From c84d42371ab2e0cc6350a7cffd4f784a54dbd91b Mon Sep 17 00:00:00 2001 From: Christian Bauer Date: Thu, 25 Nov 1999 23:30:22 +0000 Subject: [PATCH] - tutorial now built with texinfo --- Makefile.in | 2 - check/Makefile.in | 2 - configure | 87 +- configure.in | 7 +- doc/Makefile.in | 2 - doc/reference/Makefile.in | 2 - doc/tutorial/Makefile.am | 100 +- doc/tutorial/Makefile.in | 288 +- doc/tutorial/classhierarchy.txt | 1 + doc/tutorial/ginac.texi | 1821 ++++++ doc/tutorial/mdate-sh | 92 + doc/tutorial/{rep_naive.fig => repnaive.fig} | 0 doc/tutorial/repnaive.txt | 1 + doc/tutorial/{rep_pair.fig => reppair.fig} | 0 doc/tutorial/reppair.txt | 1 + doc/tutorial/{rep_real.fig => repreal.fig} | 0 doc/tutorial/repreal.txt | 1 + doc/tutorial/stamp-vti | 3 + doc/tutorial/texinfo.tex | 5484 ++++++++++++++++++ doc/tutorial/tutorial.sgml.in | 1869 ------ doc/tutorial/version.texi | 3 + ginac/Makefile.in | 2 - ginsh/Makefile.in | 2 - 23 files changed, 7644 insertions(+), 2126 deletions(-) create mode 100644 doc/tutorial/classhierarchy.txt create mode 100644 doc/tutorial/ginac.texi create mode 100755 doc/tutorial/mdate-sh rename doc/tutorial/{rep_naive.fig => repnaive.fig} (100%) create mode 100644 doc/tutorial/repnaive.txt rename doc/tutorial/{rep_pair.fig => reppair.fig} (100%) create mode 100644 doc/tutorial/reppair.txt rename doc/tutorial/{rep_real.fig => repreal.fig} (100%) create mode 100644 doc/tutorial/repreal.txt create mode 100644 doc/tutorial/stamp-vti create mode 100644 doc/tutorial/texinfo.tex delete mode 100644 doc/tutorial/tutorial.sgml.in create mode 100644 doc/tutorial/version.texi diff --git a/Makefile.in b/Makefile.in index db52f9ca..091bd6e4 100644 --- a/Makefile.in +++ b/Makefile.in @@ -74,8 +74,6 @@ GINACLIB_MICRO_VERSION = @GINACLIB_MICRO_VERSION@ GINACLIB_MINOR_VERSION = @GINACLIB_MINOR_VERSION@ GINACLIB_VERSION = @GINACLIB_VERSION@ GINSH_LIBS = @GINSH_LIBS@ -JADE = @JADE@ -JADETEX = @JADETEX@ LATEX = @LATEX@ LD = @LD@ LEX = @LEX@ diff --git a/check/Makefile.in b/check/Makefile.in index 0355d4eb..a27cc7d1 100644 --- a/check/Makefile.in +++ b/check/Makefile.in @@ -74,8 +74,6 @@ GINACLIB_MICRO_VERSION = @GINACLIB_MICRO_VERSION@ GINACLIB_MINOR_VERSION = @GINACLIB_MINOR_VERSION@ GINACLIB_VERSION = @GINACLIB_VERSION@ GINSH_LIBS = @GINSH_LIBS@ -JADE = @JADE@ -JADETEX = @JADETEX@ LATEX = @LATEX@ LD = @LD@ LEX = @LEX@ diff --git a/configure b/configure index 24e57857..d7b4b5d1 100755 --- a/configure +++ b/configure @@ -2706,82 +2706,10 @@ else echo "$ac_t""no" 1>&6 fi -# Extract the first word of "jade", so it can be a program name with args. -set dummy jade; ac_word=$2 -echo $ac_n "checking for $ac_word""... $ac_c" 1>&6 -echo "configure:2713: checking for $ac_word" >&5 -if eval "test \"`echo '$''{'ac_cv_path_JADE'+set}'`\" = set"; then - echo $ac_n "(cached) $ac_c" 1>&6 -else - case "$JADE" in - /*) - ac_cv_path_JADE="$JADE" # Let the user override the test with a path. - ;; - ?:/*) - ac_cv_path_JADE="$JADE" # Let the user override the test with a dos path. - ;; - *) - IFS="${IFS= }"; ac_save_ifs="$IFS"; IFS=":" - ac_dummy="$PATH" - for ac_dir in $ac_dummy; do - test -z "$ac_dir" && ac_dir=. - if test -f $ac_dir/$ac_word; then - ac_cv_path_JADE="$ac_dir/$ac_word" - break - fi - done - IFS="$ac_save_ifs" - test -z "$ac_cv_path_JADE" && ac_cv_path_JADE="""" - ;; -esac -fi -JADE="$ac_cv_path_JADE" -if test -n "$JADE"; then - echo "$ac_t""$JADE" 1>&6 -else - echo "$ac_t""no" 1>&6 -fi - -# Extract the first word of "jadetex", so it can be a program name with args. -set dummy jadetex; ac_word=$2 -echo $ac_n "checking for $ac_word""... $ac_c" 1>&6 -echo "configure:2749: checking for $ac_word" >&5 -if eval "test \"`echo '$''{'ac_cv_path_JADETEX'+set}'`\" = set"; then - echo $ac_n "(cached) $ac_c" 1>&6 -else - case "$JADETEX" in - /*) - ac_cv_path_JADETEX="$JADETEX" # Let the user override the test with a path. - ;; - ?:/*) - ac_cv_path_JADETEX="$JADETEX" # Let the user override the test with a dos path. - ;; - *) - IFS="${IFS= }"; ac_save_ifs="$IFS"; IFS=":" - ac_dummy="$PATH" - for ac_dir in $ac_dummy; do - test -z "$ac_dir" && ac_dir=. - if test -f $ac_dir/$ac_word; then - ac_cv_path_JADETEX="$ac_dir/$ac_word" - break - fi - done - IFS="$ac_save_ifs" - test -z "$ac_cv_path_JADETEX" && ac_cv_path_JADETEX="""" - ;; -esac -fi -JADETEX="$ac_cv_path_JADETEX" -if test -n "$JADETEX"; then - echo "$ac_t""$JADETEX" 1>&6 -else - echo "$ac_t""no" 1>&6 -fi - # Extract the first word of "latex", so it can be a program name with args. set dummy latex; ac_word=$2 echo $ac_n "checking for $ac_word""... $ac_c" 1>&6 -echo "configure:2785: checking for $ac_word" >&5 +echo "configure:2713: checking for $ac_word" >&5 if eval "test \"`echo '$''{'ac_cv_path_LATEX'+set}'`\" = set"; then echo $ac_n "(cached) $ac_c" 1>&6 else @@ -2817,7 +2745,7 @@ fi # Extract the first word of "makeindex", so it can be a program name with args. set dummy makeindex; ac_word=$2 echo $ac_n "checking for $ac_word""... $ac_c" 1>&6 -echo "configure:2821: checking for $ac_word" >&5 +echo "configure:2749: checking for $ac_word" >&5 if eval "test \"`echo '$''{'ac_cv_path_MAKEINDEX'+set}'`\" = set"; then echo $ac_n "(cached) $ac_c" 1>&6 else @@ -2853,7 +2781,7 @@ fi # Extract the first word of "dvips", so it can be a program name with args. set dummy dvips; ac_word=$2 echo $ac_n "checking for $ac_word""... $ac_c" 1>&6 -echo "configure:2857: checking for $ac_word" >&5 +echo "configure:2785: checking for $ac_word" >&5 if eval "test \"`echo '$''{'ac_cv_path_DVIPS'+set}'`\" = set"; then echo $ac_n "(cached) $ac_c" 1>&6 else @@ -2889,7 +2817,7 @@ fi # Extract the first word of "fig2dev", so it can be a program name with args. set dummy fig2dev; ac_word=$2 echo $ac_n "checking for $ac_word""... $ac_c" 1>&6 -echo "configure:2893: checking for $ac_word" >&5 +echo "configure:2821: checking for $ac_word" >&5 if eval "test \"`echo '$''{'ac_cv_path_FIG2DEV'+set}'`\" = set"; then echo $ac_n "(cached) $ac_c" 1>&6 else @@ -2926,12 +2854,11 @@ fi TUTORIAL_TARGETS= REFERENCE_TARGETS= if [ "x$enable_html_doc" = "xyes" ]; then - TUTORIAL_TARGETS="$TUTORIAL_TARGETS index.html" + TUTORIAL_TARGETS="$TUTORIAL_TARGETS ginac.html" REFERENCE_TARGETS="$REFERENCE_TARGETS index.html" fi if [ "x$enable_ps_doc" = "xyes" ]; then -# currently doesn't work -# TUTORIAL_TARGETS="$TUTORIAL_TARGETS tutorial.ps" + TUTORIAL_TARGETS="$TUTORIAL_TARGETS ginac.ps" REFERENCE_TARGETS="$REFERENCE_TARGETS reference.ps" fi @@ -3128,8 +3055,6 @@ s%@LEX_OUTPUT_ROOT@%$LEX_OUTPUT_ROOT%g s%@YACC@%$YACC%g s%@GINSH_LIBS@%$GINSH_LIBS%g s%@DOXYGEN@%$DOXYGEN%g -s%@JADE@%$JADE%g -s%@JADETEX@%$JADETEX%g s%@LATEX@%$LATEX%g s%@MAKEINDEX@%$MAKEINDEX%g s%@DVIPS@%$DVIPS%g diff --git a/configure.in b/configure.in index a2965e14..9849a68e 100644 --- a/configure.in +++ b/configure.in @@ -97,8 +97,6 @@ dnl Check for utilities needed by the different kinds of documentation. dnl Documantation needs only be built when extending it, so never mind if it dnl cannot find those helpers: AC_PATH_PROG(DOXYGEN, doxygen, "") -AC_PATH_PROG(JADE, jade, "") -AC_PATH_PROG(JADETEX, jadetex, "") AC_PATH_PROG(LATEX, latex, "") AC_PATH_PROG(MAKEINDEX, makeindex, "") AC_PATH_PROG(DVIPS, dvips, "") @@ -108,12 +106,11 @@ dnl Determine which documentation shall be built TUTORIAL_TARGETS= REFERENCE_TARGETS= if [[ "x$enable_html_doc" = "xyes" ]]; then - TUTORIAL_TARGETS="$TUTORIAL_TARGETS index.html" + TUTORIAL_TARGETS="$TUTORIAL_TARGETS ginac.html" REFERENCE_TARGETS="$REFERENCE_TARGETS index.html" fi if [[ "x$enable_ps_doc" = "xyes" ]]; then -# currently doesn't work -# TUTORIAL_TARGETS="$TUTORIAL_TARGETS tutorial.ps" + TUTORIAL_TARGETS="$TUTORIAL_TARGETS ginac.ps" REFERENCE_TARGETS="$REFERENCE_TARGETS reference.ps" fi AC_SUBST(TUTORIAL_TARGETS) diff --git a/doc/Makefile.in b/doc/Makefile.in index 694bdef3..e3e1214e 100644 --- a/doc/Makefile.in +++ b/doc/Makefile.in @@ -74,8 +74,6 @@ GINACLIB_MICRO_VERSION = @GINACLIB_MICRO_VERSION@ GINACLIB_MINOR_VERSION = @GINACLIB_MINOR_VERSION@ GINACLIB_VERSION = @GINACLIB_VERSION@ GINSH_LIBS = @GINSH_LIBS@ -JADE = @JADE@ -JADETEX = @JADETEX@ LATEX = @LATEX@ LD = @LD@ LEX = @LEX@ diff --git a/doc/reference/Makefile.in b/doc/reference/Makefile.in index 9240a2ef..0130316e 100644 --- a/doc/reference/Makefile.in +++ b/doc/reference/Makefile.in @@ -77,8 +77,6 @@ GINACLIB_MICRO_VERSION = @GINACLIB_MICRO_VERSION@ GINACLIB_MINOR_VERSION = @GINACLIB_MINOR_VERSION@ GINACLIB_VERSION = @GINACLIB_VERSION@ GINSH_LIBS = @GINSH_LIBS@ -JADE = @JADE@ -JADETEX = @JADETEX@ LATEX = @LATEX@ LD = @LD@ LEX = @LEX@ diff --git a/doc/tutorial/Makefile.am b/doc/tutorial/Makefile.am index 29fc2463..44be9f82 100644 --- a/doc/tutorial/Makefile.am +++ b/doc/tutorial/Makefile.am @@ -1,11 +1,7 @@ ## Process this file with automake to produce Makefile.in -# This section produces HTML'ed and TeX'ed versions of the tutorial using a -# SGML to TeX converter (in this case jade). As a dirty hack, we are doing -# some regexpese to tutorial.sgml prior to parsing it, in order to allow for -# different graphics output. This seems to be an ugly limitation of docbook... - -FIG = classhierarchy.fig rep_naive.fig rep_pair.fig rep_real.fig +# Graphics file conversion +FIG = classhierarchy.fig repnaive.fig reppair.fig repreal.fig PNG = $(addsuffix .png, $(basename $(FIG))) EPS = $(addsuffix .eps, $(basename $(FIG))) @@ -27,73 +23,39 @@ SUFFIXES = .fig .png .eps echo "warning: fig2dev was not found by configure"; \ fi -JADEARGS_TEX = -t tex -o tutorial.tex -d /usr/lib/sgml/stylesheet/dsssl/docbook/nwalsh/print/docbook.dsl -JADEARGS_HTML = -t sgml -d /usr/lib/sgml/stylesheet/dsssl/docbook/nwalsh/html/docbook.dsl +info_TEXINFOS = ginac.texi -index.html: tutorial.sgml.in $(PNG) - @if [ "${JADE}" ]; then \ - sed -e "s/MAJOR_VERSION/${GINACLIB_MAJOR_VERSION}/" \ - -e "s/MINOR_VERSION/${GINACLIB_MINOR_VERSION}/" \ - -e 's/graext/png/g' \ - -e 's/GRAEXT/GIF/g' tutorial.sgml.in > tutorial.sgml; \ - echo "Running ${JADE} ${JADEARGS_HTML} tutorial.sgml..."; \ - ${JADE} ${JADEARGS_HTML} tutorial.sgml; \ - if [ -f book1.html ]; then mv book1.html index.html; fi; \ - else \ - echo "warning: target tutorial_html disabled by configuration"; \ - fi +ginac.dvi: $(EPS) -tutorial.tex: tutorial.sgml.in $(EPS) - @if [ "${JADE}" -a "${LATEX}" ]; then \ - sed -e "s/MAJOR_VERSION/${GINACLIB_MAJOR_VERSION}/" \ - -e "s/MINOR_VERSION/${GINACLIB_MINOR_VERSION}/" \ - -e 's/graext/eps/g' \ - -e 's/GRAEXT/EPS/g' tutorial.sgml.in > tutorial.sgml; \ - echo "Running ${JADE} ${JADEARGS_TEX} tutorial.sgml..."; \ - ${JADE} ${JADEARGS_TEX} tutorial.sgml ; \ - else \ - echo "warning: target tutorial.tex disabled by configuration"; \ - fi - -tutorial.dvi: tutorial.tex - @if [ "${JADETEX}" ]; then \ - echo "Running ${JADETEX} tutorial.tex..."; \ - ${JADETEX} tutorial.tex && ${JADETEX} tutorial.tex && ${JADETEX} tutorial.tex; \ - else \ - echo "warning: target tutorial.dvi disabled by configuration"; \ - fi - -tutorial.ps: tutorial.dvi - @if [ "${DVIPS}" ]; then \ - echo "Running ${DVIPS} tutorial.dvi -o tutorial.ps..."; \ - ${DVIPS} tutorial.dvi -o tutorial.ps; \ - else \ - echo "warning: target tutorial.ps disabled by configuration"; \ - fi +ginac.html: ginac.texi version.texi $(PNG) + cd $(srcdir) \ + && $(MAKEINFO) --html `echo $< | sed 's,.*/,,'` ginacdocdir = $(datadir)/doc/GiNaC ginactutorialdir = $(ginacdocdir)/tutorial ginactutorial_DATA = @TUTORIAL_TARGETS@ -CLEANFILES = *.html *.png *.ps *.tex *.log *.aux *.dvi *.eps tutorial.sgml HTML.manifest -EXTRA_DIST = tutorial.sgml.in $(FIG) - -install-data-local: - @for p in *.html; do \ - echo " $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p"; \ - $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p; \ - done - @for p in *.png; do \ - echo " $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p"; \ - $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p; \ - done - -uninstall-local: - @for p in *.html; do \ - echo " rm -f $(DESTDIR)$(ginactutorialdir)/$$p"; \ - rm -f $(DESTDIR)$(ginactutorialdir)/$$p; \ - done - @for p in *.png; do \ - echo " rm -f $(DESTDIR)$(ginactutorialdir)/$$p"; \ - rm -f $(DESTDIR)$(ginactutorialdir)/$$p; \ - done +CLEANFILES = $(EPS) $(PNG) *.html +EXTRA_DIST = $(FIG) + +#CLEANFILES = *.html *.png *.ps *.tex *.log *.aux *.dvi *.eps tutorial.sgml HTML.manifest + +#install-data-local: +# @for p in *.html; do \ +# echo " $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p"; \ +# $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p; \ +# done +# @for p in *.png; do \ +# echo " $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p"; \ +# $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p; \ +# done + +#uninstall-local: +# @for p in *.html; do \ +# echo " rm -f $(DESTDIR)$(ginactutorialdir)/$$p"; \ +# rm -f $(DESTDIR)$(ginactutorialdir)/$$p; \ +# done +# @for p in *.png; do \ +# echo " rm -f $(DESTDIR)$(ginactutorialdir)/$$p"; \ +# rm -f $(DESTDIR)$(ginactutorialdir)/$$p; \ +# done diff --git a/doc/tutorial/Makefile.in b/doc/tutorial/Makefile.in index 3d2ff6a4..d08c8990 100644 --- a/doc/tutorial/Makefile.in +++ b/doc/tutorial/Makefile.in @@ -10,10 +10,7 @@ # even the implied warranty of MERCHANTABILITY or FITNESS FOR A # PARTICULAR PURPOSE. -# This section produces HTML'ed and TeX'ed versions of the tutorial using a -# SGML to TeX converter (in this case jade). As a dirty hack, we are doing -# some regexpese to tutorial.sgml prior to parsing it, in order to allow for -# different graphics output. This seems to be an ugly limitation of docbook... +# Graphics file conversion SHELL = @SHELL@ @@ -79,8 +76,6 @@ GINACLIB_MICRO_VERSION = @GINACLIB_MICRO_VERSION@ GINACLIB_MINOR_VERSION = @GINACLIB_MINOR_VERSION@ GINACLIB_VERSION = @GINACLIB_VERSION@ GINSH_LIBS = @GINSH_LIBS@ -JADE = @JADE@ -JADETEX = @JADETEX@ LATEX = @LATEX@ LD = @LD@ LEX = @LEX@ @@ -102,27 +97,31 @@ TUTORIAL_TARGETS = @TUTORIAL_TARGETS@ VERSION = @VERSION@ YACC = @YACC@ -FIG = classhierarchy.fig rep_naive.fig rep_pair.fig rep_real.fig +FIG = classhierarchy.fig repnaive.fig reppair.fig repreal.fig PNG = $(addsuffix .png, $(basename $(FIG))) EPS = $(addsuffix .eps, $(basename $(FIG))) SUFFIXES = .fig .png .eps -JADEARGS_TEX = -t tex -o tutorial.tex -d /usr/lib/sgml/stylesheet/dsssl/docbook/nwalsh/print/docbook.dsl -JADEARGS_HTML = -t sgml -d /usr/lib/sgml/stylesheet/dsssl/docbook/nwalsh/html/docbook.dsl +info_TEXINFOS = ginac.texi ginacdocdir = $(datadir)/doc/GiNaC ginactutorialdir = $(ginacdocdir)/tutorial ginactutorial_DATA = @TUTORIAL_TARGETS@ -CLEANFILES = *.html *.png *.ps *.tex *.log *.aux *.dvi *.eps tutorial.sgml HTML.manifest -EXTRA_DIST = tutorial.sgml.in $(FIG) +CLEANFILES = $(EPS) $(PNG) *.html +EXTRA_DIST = $(FIG) mkinstalldirs = $(SHELL) $(top_srcdir)/mkinstalldirs CONFIG_HEADER = ../../config.h CONFIG_CLEAN_FILES = +TEXI2DVI = texi2dvi +INFO_DEPS = ginac.info +DVIS = ginac.dvi +TEXINFOS = ginac.texi DATA = $(ginactutorial_DATA) -DIST_COMMON = Makefile.am Makefile.in +DIST_COMMON = Makefile.am Makefile.in mdate-sh stamp-vti texinfo.tex \ +version.texi DISTFILES = $(DIST_COMMON) $(SOURCES) $(HEADERS) $(TEXINFOS) $(EXTRA_DIST) @@ -131,7 +130,7 @@ TAR = tar GZIP_ENV = --best all: all-redirect .SUFFIXES: -.SUFFIXES: .eps .fig .png +.SUFFIXES: .dvi .eps .fig .info .png .ps .texi .texinfo .txi $(srcdir)/Makefile.in: @MAINTAINER_MODE_TRUE@ Makefile.am $(top_srcdir)/configure.in $(ACLOCAL_M4) cd $(top_srcdir) && $(AUTOMAKE) --gnu doc/tutorial/Makefile @@ -140,6 +139,144 @@ Makefile: $(srcdir)/Makefile.in $(top_builddir)/config.status $(BUILT_SOURCES) && CONFIG_FILES=$(subdir)/$@ CONFIG_HEADERS= $(SHELL) ./config.status +$(srcdir)/version.texi: @MAINTAINER_MODE_TRUE@stamp-vti + @: + +$(srcdir)/stamp-vti: ginac.texi $(top_srcdir)/configure.in + @echo "@set UPDATED `$(SHELL) $(srcdir)/mdate-sh $(srcdir)/ginac.texi`" > vti.tmp + @echo "@set EDITION $(VERSION)" >> vti.tmp + @echo "@set VERSION $(VERSION)" >> vti.tmp + @cmp -s vti.tmp $(srcdir)/version.texi \ + || (echo "Updating $(srcdir)/version.texi"; \ + cp vti.tmp $(srcdir)/version.texi) + -@rm -f vti.tmp + @cp $(srcdir)/version.texi $@ + +mostlyclean-vti: + -rm -f vti.tmp + +clean-vti: + +distclean-vti: + +maintainer-clean-vti: + -@MAINTAINER_MODE_TRUE@rm -f $(srcdir)/stamp-vti $(srcdir)/version.texi + +ginac.info: ginac.texi version.texi +ginac.dvi: ginac.texi version.texi + + +.texi.info: + @cd $(srcdir) && rm -f $@ $@-[0-9] $@-[0-9][0-9] + cd $(srcdir) \ + && $(MAKEINFO) `echo $< | sed 's,.*/,,'` + +.texi.dvi: + TEXINPUTS=.:$$TEXINPUTS \ + MAKEINFO='$(MAKEINFO) -I $(srcdir)' $(TEXI2DVI) $< + +.texi: + @cd $(srcdir) && rm -f $@ $@-[0-9] $@-[0-9][0-9] + cd $(srcdir) \ + && $(MAKEINFO) `echo $< | sed 's,.*/,,'` + +.texinfo.info: + @cd $(srcdir) && rm -f $@ $@-[0-9] $@-[0-9][0-9] + cd $(srcdir) \ + && $(MAKEINFO) `echo $< | sed 's,.*/,,'` + +.texinfo: + @cd $(srcdir) && rm -f $@ $@-[0-9] $@-[0-9][0-9] + cd $(srcdir) \ + && $(MAKEINFO) `echo $< | sed 's,.