recursive ones where one collects for
-exponents in one of the three variable. Since the factors are
-themselves polynomials in the remaining two variables the procedure
-can be repeated. In our expample, two possibilies would be
-<literal>(4*y + z)*x + 20*y^2 + 21*y*z + 4*z^2</literal> and
-<literal>20*y^2 + (21*z + 4*x)*y + 4*z^2 + x*z</literal>.
-</para>
-
-<para>To bring an expression into expanded form, its method
-<function>.expand()</function> may be called. In our example above,
-this corresponds to <literal>4*x*y + x*z + 20*y^2 + 21*y*z +
-4*z^2</literal>. Again, since the canonical form in GiNaC is not
-easily guessable you should be prepared to see different orderings of
-terms in such sums!</para>
-
-</sect1>
-
-<sect1><title>Collecting expressions</title>
-
-<para>Another useful representation of multivariate polynomials is as
-a univariate polynomial in one of the variables with the coefficients
-being polynomials in the remaining variables. The method
-<literal>collect()</literal> accomplishes this task:
-<funcsynopsis>
- <funcsynopsisinfo>#include <ginac/ginac.h></funcsynopsisinfo>
- <funcdef>ex <function>ex::collect</function></funcdef>
- <paramdef>symbol const & <parameter>s</parameter></paramdef>
-</funcsynopsis>
-Note that the original polynomial needs to be in expanded form in
-order to be able to find the coefficients properly. The range of
-occuring coefficients can be checked using the two methods
-<funcsynopsis>
- <funcsynopsisinfo>#include <ginac/ginac.h></funcsynopsisinfo>
- <funcdef>int <function>ex::degree</function></funcdef>
- <paramdef>symbol const & <parameter>s</parameter></paramdef>
-</funcsynopsis>
-<funcsynopsis>
- <funcdef>int <function>ex::ldegree</function></funcdef>
- <paramdef>symbol const & <parameter>s</parameter></paramdef>
-</funcsynopsis>
-where <literal>degree()</literal> returns the highest coefficient and
-<literal>ldegree()</literal> the lowest one. These two methods work
-also reliably on non-expanded input polynomials. This is illustrated
-in the following example:
-
-<example><title>Collecting expressions in multivariate polynomials</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-int main()
-{
- symbol x("x"), y("y");
- ex PolyInp = 4*pow(x,3)*y + 5*x*pow(y,2) + 3*y
- - pow(x+y,2) + 2*pow(y+2,2) - 8;
- ex Poly = PolyInp.expand();
-
- for (int i=Poly.ldegree(x); i<=Poly.degree(x); ++i) {
- cout << "The x^" << i << "-coefficient is "
- << Poly.coeff(x,i) << endl;
- }
- cout << "As polynomial in y: "
- << Poly.collect(y) << endl;
- // ...
-}
-</programlisting>
-</example>
-When run, it returns an output in the following fashion:
-<screen>
-The x^0-coefficient is y^2+11*y
-The x^1-coefficient is 5*y^2-2*y
-The x^2-coefficient is -1
-The x^3-coefficient is 4*y
-As polynomial in y: -x^2+(5*x+1)*y^2+(-2*x+4*x^3+11)*y
-</screen>
-As always, the exact output may vary between different versions of
-GiNaC or even from run to run since the internal canonical ordering is
-not within the user's sphere of influence.</para>
-
-</sect1>
-
-<sect1><title>Polynomial Arithmetic</title>
-
-<sect2><title>GCD and LCM</title>
-
-<para>The functions for polynomial greatest common divisor and least common
-multiple have the synopsis:
-<funcsynopsis>
- <funcsynopsisinfo>#include <GiNaC/normal.h></funcsynopsisinfo>
- <funcdef>ex <function>gcd</function></funcdef>
- <paramdef>const ex *<parameter>a</parameter>, const ex *<parameter>b</parameter></paramdef>
-</funcsynopsis>
-<funcsynopsis>
- <funcdef>ex <function>lcm</function></funcdef>
- <paramdef>const ex *<parameter>a</parameter>, const ex *<parameter>b</parameter></paramdef>
-</funcsynopsis></para>
-
-<para>The functions <function>gcd()</function> and <function
-id="lcm-main">lcm()</function> accepts two expressions
-<literal>a</literal> and <literal>b</literal> as arguments and return
-a new expression, their greatest common divisor or least common
-multiple, respectively. If the polynomials <literal>a</literal> and
-<literal>b</literal> are coprime <function>gcd(a,b)</function> returns 1
-and <function>lcm(a,b)</function> returns the product of
-<literal>a</literal> and <literal>b</literal>.
