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This is Info file eplain.info, produced by Makeinfo-1.55 from the input file eplain.texi. This file documents the Eplain macros. Copyright (C) 1989, 90, 91, 92, 93, 94 Karl Berry. Steven Smith wrote the documentation for the commutative diagram macros. (He also wrote the macros.) 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 also that the section entitled "GNU General Public License" is included exactly as in the original, and provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this Permission is granted to copy and distribute translations of this manual into another language, under the above conditions for modified versions, except that the section entitled "GNU General Public License" may be included in a translation approved by the author instead of in the original English. File: eplain.info, Node: Indexing, Next: Justification, Prev: Page references, Up: User definitions Indexing ======== Eplain provides support for generating raw material for an index, and for typesetting a sorted index. A separate program must do the actual collection and sorting of terms, because TeX itself has no support for sorting. Eplain's indexing commands were designed to work with the program MakeIndex, available from `ftp.math.utah.edu' in the directory `pub/tex/makeindex', and from CTAN hosts in `tex-archive/indexing/makeindex'; MakeIndex is also commonly included in prepackaged TeX distributions. It is beyond the scope of this manual to explain how to run MakeIndex, and all of its many options. *Note MAKEINDEX: (makeindex)MAKEINDEX. The basic strategy for indexing works like this: 1. For a document `foo.tex', Eplain's indexing commands (e.g., `\idx'; see the section `Indexing terms' below) write the raw index material to `foo.idx'. 2. MakeIndex reads `foo.idx', collects and sorts the index, and writes the result to `foo.ind'. 3. Eplain reads and typesets `foo.ind' on a subsequent run of TeX. See the section `Typesetting an index' below. If your document needs more than one index, each must have its own file. Therefore, Eplain provides the command `\defineindex', which takes an argument that is a single letter, which replaces `i' in the filenames and in the indexing command names described below. For example, \defineindex{m} defines the command `\mdx' to write to the file `foo.mdx'. Eplain simply does `\defineindex{i}' to define the default commands. * Menu: * Indexing terms:: Specifying what to index. * Typesetting an index:: Printing the sorted output. * Customizing indexing:: Creating commands and specifying extra actions. File: eplain.info, Node: Indexing terms, Next: Typesetting an index, Up: Indexing Indexing terms -------------- Indexing commands in Eplain come in pairs: one command that only writes the index entry to the `.idx' file (see above section), and one that also typesets the term being indexed. The former always starts with `s' (for "silent"). In either case, the name always includes `Idx', where I is the index letter, also described above. Eplain defines the index `i' itself, so that's what we'll use in the names below. The silent form of the commands take a subterm as a trailing optional argument. For example, `\sidx{truth}[definition of]' on page 75 makes an index entry that will eventually be typeset (by default) as truth definition of, 75 Also, the silent commands ignore trailing spaces. The non-silent ones do not. * Menu: * Indexing commands:: Making index entries. * Modifying index entries:: Ranges, see/see also, page number typesetting. * Proofing index terms:: Noting index entries in the margins. File: eplain.info, Node: Indexing commands, Next: Modifying index entries, Up: Indexing terms Indexing commands ................. Here are the commands. * `\sidx{TERM}[SUBTERM]' makes an index entry for TERM, optionally with subterm SUBTERM. `\idx{TERM}' also produces TERM as output. Example: \sidx{truth}[beauty of] The beauty of truth is \idx{death}. * \sidxname{FIRST M.}{VON LAST}[SUBTERM] makes an index entry for `VON LAST, FIRST M.'. You can change the `, ' by redefining `\idxnameseparator'. \idxname{FIRST M.}{VON LAST} also produces FIRST M. VON LAST as output. (These commands are useful special cases of `\idx' and `\sidx'.) Example: \sidxname{Richard}{Stark} \idxname{Donald}{Westlake} has written many kinds of novels, under almost as many names. * `\sidxmarked\CS{TERM}[SUBTERM]' makes an index entry for `TERM[SUBTERM]', but TERM will be put in the index as `\CS{term}', but still sorted as just TERM. `\idxmarked\CS{TERM}' also typesets `\CS{term}'. This provides for the usual ways of changing the typesetting of index entries. Example: \def\article#1{``#1''} \sidxmarked\article{Miss Elsa and Aunt Sophie} Peter Drucker's \idxmarked\article{The Polanyis} is a remarkable essay about a remarkable family. * `\sidxsubmarked{TERM}\CS{subterm}' makes an index entry for TERM, SUBTERM as usual, but also puts SUBTERM in the index as `\CS{term}'. `\idxsubmarked{TERM}\CS{subterm}' also typesets `TERM \CS{subterm}', in the unlikely event that your syntax is convoluted enough to make this useful. Example: \def\title#1{{\sl #1}} \sidxsubmarked{Anderson, Laurie}\title{Strange Angels} The \idxsubmarked{Anderson}\title{Carmen} is a strange twist. The commands above rely on MakeIndex's feature for separating sorting of an index entry's from its typesetting. You can use this directly by specifying an index entry as `SORT@TYPESET'. For example: \sidx{Ap-weight@$A_\pi$-weight} will sort as `Ap-weight', but print with the proper math. The `@' here is MakeIndex's default character for this purpose. *Note Style File-MakeIndex: (makeindex)Style File-MakeIndex. To make an index entry with an `@' in it, you have to escape it with a backslash; Eplain provides no macros for doing this. After any index command, Eplain runs `\hookaction{afterindexterm}'. Because the index commands always add a whatsit item to the current list, you may wish to preserve a penalty or space past the new item. For example, given a conditional `\if@aftersctnhead' set true when you're at a section heading, you could do: \hookaction{afterindexterm}{\if@aftersctnhead \nobreak \fi} File: eplain.info, Node: Modifying index entries, Next: Proofing index terms, Prev: Indexing commands, Up: Indexing terms Modifying index entries ....................... All the index commands described in the previous section take an initial optional argument before the index term, which modify the index entry's meaning in various ways. You can specify only one of the following in any given command. These work via MakeIndex's "encapsulation" feature. *Note Customizing indexing::, if you're not using the default characters for the MakeIndex operators. The other optional argument (specifying a subterm) is independent of these. Here are the possibilities: `begin' `end' These mark an index entry as the beginning or end of a range. The index entries must match exactly for MakeIndex to recognize them. Example: \sidx[begin]{future}[Cohen, Leonard] ... \sidx[end]{future}[Cohen, Leonard] will typeset as something like future, Cohen, Leonard, 65--94 `see' This marks an index entry as pointing to another; the real index term is an additional (non-optional) argument to the command. Thus you can anticipate a term readers may wish to look up, yet which you have decided not to index. Example: \sidx[see]{analysis}[archetypal]{archetypal criticism} becomes analysis, archetypal, See archetypal criticism `seealso' Similar to `see' (the previous item), but also allows for normal index entries of the referencing term. Example: \sidx[seealso]{archetypal criticism}[elements of]{dichotomies} becomes archetypal criticism, elements of, 75, 97, 114, See also dichotomies (Aside for the academically curious: The archetypally critical book I took these dichotomous examples from is Laurence Berman's `The Musical Image', which I happened to co-design and typeset.) `pagemarkup=CS' This puts `\CS' before the page number in the typeset index, thus allowing you to underline definitive entries, italicize examples, and the like. You do *not* precede the control sequence CS with a backslash. (That just leads to expansive difficulties.) Naturally it is up to you to define the control sequences you want to use. Example: \def\defn#1{{\sl #1}} \sidx[pagemarkeup=defn]{indexing} becomes something like indexing, `\defn{75}' File: eplain.info, Node: Proofing index terms, Prev: Modifying index entries, Up: Indexing terms Proofing index terms .................... As you are reading through a manuscript, it is helpful to see what terms have been indexed, so you can add others, catch miscellaneous errors, etc. (Speaking from bitter experience, I can say it is extremely error-prone to leave all indexing to the end of the writing, since it involves adding many TeX commands to the source files.) So Eplain puts index terms in the margin of each page, if you set `\indexproofingtrue'. It is `false' by default. The terms are typeset by the macro `\indexproofterm', which takes a single argument, the term to be typeset. Eplain's definition of `\indexproofterm' just puts it into an `\hbox', first doing `\indexprooffont', which Eplain defines to select the font `cmtt8'. With this definition long terms run off the page, but since this is just for proofreading anyway, it seems acceptable. On the other hand, we certainly don't want the index term to run into the text of the page, so Eplain uses the right-hand side of the page rather than the left-hand page (assuming a language read left to right here). So `\ifodd\pageno', Eplain kerns by `\outsidemargin', otherwise by `\insidemargin'. If those macros are undefined, `\indexsetmargins' defines them to be one inch plus `\hoffset'. To get the proofing index entries on the proper page, Eplain defines a new insertion class `\@indexproof'. To unbox any index proofing material, Eplain redefines `\makeheadline' to call `\indexproofunbox' before the original `\makeheadline'. Thus, if you have your own output routine, that redefines or doesn't use `\makeheadline', it's up to you to call `\indexproofunbox' at the appropriate time. File: eplain.info, Node: Typesetting an index, Next: Customizing indexing, Prev: Indexing terms, Up: Indexing Typesetting an index -------------------- The command `\readindexfile{i}' reads