*/,,'` + +.texinfo.dvi: + TEXINPUTS=.:$$TEXINPUTS \ + MAKEINFO='$(MAKEINFO) -I $(srcdir)' $(TEXI2DVI) $< + +.txi.info: + @cd $(srcdir) && rm -f $@ $@-[0-9] $@-[0-9][0-9] + cd $(srcdir) \ + && $(MAKEINFO) `echo $< | sed 's,.*/,,'` + +.txi.dvi: + TEXINPUTS=.:$$TEXINPUTS \ + MAKEINFO='$(MAKEINFO) -I $(srcdir)' $(TEXI2DVI) $< + +.txi: + @cd $(srcdir) && rm -f $@ $@-[0-9] $@-[0-9][0-9] + cd $(srcdir) \ + && $(MAKEINFO) `echo $< | sed 's,.*/,,'` +.dvi.ps: + $(DVIPS) $< -o $@ + +install-info-am: $(INFO_DEPS) + @$(NORMAL_INSTALL) + $(mkinstalldirs) $(DESTDIR)$(infodir) + @list='$(INFO_DEPS)'; \ + for file in $$list; do \ + d=$(srcdir); \ + for ifile in `cd $$d && echo $$file $$file-[0-9] $$file-[0-9][0-9]`; do \ + if test -f $$d/$$ifile; then \ + echo " $(INSTALL_DATA) $$d/$$ifile $(DESTDIR)$(infodir)/$$ifile"; \ + $(INSTALL_DATA) $$d/$$ifile $(DESTDIR)$(infodir)/$$ifile; \ + else : ; fi; \ + done; \ + done + @$(POST_INSTALL) + @if $(SHELL) -c 'install-info --version | sed 1q | fgrep -s -v -i debian' >/dev/null 2>&1; then \ + list='$(INFO_DEPS)'; \ + for file in $$list; do \ + echo " install-info --info-dir=$(DESTDIR)$(infodir) $(DESTDIR)$(infodir)/$$file";\ + install-info --info-dir=$(DESTDIR)$(infodir) $(DESTDIR)$(infodir)/$$file || :;\ + done; \ + else : ; fi + +uninstall-info: + $(PRE_UNINSTALL) + @if $(SHELL) -c 'install-info --version | sed 1q | fgrep -s -v -i debian' >/dev/null 2>&1; then \ + ii=yes; \ + else ii=; fi; \ + list='$(INFO_DEPS)'; \ + for file in $$list; do \ + test -z "$ii" \ + || install-info --info-dir=$(DESTDIR)$(infodir) --remove $$file; \ + done + @$(NORMAL_UNINSTALL) + list='$(INFO_DEPS)'; \ + for file in $$list; do \ + (cd $(DESTDIR)$(infodir) && rm -f $$file $$file-[0-9] $$file-[0-9][0-9]); \ + done + +dist-info: $(INFO_DEPS) + list='$(INFO_DEPS)'; \ + for base in $$list; do \ + d=$(srcdir); \ + for file in `cd $$d && eval echo $$base*`; do \ + test -f $(distdir)/$$file \ + || ln $$d/$$file $(distdir)/$$file 2> /dev/null \ + || cp -p $$d/$$file $(distdir)/$$file; \ + done; \ + done + +mostlyclean-aminfo: + -rm -f ginac.aux ginac.cp ginac.cps ginac.dvi ginac.fn ginac.fns \ + ginac.ky ginac.kys ginac.ps ginac.log ginac.pg ginac.toc \ + ginac.tp ginac.tps ginac.vr ginac.vrs ginac.op ginac.tr \ + ginac.cv ginac.cn + +clean-aminfo: + +distclean-aminfo: + +maintainer-clean-aminfo: + cd $(srcdir) && for i in $(INFO_DEPS); do \ + rm -f $$i; \ + if test "`echo $$i-[0-9]*`" != "$$i-[0-9]*"; then \ + rm -f $$i-[0-9]*; \ + fi; \ + done + install-ginactutorialDATA: $(ginactutorial_DATA) @$(NORMAL_INSTALL) $(mkinstalldirs) $(DESTDIR)$(ginactutorialdir) @@ -182,9 +319,10 @@ distdir: $(DISTFILES) || cp -p $$d/$$file $(distdir)/$$file || :; \ fi; \ done -info-am: + $(MAKE) $(AM_MAKEFLAGS) top_distdir="$(top_distdir)" distdir="$(distdir)" dist-info +info-am: $(INFO_DEPS) info: info-am -dvi-am: +dvi-am: $(DVIS) dvi: dvi-am check-am: all-am check: check-am @@ -193,20 +331,20 @@ installcheck: installcheck-am install-exec-am: install-exec: install-exec-am -install-data-am: install-ginactutorialDATA install-data-local +install-data-am: install-info-am install-ginactutorialDATA install-data: install-data-am install-am: all-am @$(MAKE) $(AM_MAKEFLAGS) install-exec-am install-data-am install: install-am -uninstall-am: uninstall-ginactutorialDATA uninstall-local +uninstall-am: uninstall-info uninstall-ginactutorialDATA uninstall: uninstall-am -all-am: Makefile $(DATA) +all-am: Makefile $(INFO_DEPS) $(DATA) all-redirect: all-am install-strip: $(MAKE) $(AM_MAKEFLAGS) AM_INSTALL_PROGRAM_FLAGS=-s install installdirs: - $(mkinstalldirs) $(DESTDIR)$(ginactutorialdir) + $(mkinstalldirs) $(DESTDIR)$(infodir) $(DESTDIR)$(ginactutorialdir) mostlyclean-generic: @@ -219,32 +357,35 @@ distclean-generic: -rm -f config.cache config.log stamp-h stamp-h[0-9]* maintainer-clean-generic: -mostlyclean-am: mostlyclean-generic +mostlyclean-am: mostlyclean-vti mostlyclean-aminfo mostlyclean-generic mostlyclean: mostlyclean-am -clean-am: clean-generic mostlyclean-am +clean-am: clean-vti clean-aminfo clean-generic mostlyclean-am clean: clean-am -distclean-am: distclean-generic clean-am +distclean-am: distclean-vti distclean-aminfo distclean-generic clean-am -rm -f libtool distclean: distclean-am -maintainer-clean-am: maintainer-clean-generic distclean-am +maintainer-clean-am: maintainer-clean-vti maintainer-clean-aminfo \ + maintainer-clean-generic distclean-am @echo "This command is intended for maintainers to use;" @echo "it deletes files that may require special tools to rebuild." maintainer-clean: maintainer-clean-am -.PHONY: uninstall-ginactutorialDATA install-ginactutorialDATA tags \ -distdir info-am info dvi-am dvi check check-am installcheck-am \ -installcheck install-exec-am install-exec install-data-local \ -install-data-am install-data install-am install uninstall-local \ -uninstall-am uninstall all-redirect all-am all installdirs \ -mostlyclean-generic distclean-generic clean-generic \ -maintainer-clean-generic clean mostlyclean distclean maintainer-clean +.PHONY: mostlyclean-vti distclean-vti clean-vti maintainer-clean-vti \ +install-info-am uninstall-info mostlyclean-aminfo distclean-aminfo \ +clean-aminfo maintainer-clean-aminfo uninstall-ginactutorialDATA \ +install-ginactutorialDATA tags distdir info-am info dvi-am dvi check \ +check-am installcheck-am installcheck install-exec-am install-exec \ +install-data-am install-data install-am install uninstall-am uninstall \ +all-redirect all-am all installdirs mostlyclean-generic \ +distclean-generic clean-generic maintainer-clean-generic clean \ +mostlyclean distclean maintainer-clean %.eps: %.fig @@ -263,66 +404,33 @@ maintainer-clean-generic clean mostlyclean distclean maintainer-clean echo "warning: fig2dev was not found by configure"; \ fi -index.html: tutorial.sgml.in $(PNG) - @if [ "${JADE}" ]; then \ - sed -e "s/MAJOR_VERSION/${GINACLIB_MAJOR_VERSION}/" \ - -e "s/MINOR_VERSION/${GINACLIB_MINOR_VERSION}/" \ - -e 's/graext/png/g' \ - -e 's/GRAEXT/GIF/g' tutorial.sgml.in > tutorial.sgml; \ - echo "Running ${JADE} ${JADEARGS_HTML} tutorial.sgml..."; \ - ${JADE} ${JADEARGS_HTML} tutorial.sgml; \ - if [ -f book1.html ]; then mv book1.html index.html; fi; \ - else \ - echo "warning: target tutorial_html disabled by configuration"; \ - fi - -tutorial.tex: tutorial.sgml.in $(EPS) - @if [ "${JADE}" -a "${LATEX}" ]; then \ - sed -e "s/MAJOR_VERSION/${GINACLIB_MAJOR_VERSION}/" \ - -e "s/MINOR_VERSION/${GINACLIB_MINOR_VERSION}/" \ - -e 's/graext/eps/g' \ - -e 's/GRAEXT/EPS/g' tutorial.sgml.in > tutorial.sgml; \ - echo "Running ${JADE} ${JADEARGS_TEX} tutorial.sgml..."; \ - ${JADE} ${JADEARGS_TEX} tutorial.sgml ; \ - else \ - echo "warning: target tutorial.tex disabled by configuration"; \ - fi - -tutorial.dvi: tutorial.tex - @if [ "${JADETEX}" ]; then \ - echo "Running ${JADETEX} tutorial.tex..."; \ - ${JADETEX} tutorial.tex && ${JADETEX} tutorial.tex && ${JADETEX} tutorial.tex; \ - else \ - echo "warning: target tutorial.dvi disabled by configuration"; \ - fi - -tutorial.ps: tutorial.dvi - @if [ "${DVIPS}" ]; then \ - echo "Running ${DVIPS} tutorial.dvi -o tutorial.ps..."; \ - ${DVIPS} tutorial.dvi -o tutorial.ps; \ - else \ - echo "warning: target tutorial.ps disabled by configuration"; \ - fi - -install-data-local: - @for p in *.html; do \ - echo " $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p"; \ - $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p; \ - done - @for p in *.png; do \ - echo " $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p"; \ - $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p; \ - done - -uninstall-local: - @for p in *.html; do \ - echo " rm -f $(DESTDIR)$(ginactutorialdir)/$$p"; \ - rm -f $(DESTDIR)$(ginactutorialdir)/$$p; \ - done - @for p in *.png; do \ - echo " rm -f $(DESTDIR)$(ginactutorialdir)/$$p"; \ - rm -f $(DESTDIR)$(ginactutorialdir)/$$p; \ - done +ginac.dvi: $(EPS) + +ginac.html: ginac.texi version.texi $(PNG) + cd $(srcdir) \ + && $(MAKEINFO) --html `echo $< | sed 's,.