-<example><title>Polynomal GCD/LCM</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-int main()
-{
- symbol x("x"), y("y"), z("z");
- ex P_a = 4*x*y + x*z + 20*pow(y, 2) + 21*y*z + 4*pow(z, 2);
- ex P_b = x*y + 3*x*z + 5*pow(y, 2) + 19*y*z + 12*pow(z, 2);
-
- ex P_gcd = gcd(P_a, P_b);
- // x + 5*y + 4*z
- ex P_lcm = lcm(P_a, P_b);
- // 4*x*y^2 + 13*y*x*z + 20*y^3 + 81*y^2*z + 67*y*z^2 + 3*x*z^2 + 12*z^3
- // ...
-}
-</programlisting>
-</example>
-</para>
-
-</sect2>
-
-<sect2><title>The <function>normal</function> method</title>
-
-<para>While in common symbolic code <function>gcd()</function> and
-<function>lcm()</function> are not too heavily used, simplification
-occurs frequently. Therefore <function>.normal()</function>, which
-provides some basic form of simplification, has become a method of
-class <literal>ex</literal>, just like <literal>.expand()</literal>.
-It converts a rational function into an equivalent rational function
-where numererator and denominator are coprime. This means, it finds
-the GCD of numerator and denominator and cancels it. If it encounters
-some object which does not belong to the domain of rationals (a
-function for instance), that object is replaced by a temporary symbol.
-This means that both expressions <literal>t1</literal> and
-<literal>t2</literal> are indeed simplified in this little program:
-<example><title>Cancellation of polynomial GCD (with obstacles)</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-int main()
-{
- symbol x("x");
- ex t1 = (pow(x,2) + 2*x + 1)/(x + 1);
- ex t2 = (pow(sin(x),2) + 2*sin(x) + 1)/(sin(x) + 1);
- cout << "t1 is " << t1.normal() << endl;
- cout << "t2 is " << t2.normal() << endl;
- // ...
-}
-</programlisting>
-</example>
-
-Of course this works for multivariate polynomials too, so the ratio of
-the sample-polynomials from the section about GCD and LCM above would
-be normalized to <literal>P_a/P_b</literal> =
-<literal>(4*y+z)/(y+3*z)</literal>.</para>
-
-</sect2>
-
-</sect1>
-
-<sect1><title>Symbolic Differentiation</title>
-
-<para>GiNaC's objects know how to differentiate themselves. Thus, a
-polynomial (class <literal>add</literal>) knows that its derivative is
-the sum of the derivatives of all the monomials:
-<example><title>Simple polynomial differentiation</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-int main()
-{
- symbol x("x"), y("y"), z("z");
- ex P = pow(x, 5) + pow(x, 2) + y;
-
- cout << P.diff(x,2) << endl; // 20*x^3 + 2
- cout << P.diff(y) << endl; // 1
- cout << P.diff(z) << endl; // 0
- // ...