and typesets the `.ind' file that MakeIndex outputs (from the `.idx' file which the indexing commands in the previous sections write). Eplain defines a number of commands that support the default MakeIndex output. More precisely, `\readindexfile' reads `\indexfilebasename.INDEX-LETTERnd', where the INDEX-LETTER is the argument. `\indexfilebasename' is `\jobname' by default, but if you have different indexes in different parts of a book, you may wish to change it, just as with bibliographies (*note Citations::.). MakeIndex was designed to work with LaTeX; therefore, by default the `.ind' file starts with `\begin{theindex}' and ends with `\end{theindex}'. If no `\begin' has been defined, Eplain defines one to ignore its argument and set up for typesetting the index (see below), and also defines a `\end' to ignore its argument. (In a group, naturally, since there is a primitive `\end'). Eplain calls `\indexfonts', sets `\parindent = 0pt', and does `\doublecolumns' (*note Multiple columns::.) at the `\begin{theindex}'. `\indexfonts' does nothing by default; it's just there for you to override. (Indexes are usually typeset in smaller type than the main text.) It ends the setup with `\hookrun{beginindex}', so you can override anything you like in that hook (*note Hooks::.). For example: \hookaction{beginindex}{\triplecolumns} MakeIndex turns each main index entry into an `\item', subentries into `\subitem', and subsubentries into `\subsubitem'. By default, the first line of main entries are not indented, and subentries are indented 1em per level. Main entries are preceded by a `\vskip' of `\aboveitemskipamount', `0pt plus2pt' by default. Page breaks are encouraged before main entries (`\penalty -100'), but prohibited afterwards--Eplain has no provision for "continued" index entries. All levels do the following: \hangindent = 1em \raggedright \hyphenpenalty = 10000 Each entry ends with `\hookrun{indexitem}', so you can change any of this. For example, to increase the allowable rag: \hookaction{indexitem}{\advance\rightskip by 2em} Finally, MakeIndex outputs `\indexspace' between each group of entries in the `.ind' file. Eplain makes this equivalent to `\bigbreak'. File: eplain.info, Node: Customizing indexing, Prev: Typesetting an index, Up: Indexing Customizing indexing -------------------- By default, MakeIndex outputs `, ' after each term in the index. To change this, you can add the following to your MakeIndex style (`.ist') file: delim_0 "\\afterindexterm " delim_1 "\\afterindexterm " delim_2 "\\afterindexterm " Eplain makes `\afterindexterm' equivalent to `\quad'. You can also change the keywords Eplain recognizes (*note Modifying index entries::.): `\idxbeginrangeword' `begin' `\idxendrangeword' `end `\idxseeword' `see `\idxseealsoword' `seealso' You can also change the magic characters Eplain puts into the `.idx' file, in case you've changed them in the `.ist' file: `\idxsubentryseparator' `!' `\idxencapoperator' `|' `\idxbeginrangemark' `(' `\idxendrangemark' `)' There is no macro for the `actual' (`@' by default) character, because it's impossible to make it expand properly. Finally, you can change the (imaginary) page number that "see also" entries sort as by redefining `\idxmaxpagenum'. This is 99999 by default, which is one digit too many for old versions of MakeIndex. File: eplain.info, Node: Justification, Next: Tables, Prev: Indexing, Up: User definitions Justification ============= Eplain defines three commands to conveniently justify multiple lines of text: `\flushright', `\flushleft', and `\center'. They all work in the same way; let's take `\center' as the example. To start centering lines, you say `\center' inside a group; to stop, you end the group. Between the two commands, each end-of-line in the input file also starts a new line in the output file. The entire block of text is broken into paragraphs at blank lines, so all the TeX paragraph-shaping parameters apply in the usual way. This is convenient, but it implies something else that isn't so convenient: changes to any linespacing parameters, such as `\baselineskip', will have *no effect* on the paragraph in which they are changed. TeX does not handle linespacing changes within a paragraph (because it doesn't know where the line breaks are until the end of the paragraph). The space between paragraphs is by default one blank line's worth. You can adjust this space by assigning to `\blanklineskipamount'; this (vertical) glue is inserted after each blank line. Here is an example: {\center First line. Second line, with a blank line before. } This produces: First line. Second line, with a blank line before. You may wish to use the justification macros inside of your own macros. Just be sure to put them in a group. For example, here is how a title macro might be defined: \def\title{\begingroup\titlefont\center} \def\endtitle{\endgroup} File: eplain.info, Node: Tables, Next: Margins, Prev: Justification, Up: User definitions Tables ====== Eplain provides a single command, `\makecolumns', to make generating one particular kind of table easier. More ambitious macro packages might be helpful to you for more difficult