*/,,'` + +#CLEANFILES = *.html *.png *.ps *.tex *.log *.aux *.dvi *.eps tutorial.sgml HTML.manifest + +#install-data-local: +# @for p in *.html; do \ +# echo " $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p"; \ +# $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p; \ +# done +# @for p in *.png; do \ +# echo " $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p"; \ +# $(INSTALL_DATA) $(srcdir)/$$p $(DESTDIR)$(ginactutorialdir)/$$p; \ +# done + +#uninstall-local: +# @for p in *.html; do \ +# echo " rm -f $(DESTDIR)$(ginactutorialdir)/$$p"; \ +# rm -f $(DESTDIR)$(ginactutorialdir)/$$p; \ +# done +# @for p in *.png; do \ +# echo " rm -f $(DESTDIR)$(ginactutorialdir)/$$p"; \ +# rm -f $(DESTDIR)$(ginactutorialdir)/$$p; \ +# done # Tell versions [3.59,3.63) of GNU make to not export all variables. # Otherwise a system limit (for SysV at least) may be exceeded. diff --git a/doc/tutorial/classhierarchy.txt b/doc/tutorial/classhierarchy.txt new file mode 100644 index 00000000..e312dcc7 --- /dev/null +++ b/doc/tutorial/classhierarchy.txt @@ -0,0 +1 @@ + diff --git a/doc/tutorial/ginac.texi b/doc/tutorial/ginac.texi new file mode 100644 index 00000000..c3a1813e --- /dev/null +++ b/doc/tutorial/ginac.texi @@ -0,0 +1,1821 @@ +\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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 +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 + diff --git a/doc/tutorial/mdate-sh b/doc/tutorial/mdate-sh new file mode 100755 index 00000000..37171f21 --- /dev/null +++ b/doc/tutorial/mdate-sh @@ -0,0 +1,92 @@ +#!/bin/sh +# Get modification time of a file or directory and pretty-print it. +# Copyright (C) 1995, 1996, 1997 Free Software Foundation, Inc. +# written by Ulrich Drepper , June 1995 +# +# 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, 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; if not, write to the Free Software Foundation, +# Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + +# Prevent date giving response in another language. +LANG=C +export LANG +LC_ALL=C +export LC_ALL +LC_TIME=C +export LC_TIME + +# Get the extended ls output of the file or directory. +# On HPUX /bin/sh, "set" interprets "-rw-r--r--" as options, so the "x" below. +if ls -L /dev/null 1>/dev/null 2>&1; then + set - x`ls -L -l -d $1` +else + set - x`ls -l -d $1` +fi +# The month is at least the fourth argument +# (3 shifts here, the next inside the loop). +shift +shift +shift + +# Find the month. Next argument is day, followed by the year or time. +month= +until test $month +do + shift + case $1 in + Jan) month=January; nummonth=1;; + Feb) month=February; nummonth=2;; + Mar) month=March; nummonth=3;; + Apr) month=April; nummonth=4;; + May) month=May; nummonth=5;; + Jun) month=June; nummonth=6;; + Jul) month=July; nummonth=7;; + Aug) month=August; nummonth=8;; + Sep) month=September; nummonth=9;; + Oct) month=October; nummonth=10;; + Nov) month=November; nummonth=11;; + Dec) month=December; nummonth=12;; + esac +done + +day=$2 + +# Here we have to deal with the problem that the ls output gives either +# the time of day or the year. +case $3 in + *:*) set `date`; eval year=\$$# + case $2 in + Jan) nummonthtod=1;; + Feb) nummonthtod=2;; + Mar) nummonthtod=3;; + Apr) nummonthtod=4;; + May) nummonthtod=5;; + Jun) nummonthtod=6;; + Jul) nummonthtod=7;; + Aug) nummonthtod=8;; + Sep) nummonthtod=9;; + Oct) nummonthtod=10;; + Nov) nummonthtod=11;; + Dec) nummonthtod=12;; + esac + # For the first six month of the year the time notation can also + # be used for files modified in the last year. + if (expr $nummonth \> $nummonthtod) > /dev/null; + then + year=`expr $year - 1` + fi;; + *) year=$3;; +esac + +# The result. +echo $day $month $year diff --git a/doc/tutorial/rep_naive.fig b/doc/tutorial/repnaive.fig similarity index 100% rename from doc/tutorial/rep_naive.fig rename to doc/tutorial/repnaive.fig diff --git a/doc/tutorial/repnaive.txt b/doc/tutorial/repnaive.txt new file mode 100644 index 00000000..e312dcc7 --- /dev/null +++ b/doc/tutorial/repnaive.txt @@ -0,0 +1 @@ + diff --git a/doc/tutorial/rep_pair.fig b/doc/tutorial/reppair.fig similarity index 100% rename from doc/tutorial/rep_pair.fig rename to doc/tutorial/reppair.fig diff --git a/doc/tutorial/reppair.txt b/doc/tutorial/reppair.txt new file mode 100644 index 00000000..e312dcc7 --- /dev/null +++ b/doc/tutorial/reppair.txt @@ -0,0 +1 @@ + diff --git a/doc/tutorial/rep_real.fig b/doc/tutorial/repreal.fig similarity index 100% rename from doc/tutorial/rep_real.fig rename to doc/tutorial/repreal.fig diff --git a/doc/tutorial/repreal.txt b/doc/tutorial/repreal.txt new file mode 100644 index 00000000..e312dcc7 --- /dev/null +++ b/doc/tutorial/repreal.txt @@ -0,0 +1 @@ + diff --git a/doc/tutorial/stamp-vti b/doc/tutorial/stamp-vti new file mode 100644 index 00000000..fd299ad9 --- /dev/null +++ b/doc/tutorial/stamp-vti @@ -0,0 +1,3 @@ +@set UPDATED 25 November 1999 +@set EDITION 0.4.0 +@set VERSION 0.4.0 diff --git a/doc/tutorial/texinfo.tex b/doc/tutorial/texinfo.tex new file mode 100644 index 00000000..aa52853e --- /dev/null +++ b/doc/tutorial/texinfo.tex @@ -0,0 +1,5484 @@ +% texinfo.tex -- TeX macros to handle Texinfo files. +% +% Load plain if necessary, i.e., if running under initex. +\expandafter\ifx\csname fmtname\endcsname\relax\input plain\fi +% +\def\texinfoversion{1999-01-05}% +% +% Copyright (C) 1985, 86, 88, 90, 91, 92, 93, 94, 95, 96, 97, 98 +% Free Software Foundation, Inc. +% +% This texinfo.tex file 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, or (at +% your option) any later version. +% +% This texinfo.tex file 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 texinfo.tex file; see the file COPYING. If not, write +% to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, +% Boston, MA 02111-1307, USA. +% +% In other words, you are welcome to use, share and improve this program. +% You are forbidden to forbid anyone else to use, share and improve +% what you give them. Help stamp out software-hoarding! +% +% Please try the latest version of texinfo.tex before submitting bug +% reports; you can get the latest version from: +% ftp://ftp.gnu.org/pub/gnu/texinfo.tex +% /home/gd/gnu/doc/texinfo.tex on the GNU machines. +% (and all GNU mirrors, see http://www.gnu.org/order/ftp.html) +% ftp://tug.org/tex/texinfo.tex +% ftp://ctan.org/macros/texinfo/texinfo.tex +% (and all CTAN mirrors, finger ctan@ctan.org for a list). +% The texinfo.tex in the texinfo distribution itself could well be out +% of date, so if that's what you're using, please check. +% +% Send bug reports to bug-texinfo@gnu.org. +% Please include a precise test case in each bug report, +% including a complete document with which we can reproduce the problem. +% +% To process a Texinfo manual with TeX, it's most reliable to use the +% texi2dvi shell script that comes with the distribution. For simple +% manuals, however, you can get away with: +% tex foo.texi +% texindex foo.?? +% tex foo.texi +% tex foo.texi +% dvips foo.dvi -o # or whatever, to process the dvi file. +% The extra runs of TeX get the cross-reference information correct. +% Sometimes one run after texindex suffices, and sometimes you need more +% than two; texi2dvi does it as many times as necessary. + +\message{Loading texinfo [version \texinfoversion]:} + +% If in a .fmt file, print the version number +% and turn on active characters that we couldn't do earlier because +% they might have appeared in the input file name. +\everyjob{\message{[Texinfo version \texinfoversion]}% + \catcode`+=\active \catcode`\_=\active} + +% Save some parts of plain tex whose names we will redefine. + +\let\ptexb=\b +\let\ptexbullet=\bullet +\let\ptexc=\c +\let\ptexcomma=\, +\let\ptexdot=\. +\let\ptexdots=\dots +\let\ptexend=\end +\let\ptexequiv=\equiv +\let\ptexexclam=\! +\let\ptexi=\i +\let\ptexlbrace=\{ +\let\ptexrbrace=\} +\let\ptexstar=\* +\let\ptext=\t + +% We never want plain's outer \+ definition in Texinfo. +% For @tex, we can use \tabalign. +\let\+ = \relax + + +\message{Basics,} +\chardef\other=12 + +% If this character appears in an error message or help string, it +% starts a new line in the output. +\newlinechar = `^^J + +% Set up fixed words for English if not already set. +\ifx\putwordAppendix\undefined \gdef\putwordAppendix{Appendix}\fi +\ifx\putwordChapter\undefined \gdef\putwordChapter{Chapter}\fi +\ifx\putwordfile\undefined \gdef\putwordfile{file}\fi +\ifx\putwordInfo\undefined \gdef\putwordInfo{Info}\fi +\ifx\putwordMethodon\undefined \gdef\putwordMethodon{Method on}\fi +\ifx\putwordon\undefined \gdef\putwordon{on}\fi +\ifx\putwordpage\undefined \gdef\putwordpage{page}\fi +\ifx\putwordsection\undefined \gdef\putwordsection{section}\fi +\ifx\putwordSection\undefined \gdef\putwordSection{Section}\fi +\ifx\putwordsee\undefined \gdef\putwordsee{see}\fi +\ifx\putwordSee\undefined \gdef\putwordSee{See}\fi +\ifx\putwordShortContents\undefined \gdef\putwordShortContents{Short Contents}\fi +\ifx\putwordTableofContents\undefined\gdef\putwordTableofContents{Table of Contents}\fi + +% Ignore a token. +% +\def\gobble#1{} + +\hyphenation{ap-pen-dix} +\hyphenation{mini-buf-fer mini-buf-fers} +\hyphenation{eshell} +\hyphenation{white-space} + +% Margin to add to right of even pages, to left of odd pages. +\newdimen \bindingoffset +\newdimen \normaloffset +\newdimen\pagewidth \newdimen\pageheight + +% Sometimes it is convenient to have everything in the transcript file +% and nothing on the terminal. We don't just call \tracingall here, +% since that produces some useless output on the terminal. +% +\def\gloggingall{\begingroup \globaldefs = 1 \loggingall \endgroup}% +\ifx\eTeXversion\undefined +\def\loggingall{\tracingcommands2 \tracingstats2 + \tracingpages1 \tracingoutput1 \tracinglostchars1 + \tracingmacros2 \tracingparagraphs1 \tracingrestores1 + \showboxbreadth\maxdimen\showboxdepth\maxdimen +}% +\else +\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 . + % + \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 to achieve this: TeX expands \the only once, +% simply yielding the contents of . (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 + \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 +% 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. + +\newdimen\defaultparindent \defaultparindent = 15pt + +\chapheadingskip = 15pt plus 4pt minus 2pt +\secheadingskip = 12pt plus 3pt minus 2pt +\subsecheadingskip = 9pt plus 2pt minus 2pt + +% Prevent underfull vbox error messages. +\vbadness = 10000 + +% Don't be so finicky about underfull hboxes, either. +\hbadness = 2000 + +% Following George Bush, just get rid of widows and orphans. +\widowpenalty=10000 +\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}% + % + \lispnarrowing = 0.3in + \tolerance = 700 + \hfuzz = 1pt + \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=`\< +\catcode`\<=\active +\def<{{\tt \less}} +\chardef \gtr=`\> +\catcode`\>=\active +\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=`\\ +%{\catcode`\\=\other +%@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 +@let~=@normaltilde +@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 +% makes sure that the current font starts out as the newly loaded cmr10 +@catcode`@$=@other @catcode`@%=@other @catcode`@&=@other @catcode`@#=@other + +@textfonts +@rm + +@c Local variables: +@c eval: (add-hook 'write-file-hooks 'time-stamp) +@c page-delimiter: "^\\\\message" +@c time-stamp-start: "def\\\\texinfoversion{" +@c time-stamp-format: "%:y-%02m-%02d" +@c time-stamp-end: "}" +@c End: diff --git a/doc/tutorial/tutorial.sgml.in b/doc/tutorial/tutorial.sgml.in deleted file mode 100644 index aa0cb900..00000000 --- a/doc/tutorial/tutorial.sgml.in +++ /dev/null @@ -1,1869 +0,0 @@ - - - -GiNaC MAJOR_VERSION.MINOR_VERSION Tutorial - -An open framework for symbolic computation within the C++ programming language - - - - The GiNaC Group - - - ChristianBauer - -
Christian.Bauer@Uni-Mainz.DE
- - - - AlexanderFrink - -
Alexander.Frink@Uni-Mainz.DE
- - - - RichardB.Kreckel - -
Richard.Kreckel@Uni-Mainz.DE
- - - - - - - -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 directly at URL http://www.ginac.de/reference/. -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. - -License - -The GiNaC framework for symbolic computation within the C++ -programming language is Copyright (C) 1999 Johannes Gutenberg -Universität 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. - - - - -A Tour of GiNaC - -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. - -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: - -My first GiNaC program (a bivariate polynomial) - -#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; -} - -Assuming the file is called hello.cc, on -our system we can compile and run it like this: - -$ c++ hello.cc -o hello -lcln -lginac -$ ./hello -355687428096000*x*y+20922789888000*y^2+6402373705728000*x^2 - - - - -Next, there is a more meaningful C++ program that calls a -function which generates Hermite polynomials in a specified free -variable. - -My second GiNaC program (Hermite polynomials) - -#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; -} - -When run, this will type out - -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 - - -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 ginsh, a simple GiNaC interactive -shell that provides a convenient window into GiNaC's capabilities. - - -What it can do for you - -After invoking 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 -ginsh syntax we refer to its accompanied man-page. -Suffice to say that assignments and comparisons in -ginsh are written as they are in C, -i.e. = assigns and == -compares. - -It can manipulate arbitrary precision integers in a very fast -way. Rational numbers are automatically converted to fractions of -coprime integers: - -> x=3^150; -369988485035126972924700782451696644186473100389722973815184405301748249 -> y=3^149; -123329495011708990974900260817232214728824366796574324605061468433916083 -> x/y; -3 -> y/x; -1/3 - - - -All numbers occuring in GiNaC's expressions can be converted -into floating point numbers with the evalf method, -to arbitrary accuracy: - -> evalf(1/7); -0.14285714285714285714 -> Digits=150; -150 -> evalf(1/7); -0.1428571428571428571428571428571428571428571428571428571428571428571428 -5714285714285714285714285714285714285 - - - -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): - -> a=Pi^2+x; -x+Pi^2 -> evalf(a); -x+9.869604401089358619L0 -> x=2; -2 -> evalf(a); -11.869604401089358619L0 - - - -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: - -> cos(42*Pi); -1 -> cos(acos(x)); -x -> acos(cos(x)); -acos(cos(x)) - -(Note that converting the last input to x would -allow one to conclude that 42*Pi is equal to -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 -ginsh's notation of double brackets to type them -in: - -> 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 - - - -Multivariate polynomials and rational functions may be expanded, -collected and normalized (i.e. converted to a ratio of two coprime -polynomials): - -> 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 - - - -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): - -> 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) - - - -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: - -> in=.0254*m; -0.0254*m -> lb=.45359237*kg; -0.45359237*kg -> 200*lb/in^2; -140613.91592783185568*kg*m^(-2) - - - - - - - - - -Installation - -GiNaC's installation follows the spirit of most GNU software. It is -easily installed on your system by three steps: configuration, build, -installation. - -Prerequistes - -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 ISO/IEC 14882:1998(E). We used -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 /bin/sh, -GNU 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 -CLN is extensively used and needs to be installed -on your system. Please get it from ftp://ftp.santafe.edu/pub/gnu/ -or from ftp://ftp.ilog.fr/pub/Users/haible/gnu/ -(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. - -Configuration - -To configure GiNaC means to prepare the source distribution for -building. It is done via a shell script called -configure that is shipped with the sources. -(Actually, this script is by itself created with GNU Autoconf from the -files configure.in and -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 --help option. The most important ones -will be shortly described in what follows: - - - --disable-shared: When given, this option - switches off the build of a shared library, i.e. a - .so-file. This may be convenient when developing - because it considerably speeds up compilation. - - - --prefix=PREFIX: The - directory where the compiled library and headers are installed. It - defaults to /usr/local which means that the - library is installed in the directory - /usr/local/lib and the header files in - /usr/local/include/GiNaC and the documentation - (like this one) into /usr/local/share/doc/GiNaC. - - - --libdir=LIBDIR: Use - this option in case you want to have the library installed in some - other directory than - PREFIX/lib/. - - - --includedir=INCLUDEDIR: - Use this option in case you want to have the header files - installed in some other directory than - PREFIX/include/ginac/. For - instance, if