-}
-</programlisting>
-</example>
-If a second integer parameter <emphasis>n</emphasis> is given the
-<function>diff</function> method returns the <emphasis>n</emphasis>th
-derivative.</para>
-
-<para>If <emphasis>every</emphasis> object and every function is told
-what its derivative is, all derivatives of composed objects can be
-calculated using the chain rule and the product rule. Consider, for
-instance the expression <literal>1/cosh(x)</literal>. Since the
-derivative of <literal>cosh(x)</literal> is <literal>sinh(x)</literal>
-and the derivative of <literal>pow(x,-1)</literal> is
-<literal>-pow(x,-2)</literal>, GiNaC can readily compute the
-composition. It turns out that the composition is the generating
-function for Euler Numbers, i.e. the so called
-<emphasis>n</emphasis>th Euler number is the coefficient of
-<literal>x^n/n!</literal> in the expansion of
-<literal>1/cosh(x)</literal>. We may use this identity to code a
-function that generates Euler numbers in just three lines:
-<example><title>Differentiation with nontrivial functions: Euler numbers</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-ex EulerNumber(unsigned n)
-{
- symbol x;
- ex generator = pow(cosh(x),-1);
- return generator.diff(x,n).subs(x==0);
-}
-
-int main()
-{
- for (unsigned i=0; i<11; i+=2)
- cout << EulerNumber(i) << endl;
- return 0;
-}
-</programlisting>
-</example>
-When you run it, it produces the sequence <literal>1</literal>,
-<literal>-1</literal>, <literal>5</literal>, <literal>-61</literal>,
-<literal>1385</literal>, <literal>-50521</literal>. We increment the
-loop variable <literal>i</literal> by two since all odd Euler numbers
-vanish anyways.</para>
-
-</sect1>
-
-<sect1><title>Series Expansion</title>
-
-<para>Expressions know how to expand themselves as a Taylor series or
-(more generally) a Laurent series. As in most conventional Computer
-Algebra Systems no distinction is made between those two. There is a
-class of its own for storing such series as well as a class for
-storing the order of the series. A sample program could read:
-<example><title>Series expansion</title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-int main()
-{
- symbol x("x");
- numeric point(0);
- ex MyExpr1 = sin(x);
- ex MyExpr2 = 1/(x - pow(x, 2) - pow(x, 3));
- ex MyTailor, MySeries;
-
- MyTailor = MyExpr1.series(x, point, 5);
- cout << MyExpr1 << " == " << MyTailor
- << " for small " << x << endl;
- MySeries = MyExpr2.series(x, point, 7);
- cout << MyExpr2 << " == " << MySeries
- << " for small " << x << endl;
- // ...
-}
-</programlisting>
-</example>
-</para>
-
-<para>As an instructive application, let us calculate the numerical
-value of Archimedes' constant (for which there already exists the
-built-in constant <literal>Pi</literal>) using Méchain's
-mysterious formula <literal>Pi==16*atan(1/5)-4*atan(1/239)</literal>.
-We may expand the arcus tangent around <literal>0</literal> and insert
-the fractions <literal>1/5</literal> and <literal>1/239</literal>.
-But, as we have seen, a series in GiNaC carries an order term with it.
-The function <literal>series_to_poly</literal> may be used to strip
-this off:
-<example><title>Series expansion using Méchain's formula for
-<literal>Pi</literal></title>
-<programlisting>
-#include <ginac/ginac.h>
-using namespace GiNaC;
-
-ex mechain_pi(int degr)
-{
- symbol x;
- ex pi_expansion = series_to_poly(atan(x).series(x,0,degr));
- ex pi_approx = 16*pi_expansion.subs(x==numeric(1,5))
- -4*pi_expansion.subs(x==numeric(1,239));
- return pi_approx;
-}
-
-int main()
-{
- ex pi_frac;
- for (int i=2; i<12; i+=2) {
- pi_frac = mechain_pi(i);
- cout << i << ":\t" << pi_frac << endl
- << "\t" << pi_frac.evalf() << endl;
- }
- return 0;
-}
-</programlisting>
-<para>When you run this program, it will type out:</para>
-<screen>
-2: 3804/1195
- 3.1832635983263598326
-4: 5359397032/1706489875
- 3.1405970293260603143
-6: 38279241713339684/12184551018734375
- 3.141621029325034425
-8: 76528487109180192540976/24359780855939418203125
- 3.141591772182177295
-10: 327853873402258685803048818236/104359128170408663038552734375
- 3.1415926824043995174
-</screen>
-</example>
-</para>
-
-</sect1>
-
-</chapter>
-
-
-<chapter>
-<title>Extending GiNaC</title>
-
-<para>By reading so far you should have gotten a fairly good
-understanding of GiNaC's design-patterns. From here on you should
-start reading the sources. All we can do now is issue some
-recommendations how to tackle GiNaC's many loose ends in order to