applications. The files `ruled.tex' and `TXSruled.tex', available from `lifshitz.ph.utexas.edu' in `texis/tables', is the only one I know of. Many tables are homogenous, i.e., all the entries are semantically the same. The arrangement into columns is to save space on the page, not to encode different meanings. In this kind of the table, it is useful to have the column breaks chosen automatically, so that you can add or delete entries without worrying about the column breaks. `\makecolumns' takes two arguments: the number of entries in the table, and the number of columns to break them into. As you can see from the example below, the first argument is delimited by a slash, and the second by a colon and a space (or end-of-line). The entries for the table then follow, one per line (not including the line with the `\makecolumns' command itself). `\parindent' defines the space to the left of the table. `\hsize' defines the width of the table. So you can adjust the position of the table on the page by assignments to these parameters, probably inside a group. You can also control the penalty at a page break before the `\makecolumns' by setting the parameter `\abovecolumnspenalty'. Usually, the table is preceded by some explanatory text. You wouldn't want a page break to occur after the text and before the table, so Eplain sets it to `10000'. But if the table produced by `\makecolumns' is standing on its own, `\abovecolumnspenalty' should be decreased. If you happen to give `\makecolumns' a smaller number of entries than you really have, some text beyond the (intended) end of the table will be incorporated into the table, probably producing an error message, or at least some strange looking entries. And if you give `\makecolumns' a larger number of entries than you really have, some of the entries will be typeset as straight text, probably also looking somewhat out of place. Here is an example: % Arrange 6 entries into 2 columns: \makecolumns 6/2: % This line doesn't have an entry. one two three four five six Text after the table. This produces `one', `two', and `three' in the first column, and `four', `five', and `six' in the second. File: eplain.info, Node: Margins, Next: Multiple columns, Prev: Tables, Up: User definitions Margins ======= TeX's primitives describe the type area in terms of an offset from the upper left corner, and the width and height of the type. Some people prefer to think in terms of the "margins" at the top, bottom, left, and right of the page, and most composition systems other than TeX conceive of the page laid out in this way. Therefore, Eplain provides commands to directly assign and increment the margins. `\topmargin = DIMEN' `\bottommargin = DIMEN' `\leftmargin = DIMEN' `\rightmargin = DIMEN' These commands set the specified margin to the DIMEN given. The `=' and the spaces around it are optional. The control sequences here are not TeX registers, despite appearances; therefore, commands like `\showthe\topmargin' will not do what you expect. `\advancetopmargin by DIMEN' `\advancebottommargin by DIMEN' `\advanceleftmargin by DIMEN' `\advancerightmargin by DIMEN' These commands change the specified margin by the DIMEN given. Regardless of whether you use the assignment or the advance commands, Eplain always changes the type area in response, not the other margins. For example, when TeX starts, the left and right margins are both one inch. If you then say `\leftmargin = 2in', the right margin will remain at one inch, and the width of the lines (i.e., `\hsize') will decrease by one inch. When you use any of these commands, Eplain computes the old value of the particular margin, by how much you want to change it, and then resets the values of TeX's primitive parameters to correspond. Unfortunately, Eplain cannot compute the right or bottom margin without help: you must tell it the full width and height of the final output page. It defines two new parameters for this: `\paperheight' The height of the output page; default is 11in. `\paperwidth' The width of the output page; default is 8.5in. If your output page has different dimensions than this, you must reassign to these parameters, as in \paperheight = 11in \paperwidth = 17in File: eplain.info, Node: Multiple columns, Next: Footnotes, Prev: Margins, Up: User definitions Multiple columns ================ Eplain provides for double, triple, and quadruple column output: say `\doublecolumns', `\triplecolumns', or `\quadcolumns', and from that point on, the manuscript will be set in columns. To go back to one column, say `\singlecolumn'. You may need to invoke `\singlecolumn' to balance the columns on the last page of output. To do a "column eject", i.e., move to the top of the next column, do `\columnfill'. This does not actually force an eject, however: it merely inserts a kern of size `\@normalvsize' minus `\pagetotal' (`\@normalvsize' being the usual height of the page; to implement multicolumns, Eplain multiplies `\vsize' itself by the number of columns). In most circumstances, a column break will be forced after this kern (during the column splitting operation when the whole page is output), as desired. The columns are