you specify - --includedir=/usr/include you will end up with - the header files sitting in the directory - /usr/include/ginac/. Note that the subdirectory - 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). - - - --datadir=DATADIR: - This option may be given in case you want to have the documentation - installed in some other directory than - PREFIX/share/doc/GiNaC/. - - - - -In addition, you may specify some environment variables. -CXX holds the path and the name of the C++ compiler -in case you want to override the default in your path. (The -configure script searches your path for -c++, g++, -gcc, CC, cxx -and cc++ in that order.) It may be very useful to -define some compiler flags with the CXXFLAGS -environment variable, like optimization, debugging information and -warning levels. If ommitted, it defaults to -g --O2. - -The whole process is illustrated in the following two -examples. (Substitute setenv VARIABLE value for -export VARIABLE=value if the Berkeley C shell is -your login shell.) - -Sample sessions of how to call the -configure-script Simple configuration for a site-wide -GiNaC library assuming everything is in default paths: - -$ export CXXFLAGS="-Wall -O2" -$ ./configure - -Configuration for a private static GiNaC library with several -components sitting in custom places (site-wide GCC -and private CLN), the compiler pursueded to be -picky and full assertions switched on: - -$ 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} - - - - - - -Building GiNaC - -After proper configuration you should just build the whole -library by typing make 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 make check. This will compile some -sample programs, run them and compare the output to reference output. -Each of the checks should return a message 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 CLN was installed all right -this step is unlikely to return any errors. - - - -Installation - -To install GiNaC on your system, simply type make -install. 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): - - - libginac.a will go into - PREFIX/lib/ (or - LIBDIR) which defaults to - /usr/local/lib/. So will - libginac.so if the the configure script was - given the option --enable-shared. In that - case, the proper symlinks will be established as well (by running - ldconfig). - - - All the header files will be installed into - PREFIX/include/ginac/ (or - INCLUDEDIR/ginac/, if - specified). - - - All documentation (HTML, Postscript and DVI) will be stuffed - into - PREFIX/share/doc/GiNaC/ - (or DATADIR/doc/GiNaC/, if - specified). - - - - -Just for the record we will list some other useful make targets: -make clean deletes all files generated by -make, i.e. all the object files. In addition -make distclean removes all files generated by -configuration. And finally make uninstall removes -the installed library and header files. - - Uninstallation does not work - after you have called make distclean since the - Makefile is itself generated by the configuration - from Makefile.in and hence deleted by - make distclean. There are two obvious ways out - of this dilemma. First, you can run the configuration again with - the same PREFIX thus creating a - Makefile with a working - uninstall target. Second, you can do it by hand - since you now know where all the files went during - installation. - - - - - - - -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. - -Expressions - -The most common class of objects a user deals with is the -expression 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: -Examples of expressions - - 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 - - -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. - -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 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: -Simple copy-on-write semantics - -#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 - // ... -} - - -The line e2 = e1; creates a second expression -pointing to the object held already by e1. The -time involved for this operation is therefore constant, no matter how -large e1 was. Actual copying, however, must take -place in the line e2 += 1 because -e1 and e2 are not handles for -the same object any more. This concept is called -copy-on-write semantics. It increases -performance considerably whenever one object occurs multiple times and -represents a simple garbage collection scheme because when an -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. Advanced -copy-on-write semantics - -#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) - // ... -} - - -Here, e1 will actually be referenced three times -while 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 -e1 is involved when e3 is -constructed. So, when e3 is constructed it will -print as 3*(x+3*y)^2*cos((x+3*y)^3) but the -argument of cos() only holds a reference to -e2 and the factor in front is just -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 -C++-FAQ lite 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 http://www.cerfnet.com/~mpcline/c++-faq-lite/. - -So much for expressions. But what exactly are these expressions -handles of? This will be answered in the following sections. - - - -The Class Hierarchy - -GiNaC's class hierarchy consists of several classes representing -mathematical objects, all of which (except for ex -and some helpers) are internally derived from one abstract base class -called basic. You do not have to deal with objects -of class 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. -
-The GiNaC class hierarchy - -
-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 expairseq, which is a container -for a sequence of pairs each consisting of one expression and a number -(numeric). What is visible to -the user are the derived classes add and -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. - -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 -2*d3*(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: -
-Naive internal representation-tree for <emphasis>2*d<superscript>3</superscript>*(4*a+5*b-3)</emphasis> - -
-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. -
-Pair-wise internal representation-tree for <emphasis>2*d<superscript>3</superscript>*(4*a+5*b-3)</emphasis> - -
-The number 3 above the symbol d -shows that mul objects are treated similarly where -the coefficients are interpreted as 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 2 and -the additive term -3 look somewhat cumbersome in -this representation, however, since they are still carrying a trivial -exponent and multiplicative factor 1 respectively. -Within GiNaC, this is avoided by adding a field that carries overall -numeric coefficient. -
-Realistic picture of GiNaC's representation-tree for <emphasis>2*d<superscript>3</superscript>*(4*a+5*b-3)</emphasis> - -
-This also allows for a better handling of numeric radicals, since -sqrt(2) can now be carried along calculations. Now -it should be clear, why both classes add and -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 add and mul, -but the data structure is inherited from -expairseq. - - - -Symbols - -Symbols are for symbolic manipulation what atoms are for -chemistry. You can declare objects of class symbol -as any other object simply by saying 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 -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 symbol x("x"),y("x"); but it is -likely to lead into trouble. Here, x and -y are different symbols and statements like -x-y will not be simplified to zero although the -output 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 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 .subs() -method. - - - -Numbers - -For storing numerical things, GiNaC uses Bruno Haible's library -CLN. The classes therein serve as foundation -classes for GiNaC. CLN stands for Class Library -for Numbers or alternatively for Common Lisp Numbers. In order to -find out more about 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 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. CLN extends -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 -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. -Construction of numbers - -#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... - // ... -} - - -Note that all those constructors are explicit -which means you are not allowed to write numeric -two=2;. This is because the basic objects