-fulfill everybody's dreams.</para>
-
-<sect1><title>What doesn't belong into GiNaC</title>
-
-<para>First of all, GiNaC's name must be read literally. It is
-designed to be a library for use within C++. The tiny
-<literal>ginsh</literal> accompanying GiNaC makes this even more
-clear: it doesn't even attempt to provide a language. There are no
-loops or conditional expressions in <literal>ginsh</literal>, it is
-merely a window into the library for the programmer to test stuff (or
-to show off). Still, the design of a complete CAS with a language of
-its own, graphical capabilites and all this on top of GiNaC is
-possible and is without doubt a nice project for the future.</para>
-
-<para>There are many built-in functions in GiNaC that do not know how
-to evaluate themselves numerically to a precision declared at runtime
-(using <literal>Digits</literal>). Some may be evaluated at certain
-points, but not generally. This ought to be fixed. However, doing
-numerical computations with GiNaC's quite abstract classes is doomed
-to be inefficient. For this purpose, the underlying bignum-package
-<literal>CLN</literal> is much better suited.</para>
-
-</sect1>
-
-<sect1><title>Other symbolic functions</title>
-
-<para>The easiest and most instructive way to start with is probably
-to implement your own function. Objects of class
-<literal>function</literal> are inserted into the system via a kind of
-"registry". They get a serial number that is used internally to
-identify them but you usually need not worry about this. What you
-have to care for are functions that are called when the user invokes
-certain methods. These are usual C++-functions accepting a number of
-<literal>ex</literal> as arguments and returning one
-<literal>ex</literal>. As an example, if we have a look at a
-simplified implementation of the cosine trigonometric function, we
-first need a function that is called when one wishes to
-<literal>eval</literal> it. It could look something like this:
-
-<programlisting>
-static ex cos_eval_method(ex const & x)
-{
- // if x%2*Pi return 1
- // if x%Pi return -1
- // if x%Pi/2 return 0
- // care for other cases...
- return cos(x).hold();
-}
-</programlisting>
-The last line returns <literal>cos(x)</literal> if we don't know what
-else to do and stops a potential recursive evaluation by saying
-<literal>.hold()</literal>. We should also implement a method for
-numerical evaluation and since we are lazy we sweep the problem under
-the rug by calling someone else's function that does so, in this case
-the one in class <literal>numeric</literal>:
-<programlisting>
-static ex cos_evalf_method(ex const & x)
-{
- return sin(ex_to_numeric(x));
-}
-</programlisting>
-Differentiation will surely turn up and so we need to tell
-<literal>sin</literal> how to differentiate itself:
-<programlisting>
-static ex cos_diff_method(ex const & x, unsigned diff_param)
-{
- return cos(x);
-}
-</programlisting>
-
-The second parameter is obligatory but uninteresting at this point.
-It is used for correct handling of the product rule only. For Taylor
-expansion, it is enough to know how to differentiate. But if the
-function you want to implement does have a pole somewhere in the
-complex plane, you need to write another method for Laurent expansion
-around that point.</para>
-
-<para>Now that everything has been written for <literal>cos</literal>,
-we need to tell the system about it. This is done by a macro and we
-are not going to descibe how it expands, please consult your
-preprocessor if you are curious:
-<programlisting>
-REGISTER_FUNCTION(cos, cos_eval_method, cos_evalf_method, cos_diff, NULL);
-</programlisting>
-The first argument is the function's name, the second, third and
-fourth bind the corresponding methods to this objects and the fifth is
-a slot for inserting a method for series expansion. Also, the new
-function needs to be declared somewhere. This may also be done by a
-convenient preprocessor macro:
-<programlisting>
-DECLARE_FUNCTION_1P(cos)
-</programlisting>
-The suffix <literal>_1P</literal> stands for <emphasis>one
-parameter</emphasis>. Of course, this implementation of
-<literal>cos</literal> is very incomplete and lacks several safety
-mechanisms. Please, have a look at the real implementation in GiNaC.
-(By the way: in case you are worrying about all the macros above we
-can assure you that functions are GiNaC's most macro-intense classes.