separated by the value of the dimen parameter `\gutter'. Default value is two picas. All the `\...columns' macros insert the value of the glue parameter `\abovedoublecolumnskip' before the multicolumn text, and the value of the glue parameter `\belowdoublecolumnskip' after it. The default value for both of these parameters is `\bigskipamount', i.e., one linespace in plain TeX. The macros take into account only the insertion classes defined by plain TeX; namely, footnotes and `\topinsert's. If you have additional insertion classes, you will need to change the implementation. Also, Eplain makes insertions the full page width. There is no provision for column-width insertions. File: eplain.info, Node: Footnotes, Next: Fractions, Prev: Multiple columns, Up: User definitions Footnotes ========= The most common reference mark for footnotes is a raised number, incremented on each footnote. The `\numberedfootnote' macro provides this. It takes one argument, the footnote text. If your document uses only numbered footnotes, you could make typing `\numberedfootnote' more convenient with a command such as: \let\footnote = \numberedfootnote After doing this, you can type your footnotes as `\footnote{FOOTNOTE TEXT}', instead of as `\numberedfootnote{FOOTNOTE TEXT}'. Eplain keeps the current footnote number in the count register `\footnotenumber'. So, to reset the footnote number to zero, as you might want to do at, for example, the beginning of a chapter, you could say `\footnotenumber=0'. Plain TeX separates the footnote marker from the footnote text by an en space (it uses the `\textindent' macro). In Eplain, you can change this space by setting the dimension register `\footnotemarkseparation'. The default is still an en. You can produce a space between footenotes by setting the glue register `\interfootnoteskip'. The default is zero. `\parskip' is also set to zero by default before the beginning of each footnote (but not for the text of the footnote). You can also control footnote formatting in a more general way: Eplain expands the token register `\everyfootnote' before a footnote is typeset, but after the default values for all the parameters have been established. For example, if you want your footnotes to be printed in seven-point type, indented by one inch, you could say: \everyfootnote = {\sevenrm \leftskip = 1in} By default, an `\hrule' is typeset above each group of footnotes on a page. You can control the dimensions of this rule by setting the dimension registers `\footnoterulewidth' and `\footnoteruleheight'. The space between the rule and the first footnote on the page is determined by the dimension register `\belowfootnoterulespace'. If you don't want any rule at all, set `\footenoteruleheight=0pt', and, most likely, `\belowfootnoterulespace=0pt'. The defaults for these parameters typeset the rule in the same way as plain TeX: the rule is 0.4 points high, 2 true inches wide, with 2.6 points below it. The space above the rule and below the text on the page is controlled by the glue register `\skip\footins'. The default is a plain TeX `\bigskip'. File: eplain.info, Node: Fractions, Next: Paths, Prev: Footnotes, Up: User definitions Fractions ========= Exercise 11.6 of `The TeXbook' describes a macro `\frac' for setting fractions, but `\frac' never made it into plain TeX. So Eplain includes it. `\frac' typesets the numerator and denominator in `\scriptfont0', slightly raised and lowered. The numerator and denominator are separated by a slash. The denominator must be enclosed in braces if it's more than one token long, but the numerator need not be. (This is a consequence of `\frac' taking delimited arguments; see page 203 of `The TeXbook' for an explanation of delimited macro arguments.) For example, `\frac 23/{64}' turns `23/64' into 23/64 (you can't see the difference in the Info file). File: eplain.info, Node: Paths, Next: Logos, Prev: Fractions, Up: User definitions Paths ===== When you typeset long pathnames, electronic mail addresses, or other such "computer" names, you would like TeX to break lines at punctuation characters within the name, rather than trying to find hyphenation points within the words. For example, it would be better to break the email address `letters@alpha.gnu.ai.mit.edu' at the `@' or a `.', rather than at the hyphenation points in `letters' and `alpha'. If you use the `\path' macro to typeset the names, TeX will find these good breakpoints. The argument to `\path' is delimited by any other other than `\' which does not appear in the name itself. `|' is often a good choice, as in: \path|letters@alpha.gnu.ai.mit.edu| You can control the exact set of characters at which breakpoints will be allowed by calling `\discretionaries'. This takes the same sort of delimited argument; any character in the argument will henceforth be a valid breakpoint within `\path'. The default set is essentially all the punctuation characters: \discretionaries |~!@$%^&*()_+`-=#{}[]:";'<>,.?