to be handled by -GiNaC are the expressions ex and we want to keep -things simple and wish objects like pow(x,2) to be -handled the same way as pow(x,a), which means that -we need to allow a general 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 numeric -r(3/2). This would, however, call C's built-in operator -/ for integers first and result in a numeric -holding a plain integer 1. Never use -/ on integers! Use -the constructor from two integers instead, as shown in the example -above. Writing 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 global variable, called -Digits. (For those readers who know about Maple: -it behaves very much like Maple's Digits). All -objects of class numeric that are constructed from then on will be -stored with a precision matching that number of decimal digits: -Controlling the precision of floating point numbers - -#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; -} - - -The above example prints the following output to screen: - -in 17 digits: -0.333333333333333333 -3.14159265358979324 -in 60 digits: -0.333333333333333333333333333333333333333333333333333333333333333333 -3.14159265358979323846264338327950288419716939937510582097494459231 - - - -It should be clear that objects of class -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 ex. - -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: -Sample test on objects of type numeric - -#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! - // ... -} - - - -Note that the variable answer is constructed here -as an integer by 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 -CLN is responsible for this behaviour and we refer -the reader to 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. - - - - - - - - Method - Returns true if... - - - - - .is_zero() - object is equal to zero - - - .is_positive() - object is not complex and greater than 0 - - - .is_integer() - object is a (non-complex) integer - - - .is_pos_integer() - object is an integer and greater than 0 - - - .is_nonneg_integer() - object is an integer and greater equal 0 - - - .is_even() - object is an even integer - - - .is_odd() - object is an odd integer - - - .is_prime() - object is a prime integer (probabilistic primality test) - - - .is_rational() - object is an exact rational number (integers are rational, too, as are complex extensions like 2/3+7/2*I) - - - .is_real() - object is a real integer, rational or float (i.e. is not complex) - - - - - - - - - - - -Constants - -Constants behave pretty much like symbols except that that they return -some specific number when the method .evalf() is called. - - -The predefined known constants are: - - - - - - - - Name - Common Name - Numerical Value (35 digits) - - - - - Pi - Archimedes' constant - 3.14159265358979323846264338327950288 - - Catalan - Catalan's constant - 0.91596559417721901505460351493238411 - - EulerGamma - Euler's (or Euler-Mascheroni) constant - 0.57721566490153286060651209008240243 - - - - - - - - -Fundamental operations: The <literal>power</literal>, <literal>add</literal> and <literal>mul</literal> classes - -Simple polynomial expressions are written down in GiNaC pretty -much like in other CAS. The necessary operators +, --, * and / -have been overloaded to achieve this goal. When you run the following -program, the constructor for an object of type mul -is automatically called to hold the product of a -and b and then the constructor for an object of -type add is called to hold the sum of that -mul object and the number one: -Construction of <literal>add</literal> and <literal>mul</literal> objects - -#include <ginac/ginac.h> -using namespace GiNaC; - -int main() -{ - symbol a("a"), b("b"); - ex MyTerm = 1+a*b; - // ... -} - - - -For exponentiation, you have already seen the somewhat clumsy -(though C-ish) statement pow(x,2); to represent -x squared. This direct construction is necessary -since we cannot safely overload the constructor ^ -in C++ to construct a power -object. If we did, it would have several counterintuitive effects: - - - Due to C's operator precedence, - 2*x^2 would be parsed as (2*x)^2. - - - Due to the binding of the operator ^, - x^a^b would result in (x^a)^b. - This would be confusing since most (though not all) other CAS - interpret this as x^(a^b). - - - Also, expressions involving integer exponents are very - frequently used, which makes it even more dangerous to overload - ^ since it is then hard to distinguish between the - semantics as exponentiation and the one for exclusive or. (It would - be embarassing to return 1 where one has requested - 2^3.) - - -All effects are contrary to mathematical notation and differ from the -way most other CAS handle exponentiation, therefore overloading -^ is ruled out for GiNaC's C++ part. The situation -is different in ginsh, there the -exponentiation-^ exists. (Also note, that the -other frequently used exponentiation operator ** -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 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 pow(pow(x,2),3) to -x^6 automatically are only performed when -this is mathematically possible. If we replace the outer exponent -three in the example by some symbols a, the -simplification is not safe and will not be performed, since -a might be 1/2 and -x negative. - -Objects of type add and -mul are containers with an arbitrary number of -slots for expressions to be inserted. Again, simple and safe -simplifications are carried out like transforming -3*x+4-x to 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 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. - - - -Built-in Functions - -There are quite a number of useful functions built into GiNaC. -They are all objects of class 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: -Evaluation of built-in functions - -#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; - // ... -} - -This program will type out two times a function and then an -expression that may be really useful: - -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) - - -Most of these functions can be differentiated, series expanded so on. -Read the next chapter in order to learn more about this.. - - - - - - - -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: -Methods vs. wrapper functions - -#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; - // ... -} - - -The general rule is that wherever methods accept one or more -parameters (arg1, arg2, ...) -the order of arguments the function wrapper accepts is the same but -preceded by the object to act on (object, -arg1, arg2, ...). 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 -A:=x+1; subs(x=2,A); GiNaC would require -A=x+1; subs(A,x==2); (after proper declaration of A -and x). On the other hand, since MapleV returns 3 on -A:=x^2+3; coeff(A,x,0); (GiNaC: -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 ex and sometimes calling a function cannot be -avoided. - - -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 4*x*y + x*z + 20*y^2 + -21*y*z + 4*z^2. It is equivalent to the factorized -polynomial (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 -(4*y + z)*x + 20*y^2 + 21*y*z + 4*z^2 and -20*y^2 + (21*z + 4*x)*y + 4*z^2 + x*z. - - -To bring an expression into expanded form, its method -.expand() may be called. In our example above, -this corresponds to 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! - - - -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 -collect() accomplishes this task: - - #include <ginac/ginac.h> - ex ex::collect - symbol const & s - -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 - - #include <ginac/ginac.h> - int ex::degree - symbol const & s - - - int ex::ldegree - symbol const & s - -where degree() returns the highest coefficient and -ldegree() the lowest one. These two methods work -also reliably on non-expanded input polynomials. This is illustrated -in the following example: - -Collecting expressions in multivariate polynomials - -#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; - // ... -} - - -When run, it returns an output in the following fashion: - -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 - -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. - - - -Polynomial Arithmetic - -GCD and LCM - -The functions for polynomial greatest common divisor and least common -multiple have the synopsis: - - #include <GiNaC/normal.h> - ex gcd - const ex *a, const ex *b - - - ex lcm - const ex *a, const ex *b - - -The functions gcd() and lcm() accepts two expressions -a and b as arguments and return -a new expression, their greatest common divisor or least common -multiple, respectively. If the polynomials a and -b are coprime gcd(a,b) returns 1 -and lcm(a,b) returns the product of -a and b. -Polynomal GCD/LCM - -#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 - // ... -} - - - - - - -The <function>normal</function> method - -While in common symbolic code gcd() and -lcm() are not too heavily used, simplification -occurs frequently. Therefore .normal(), which -provides some basic form of simplification, has become a method of -class ex, just like .