-We have done our best to avoid them where we can.)</para>
-
-<para>That's it. May the source be with you!</para>
-
-</sect1>
-
-</chapter>
-
-
-<chapter>
-<title>A Comparison with other CAS</title>
-
-<para>This chapter will give you some information on how GiNaC
-compares to other, traditional Computer Algebra Systems, like
-<literal>Maple</literal>, <literal>Mathematica</literal> or
-<literal>Reduce</literal>, where it has advantages and disadvantages
-over these systems.</para>
-
-<sect1><title>Advantages</title>
-
-<para>GiNaC has several advantages over traditional Computer
-Algebra Systems, like
-
-<itemizedlist>
- <listitem>
- <para>familiar language: all common CAS implement their own
- proprietary grammar which you have to learn first (and maybe learn
- again when your vendor chooses to "enhance" it). With GiNaC you
- can write your program in common <literal>C++</literal>, which is
- standardized.</para>
- </listitem>
- <listitem>
- <para>structured data types: you can build up structured data
- types using <literal>struct</literal>s or <literal>class</literal>es
- together with STL features instead of using unnamed lists of lists
- of lists.</para>
- </listitem>
- <listitem>
- <para>strongly typed: in CAS, you usually have only one kind of
- variables which can hold contents of an arbitrary type. This
- 4GL like feature is nice for novice programmers, but dangerous.
- </para>
- </listitem>
- <listitem>
- <para>development tools: powerful development tools exist for
- <literal>C++</literal>, like fancy editors (e.g. with automatic
- indentation and syntax highlighting), debuggers, visualization
- tools, documentation tools...</para>
- </listitem>
- <listitem>
- <para>modularization: <literal>C++</literal> programs can
- easily be split into modules by separating interface and
- implementation.</para>
- </listitem>
- <listitem>
- <para>price: GiNaC is distributed under the GNU Public License
- which means that it is free and available with source code. And
- there are excellent <literal>C++</literal>-compilers for free, too.
- </para>
- </listitem>
- <listitem>
- <para>extendable: you can add your own classes to GiNaC, thus
- extending it on a very low level. Compare this to a traditional
- CAS that you can usually only extend on a high level by writing in
- the language defined by the parser. In particular, it turns out
- to be almost impossible to fix bugs in a traditional system.
- </listitem>
- <listitem>
- <para>seemless integration: it is somewhere between difficult
- and impossible to call CAS functions from within a program
- written in <literal>C++</literal> or any other programming
- language and vice versa. With GiNaC, your symbolic routines
- are part of your program. You can easily call third party
- libraries, e.g. for numerical evaluation or graphical
- interaction. All other approaches are much more cumbersome: they
- range from simply ignoring the problem
- (i.e. <literal>Maple</literal>) to providing a
- method for "embedding" the system
- (i.e. <literal>Yacas</literal>).</para>
- </listitem>
- <listitem>
- <para>efficiency: often large parts of a program do not need
- symbolic calculations at all. Why use large integers for loop
- variables or arbitrary precision arithmetics where double
- accuracy is sufficient? For pure symbolic applications,
- GiNaC is comparable in speed with other CAS.
- </listitem>
-</itemizedlist>
-</para>
-
-<sect1><title>Disadvantages</title>
-
-<para>Of course it also has some disadvantages
-
-<itemizedlist>
- <listitem>
- <para>not interactive: GiNaC programs have to be written in
- an editor, compiled and executed. You cannot play with
- expressions interactively. However, such an extension is not
- inherently forbidden by design. In fact, two interactive
- interfaces are possible: First, a simple shell that exposes GiNaC's
- types to a command line can readily be written (and has been
- written) and second, as a more consistent approach we plan
- an integration with the <literal>CINT</literal>
- <literal>C++</literal> interpreter.</para>
- </listitem>
- <listitem>
- <para>advanced features: GiNaC cannot compete with a program
- like <literal>Reduce</literal> which exists for more than
- 30 years now or <literal>Maple</literal> which grows since
- 1981 by the work of dozens of programmers, with respect to
- mathematical features. Integration, factorization, non-trivial
- simplifications, limits etc. are missing in GiNaC (and are not
- planned for the near future).</para>
- </listitem>
- <listitem>
- <para>portability: While the GiNaC library itself is designed
- to avoid any platform dependent features (it should compile
- on any ANSI compliant <literal>C++</literal> compiler), the
- currently used version of the CLN library (fast large integer and
- arbitrary precision arithmetics) can be compiled only on systems
- with a recently new <literal>C++</literal> compiler from the
- GNU Compiler Collection (<literal>GCC</literal>). GiNaC uses
- recent language features like explicit constructors, mutable
- members, RTTI, dynamic_casts and STL, so ANSI compliance is meant
- literally. Recent <literal>GCC</literal> versions starting at
- 2.95, although itself not yet ANSI compliant, support all needed
- features.