\/| If for some reason you absolutely must use `\' as the delimiter character for `\path', you can set `\specialpathdelimiterstrue'. (Other delimiter characters can still be used.) TeX then processes the `\path' argument about four times more slowly. File: eplain.info, Node: Logos, Next: Boxes, Prev: Paths, Up: User definitions Logos ===== Eplain redefines the `\TeX' macro of plain TeX to end with `\null', so that the proper spacing is produced when `\TeX' is used at the end of a sentence. The other ...TeX macros listed here do this, also. Eplain defines `\AMSTeX', `\BibTeX' `\AMSLaTeX', `\LAMSTeX', `\LaTeX' `\MF', and `\SLiTeX' to produce their respective logos. (Sorry, the logos are not shown here.) Some spelling variants of these are also supported. File: eplain.info, Node: Boxes, Prev: Logos, Up: User definitions Boxes ===== The solid rectangle that Eplain uses as a marker in unordered lists (*note Lists::.) is available by itself: just say `\blackbox'. You can create black boxes of arbitrary size with `\hrule' or `\vrule'. You can also get unfilled rectangles with `\makeblankbox'. This takes two explicit arguments: the height and depth of the rules that define the top and bottom of the rectangle. (The two arguments are added to get the width of the left and right borders, so that the thickness of the border is the same on all four sides.) It also uses, as implicit arguments, the dimensions of `\box0' to define the dimensions of the rectangle it produces. (The contents of `\box0' are ignored.) Here is an example. This small raised open box is suitable for putting next to numbers in, e.g., a table of contents. \def\openbox{% \ht0 = 1.75pt \dp0 = 1.75pt \wd0 = 3.5pt \raise 2.75pt \makeblankbox{.2pt}{.2pt} } Finally, you can put a box around arbitrary text with `\boxit'. This takes one argument, which must itself be a (TeX) box, and puts a printed box around it, separated by `\boxitspace' white space (3 points by default) on all four sides. For example: \boxit{\hbox{This text is boxed.}} The reason that the argument must be a box is that when the text is more than one line long, TeX cannot figure out the line length for itself. Eplain does set `\parindent' to zero inside `\boxit', since it is very unlikely you would want indentation there. (If you do, you can always reset it yourself.) `\boxit' uses `\ehrule' and `\evrule' so that you can easily adjust the thicknesses of the box rules. *Note Rules::. File: eplain.info, Node: Arrow theoretic diagrams, Next: Programming definitions, Prev: User definitions, Up: Top Arrow theoretic diagrams ************************ This chapter describes definitions for producing commutative diagrams. Steven Smith wrote this documentation (and the macros). * Menu: * Slanted lines and vectors:: * Commutative diagrams:: File: eplain.info, Node: Slanted lines and vectors, Next: Commutative diagrams, Up: Arrow theoretic diagrams Slanted lines and vectors ========================= The macros `\drawline' and `\drawvector' provide the capability found in LaTeX's picture mode to draw slanted lines and vectors of certain directions. Both of these macros take three arguments: two integer arguments to specify the direction of the line or vector, and one argument to specify its length. For example, `\drawvector(-4,1){60pt}' produces the vector (A vector in the 2d quadrant of length 60 pt appears here.) which lies in the 2d quadrant, has a slope of minus 1/4, and a width of 60 pt. Note that if an `\hbox' is placed around `\drawline' or `\drawvector', then the width of the `\hbox' will be the positive dimension specified in the third argument, except when a vertical line or vector is specified, e.g., `\drawline(0,1){1in}', which has zero width. If the specified direction lies in the 1st or 2d quadrant (e.g., `(1,1)' or `(-2,3)'), then the `\hbox' will have positive height and zero depth. Conversely, if the specified direction lies in the 3d or 4th quadrant (e.g., `(-1,-1)' or `(2,-3)'), then the `\hbox' will have positive depth and zero height. There are a finite number of directions that can be specified. For `\drawline', the absolute value of each integer defining the direction must be less than or equal to six, i.e., `(7,-1)' is incorrect, but `(6,-1)' is acceptable. For `\drawvector', the absolute value of each integer must be less than or equal to four. Furthermore, the two integers cannot have common divisors; therefore, if a line with slope 2 is desired, say `(2,1)' instead of `(4,2)'. Also, specify `(1,0)' instead of, say, `(3,0)' for horizontal lines and likewise for vertical lines. Finally, these macros depend upon the LaTeX font `line10'. If your site doesn't have this font, ask your system administrator to get it. Future enhancements will include macros to draw dotted lines and dotted vectors of various directions. File: eplain.info, Node: Commutative diagrams, Prev: Slanted lines and vectors, Up: Arrow theoretic diagrams Commutative diagrams ==================== The primitive commands `\drawline' and `\drawvector' can be used to typeset arrow theoretic diagrams. This section describes (1) macros to facilitate typesetting arrows and morphisms, and (2) macros to facilitate the construction of commutative diagrams. All macros described in this section must be used in math mode. * Menu: * Arrows and morphisms:: * Construction of commutative diagrams:: * Commutative diagram parameters:: File: eplain.info, Node: Arrows and morphisms, Next: Construction of commutative diagrams, Up: Commutative diagrams Arrows and morphisms -------------------- The macros `\mapright' and `\mapleft' produce right and left pointing arrows, respectively. Use superscript (`^') to place a morphism above the arrow, e.g., `\mapright^\alpha'; use subscript (`_') to place a morphism below the arrow, e.g., `\mapright_{\tilde l}'. Superscripts and subscripts may be used simulataneously, e.g., `\mapright^\pi_{\rm epimor.