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 t1 and -t2 are indeed simplified in this little program: -Cancellation of polynomial GCD (with obstacles) - -#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; - // ... -} - - - -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 P_a/P_b = -(4*y+z)/(y+3*z). - - - - - -Symbolic Differentiation - -GiNaC's objects know how to differentiate themselves. Thus, a -polynomial (class add) knows that its derivative is -the sum of the derivatives of all the monomials: -Simple polynomial differentiation - -#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 - // ... -} - - -If a second integer parameter n is given the -diff method returns the nth -derivative. - -If 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 1/cosh(x). Since the -derivative of cosh(x) is sinh(x) -and the derivative of pow(x,-1) is --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 -nth Euler number is the coefficient of -x^n/n! in the expansion of -1/cosh(x). We may use this identity to code a -function that generates Euler numbers in just three lines: -Differentiation with nontrivial functions: Euler numbers - -#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; -} - - -When you run it, it produces the sequence 1, --1, 5, -61, -1385, -50521. We increment the -loop variable i by two since all odd Euler numbers -vanish anyways. - - - -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: -Series expansion - -#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; - // ... -} - - - - -As an instructive application, let us calculate the numerical -value of Archimedes' constant (for which there already exists the -built-in constant Pi) using Méchain's -mysterious formula Pi==16*atan(1/5)-4*atan(1/239). -We may expand the arcus tangent around 0 and insert -the fractions 1/5 and 1/239. -But, as we have seen, a series in GiNaC carries an order term with it. -The function series_to_poly may be used to strip -this off: -Series expansion using Méchain's formula for -<literal>Pi</literal> - -#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; -} - -When you run this program, it will type out: - -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 - - - - - - - - - - -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. - -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 -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 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 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 -CLN is much better suited. - - - -Other symbolic functions - -The easiest and most instructive way to start with is probably -to implement your own function. Objects of class -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 -ex as arguments and returning one -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 -eval it. It could look something like this: - - -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(); -} - -The last line returns cos(x) if we don't know what -else to do and stops a potential recursive evaluation by saying -.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 numeric: - -static ex cos_evalf_method(ex const & x) -{ - return sin(ex_to_numeric(x)); -} - -Differentiation will surely turn up and so we need to tell -sin how to differentiate itself: - -static ex cos_diff_method(ex const & x, unsigned diff_param) -{ - return cos(x); -} - - -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 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: - -REGISTER_FUNCTION(cos, cos_eval_method, cos_evalf_method, cos_diff, NULL); - -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: - -DECLARE_FUNCTION_1P(cos) - -The suffix _1P stands for one -parameter. Of course, this implementation of -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! - - - - - - - -A Comparison with other CAS - -This chapter will give you some information on how GiNaC -compares to other, traditional Computer Algebra Systems, like -Maple, Mathematica or -Reduce, where it has advantages and disadvantages -over these systems. - -Advantages - -GiNaC has several advantages over traditional Computer -Algebra Systems, like - - - - 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. - - - structured data types: you can build up structured data - types using structs or classes - together with STL features instead of using unnamed lists of lists - of lists. - - - 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. - - - - development tools: powerful development tools exist for - C++, like fancy editors (e.g. with automatic - indentation and syntax highlighting), debuggers, visualization - tools, documentation tools... - - - modularization: C++ programs can - easily be split into modules by separating interface and - implementation. - - - 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. - - - - 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. - - - 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. Maple) to providing a - method for "embedding" the system - (i.e. Yacas). - - - 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. - - - - -Disadvantages - -Of course it also has some disadvantages - - - - 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 CINT - C++ interpreter. - - - advanced features: GiNaC cannot compete with a program - like Reduce which exists for more than - 30 years now or 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). - - - 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 (GCC). GiNaC uses - recent language features like explicit constructors, mutable - members, RTTI, dynamic_casts and STL, so ANSI compliance is meant - literally. Recent GCC versions starting at - 2.95, although itself not yet ANSI compliant, support all needed - features. - - - - - -Why <literal>C++</literal>? - -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 + operator is rarely meaningful, it is -perfectly suited for algebraic expressions. Writing 3x+5y as -3*x+5*y instead of -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. - - - - - - - - - - ISO/IEC 14882:1998 - Programming Languages: C++ - - - - - CLN: A Class Library for Numbers - - - BrunoHaible -
haible@ilog.fr
 - - - - - - - The C++ Programming Language - BjarneStroustrup - 3 - 0-201-88954-4 - Addison Wesley - - - - - - C++ FAQs - MarshallCline - 0-201-58958-3 - 1995 - Addison Wesley - - - - - - Algorithms for Computer Algebra - - KeithO.Geddes - StephenR.Czapor - GeorgeLabahn - - 0-7923-9259-0 - 1992 - - Kluwer Academic Publishers -
Norwell, Massachusetts
- - - - - - - Computer Algebra - Systems and Algorithms for Algebraic Computation - - J.H.Davenport - Y.Siret - E.Tournier - - 0-12-204230-1 - 1988 - - Academic Press -
London
- - - - - - - - diff --git a/doc/tutorial/version.texi b/doc/tutorial/version.texi new file mode 100644 index 00000000..fd299ad9 --- /dev/null +++ b/doc/tutorial/version.texi @@ -0,0 +1,3 @@ +@set UPDATED 25 November 1999 +@set EDITION 0.4.0 +@set VERSION 0.4.0 diff --git a/ginac/Makefile.in b/ginac/Makefile.in index 3c07c90e..9e0fc163 100644 --- a/ginac/Makefile.in +++ b/ginac/Makefile.in @@ -74,8 +74,6 @@ GINACLIB_MICRO_VERSION = @GINACLIB_MICRO_VERSION@ GINACLIB_MINOR_VERSION = @GINACLIB_MINOR_VERSION@ GINACLIB_VERSION = @GINACLIB_VERSION@ GINSH_LIBS = @GINSH_LIBS@ -JADE = @JADE@ -JADETEX = @JADETEX@ LATEX = @LATEX@ LD = @LD@ LEX = @LEX@ diff --git a/ginsh/Makefile.in b/ginsh/Makefile.in index 468cd322..d755e04e 100644 --- a/ginsh/Makefile.in +++ b/ginsh/Makefile.in @@ -74,8 +74,6 @@ GINACLIB_MICRO_VERSION = @GINACLIB_MICRO_VERSION@ GINACLIB_MINOR_VERSION = @GINACLIB_MINOR_VERSION@ GINACLIB_VERSION = @GINACLIB_VERSION@ GINSH_LIBS = @GINSH_LIBS@ -JADE = @JADE@ -JADETEX = @JADETEX@ LATEX = @LATEX@ LD = @LD@ LEX = @LEX@ -- 2.44.0