- </para>
- </listitem>
-</itemizedlist>
-</para>
-
-<sect1><title>Why <literal>C++</literal>?</title>
-
-<para>Why did we choose to implement GiNaC in <literal>C++</literal>
-instead of <literal>Java</literal> or any other language?
-<literal>C++</literal> is not perfect: type checking is not strict
-(casting is possible), separation between interface and implementation
-is not complete, object oriented design is not enforced. The main
-reason is the often scolded feature of operator overloading in
-<literal>C++</literal>. While it may be true that operating on classes
-with a <literal>+</literal> operator is rarely meaningful, it is
-perfectly suited for algebraic expressions. Writing 3x+5y as
-<literal>3*x+5*y</literal> instead of
-<literal>x.times(3).plus(y.times(5))</literal> looks much more
-natural. Furthermore, the main developers are more familiar with
-<literal>C++</literal> than with any other programming
-language.</para>
-
-</chapter>
-
-
-<bibliography>
-<bibliodiv>
-
-<biblioentry>
- <bookbiblio>
- <title>ISO/IEC 14882:1998</title>
- <subtitle>Programming Languages: C++</subtitle>
- </bookbiblio>
-</biblioentry>
-
-<bibliomixed>
- <title>CLN: A Class Library for Numbers</title>
- <authorgroup>
- <author>
- <firstname>Bruno</firstname><surname>Haible</surname>
- <affiliation><address><email>haible@ilog.fr</email></address></affiliation>
- </author>
- </authorgroup>
-</bibliomixed>
-
-<biblioentry>
- <bookbiblio>
- <title>The C++ Programming Language</title>
- <authorgroup><author><firstname>Bjarne</firstname><surname>Stroustrup</surname></author></authorgroup>
- <edition>3</edition>
- <isbn>0-201-88954-4</isbn>
- <publisher><publishername>Addison Wesley</publishername></publisher>
- </bookbiblio>
-</biblioentry>
-
-<biblioentry>
- <bookbiblio>
- <title>C++ FAQs</title>
- <authorgroup><author><firstname>Marshall</firstname><surname>Cline</surname></author></authorgroup>
- <isbn>0-201-58958-3</isbn>
- <pubdate>1995</pubdate>
- <publisher><publishername>Addison Wesley</publishername></publisher>
- </bookbiblio>
-</biblioentry>
-
-<biblioentry>
- <bookbiblio>
- <title>Algorithms for Computer Algebra</title>
- <authorgroup>
- <author><firstname>Keith</firstname><othername>O.</othername><surname>Geddes</surname></author>
- <author><firstname>Stephen</firstname><othername>R.</othername><surname>Czapor</surname></author>
- <author><firstname>George</firstname><surname>Labahn</surname></author>
- </authorgroup>
- <isbn>0-7923-9259-0</isbn>
- <pubdate>1992</pubdate>
- <publisher>
- <publishername>Kluwer Academic Publishers</publishername>
- <address><city>Norwell</city>, <state>Massachusetts</state></address>
- </publisher>
- </bookbiblio>
-</biblioentry>
-
-<biblioentry>
- <bookbiblio>
- <title>Computer Algebra</title>
- <subtitle>Systems and Algorithms for Algebraic Computation</subtitle>
- <authorgroup>
- <author><firstname>J.</firstname><othername>H.</othername><surname>Davenport</surname></author>
- <author><firstname>Y.</firstname><surname>Siret</surname></author>
- <author><firstname>E.</firstname><surname>Tournier</surname></author>
- </authorgroup>
- <isbn>0-12-204230-1</isbn>
- <pubdate>1988</pubdate>
- <publisher>
- <publishername>Academic Press</publishername>
- <address><city>London</city></address>
- </publisher>
- </bookbiblio>
-</biblioentry>
-
-</bibliodiv>
-</bibliography>
-
-</book>
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