}'. Similarly, the macros `\mapup' and `\mapdown' produce up and down pointing arrows, respectively. Use `\rt' to place a morphism to the right of the arrow, e.g., `\mapup\rt{\rm id}'; use `\lft' to place a morphism to the left of the arrow, e.g., `\mapup\lft\omega'. `\lft' and `\rt' may be used simultaneously, e.g., `\mapdown\lft\pi\rt{\rm monomor.}'. Slanted arrows are produced by the macro `\arrow', which takes a direction argument (e.g., `\arrow(3,-4)'). Use `\rt' and `\lft' to place morphisms to the right and left, respectively, of the arrow. A slanted line (no arrowhead) is produced with the macro `\sline', whose syntax is identical to that of `\arrow'. The length of these macros is predefined by the default TeX dimensions `\harrowlength', for horizontal arrows (or lines), `\varrowlength', for vertical arrows (or lines), and `\sarrowlength', for slanted arrows (or lines). To change any of these dimensions, say, e.g., `\harrowlength=40pt'. As with all other TeX dimensions, the change may be as global or as local as you like. Furthermore, the placement of morphisms on the arrows is controlled by the dimensions `\hmorphposn', `\vmorphposn', and `\morphdist'. The first two dimensions control the horizontal and vertical position of the morphism from its default position; the latter dimension controls the distance of the morphism from the arrow. If you have more than one morphism per arrow (i.e., a `^'/`_' or `\lft'/`\rt' construction), use the parameters `\hmorphposnup', `\hmorphposndn', `\vmorphposnup', `\vmorphposndn', `\hmorphposnrt', `\hmorphposnlft', `\vmorphposnrt', and `\vmorphposnlft'. The default values of all these dimensions are provided in the section on parameters that follows below. There is a family of macros to produce horizontal lines, arrows, and adjoint arrows. The following macros produce horizontal maps and have the same syntax as `\mapright': `\mapright' `$X\mapright Y$' = (a right arrow). `\mapleft' `$X\mapleft Y$' = (a left arrow). `\hline' `$X\hline Y$' = (horizontal line) `\bimapright' `$X\bimapright Y$' = (two right arrows). `\bimapleft' `$X\bimapleft Y$' = (two left arrows) `\adjmapright' `$X\adjmapright Y$' = (two adjoint arrows; left over right) `\adjmapleft' `$X\adjmapleft Y$' = (two adjoint arrows; right over left) `\bihline' `$X\bihline Y$' = (two horizontal lines) There is also a family of macros to produce vertical lines, arrows, and adjoint arrows. The following macros produce vertical maps and have the same syntax as `\mapdown': `\mapdown' (a down arrow) `\mapup' (an up arrow) `\vline' (vertical line) `\bimapdown' (two down arrows) `\bimapup' (two up arrows) `\adjmapdown' (two adjoint arrows; down then up) `\adjmapup' (two adjoint arrows; up then down) `\bivline' (two vertical lines) Finally, there is a family of macros to produce slanted lines, arrows, and adjoint arrows. The following macros produce slanted maps and have the same syntax as `\arrow': `\arrow' (a slanted arrow) `\sline' (a slanted line) `\biarrow' (two straight arrows) `\adjarrow' (two adjoint arrows) `\bisline' (two straight lines) The width between double arrows is controlled by the parameter `\channelwidth'. The parameters `\hchannel' and `\vchannel', if nonzero, override `\channelwidth' by controlling the horizontal and vertical shifting from the first arrow to the second. There are no adornments on these arrows to distinguish inclusions from epimorphisms from monomorphisms. Many texts, such as Lang's book `Algebra', use as a tasteful alternative the symbol `inc' (in roman) next to an arrow to denote inclusion. Future enhancements will include a mechanism to draw curved arrows found in, e.g., the Snake Lemma, by employing a version of the `\path' macros of Appendix D of `The TeXbook'. File: eplain.info, Node: Construction of commutative diagrams, Next: Commutative diagram parameters, Prev: Arrows and morphisms, Up: Commutative diagrams Construction of commutative diagrams ------------------------------------ There are two approaches to the construction of commutative diagrams described here. The first approach, and the simplest, treats commutative diagrams like fancy matrices, as Knuth does in Exercise 18.46 of `The TeXbook'. This case is covered by the macro `\commdiag', which is an altered version of the Plain TeX macro `\matrix'. An example suffices to demonstrate this macro. The following commutative diagram (illustrating the covering homotopy property; Bott and Tu, `Differential Forms in Algebraic Topology') (A commutative diagram appears here in the printed output.) is produced with the code $$\commdiag{Y&\mapright^f&E\cr \mapdown&\arrow(3,2)\lft{f_t}&\mapdown\cr Y\times I&\mapright^{\bar f_t}&X}$$ Of course, the parameters may be changed to produce a different effect. The following commutative diagram (illustrating the universal mapping property; Warner, `Foundations of Differentiable Manifolds and Lie Groups') (A commutative diagram appears here in the printed output.) is produced with the code $$\varrowlength=20pt \commdiag{V\otimes W\cr \mapup\lft\phi&\arrow(3,-1)\rt{\tilde l}\cr V\times W&\mapright^l&U\cr}$$ A diagram containing isosceles triangles is achieved by placing the apex of the triangle in the center column, as shown in the example (illustrating all constant minimal realizations of a linear system; Brockett, `Finite Dimensional Linear Systems') (A commutative diagram appears here in the printed output.) which is produced with the code $$\sarrowlength=.42\harrowlength \commdiag{&R^m\cr &\arrow(-1,-1)\lft{\bf B}\quad \arrow(1,-1)\rt{\bf G}\cr R^n&\mapright^{\bf P}&R^n\cr \mapdown\lft{e^{{\bf A}t}}&&\mapdown\rt{e^{{\bf F}t}}\cr R^n&\mapright^{\bf P}&R^n\cr &\arrow(1,-1)\lft{\bf C}\quad \arrow(-1,-1)\rt{\bf H}\cr &R^q\cr}$$ Other commutative diagram examples appear in the file `commdiags.tex', which is distributed with this package. In these examples the arrow lengths and line slopes were carefully chosen to blend with each other. In the first example, the default settings for the arrow lengths are used, but a direction for the arrow must be chosen. The ratio of the default horizontal and vertical arrow lengths is approximately the golden mean gamma=1.618...; the arrow direction closest to this mean is `(3,2)'. In the second example, a slope of -1/3 is desired and the default horizontal arrow length is 60 pt; therefore, choose a vertical arrow length of 20 pt. You may affect the interline glue settings of `\commdiag' by redefining the macro `\commdiagbaselines'. (cf. Exercise 18.46 of `The TeXbook' and the section on parameters below.) The width, height, and depth of all morphisms are hidden so that the morphisms' size do not affect arrow positions. This can cause a large morphism at the top or bottom of a diagram to impinge upon the text surrounding the diagram. To overcome this problem, use TeX's `\noalign' primitive to insert a `\vskip' immediately above or below the offending line, e.g., `$$\commdiag{\noalign{\vskip6pt}X&\mapright^\int&Y\cr ...}'. The macro `\commdiag' is too simple to be used for more complicated diagrams, which may have intersecting or overlapping arrows. A second approach, borrowed from Francis Borceux's `Diagram' macros for LaTeX, treats the commutative diagram like a grid of identically shaped boxes. To compose the commutative diagram, first draw an equally spaced grid, e.g., . . . . . . . . . . . . . . . . . . . . . . . . on a piece of scratch paper. Then draw each element (vertices and arrows) of the commutative diagram on this grid, centered at each grid point. Finally, use the macro `\gridcommdiag' to implement your design as a TeX alignment. For example, the cubic diagram (A commutative diagram appears here.) that appears in Francis Borceux's documentation can be implemented on a 7 by 7 grid, and is achieved with the code $$\harrowlength=48pt \varrowlength=48pt \sarrowlength=20pt \def\cross#1#2{\setbox0=\hbox{$#1$}% \hbox to\wd0{\hss\hbox{$#2$}\hss}\llap{\unhbox0}} \gridcommdiag{&&B&&\mapright^b&&D\cr &\arrow(1,1)\lft a&&&&\arrow(1,1)\lft d\cr A&&\cross{\hmorphposn=12pt\mapright^c}{\vmorphposn=-12pt\mapdown\lft f} &&C&&\mapdown\rt h\cr\cr \mapdown\lft e&&F&&\cross{\hmorphposn=-12pt\mapright_j} {\vmorphposn=12pt\mapdown\rt g}&&H\cr &\arrow(1,1)\lft i&&&&\arrow(1,1)\rt l\cr E&&\mapright_k&&G\cr}$$ The dimensions `\hgrid' and `\vgrid' control the horizontal and vertical spacing of the grid used by `\gridcommdiag'. The default setting for both of these dimensions is 15 pt. Note that in the example of the cube the arrow lengths must be adjusted so that the arrows overlap into neighboring boxes by the desired amount. Hence, the `\gridcommdiag' method, albeit more powerful, is less automatic than the simpler `\commdiag' method. Furthermore, the ad hoc macro `\cross' is introduced to allow the effect of overlapping arrows. Finally, note that the positions of four of the morphisms are adjusted by setting `\hmorphposn' and `\vmorphposn'. One is not restricted to a square grid. For example, the proof of Zassenhaus's Butterfly Lemma can be illustrated by the diagram (appearing in Lang's book `Algebra') (A commutative diagram appears here.) This diagram may be implemented on a 9 by 12 grid with an aspect ratio of 1/2, and is set with the code $$\hgrid=16pt \vgrid=8pt \sarrowlength=32pt \def\cross#1#2{\setbox0=\hbox{$#1$}% \hbox to\wd0{\hss\hbox{$#2$}\hss}\llap{\unhbox0}} \def\l#1{\llap{$#1$\hskip.5em}} \def\r#1{\rlap{\hskip.5em$#1$}} \gridcommdiag{&&U&&&&V\cr &&\bullet&&&&\bullet\cr &&\sarrowlength=16pt\sline(0,1)&&&&\sarrowlength=16pt\sline(0,1)\cr &&\l{u(U\cap V)}\bullet&&&&\bullet\r{(U\cap V)v}\cr &&&\sline(2,-1)&&\sline(2,1)\cr &&\cross{=}{\sline(0,1)}&&\bullet&&\cross{=}{\sline(0,1)}\cr\cr &&\l{^{\textstyle u(U\cap v)}}\bullet&&\cross{=}{\sline(0,1)}&& \bullet\r{^{\textstyle(u\cap V)v}}\cr &\sline(2,1)&&\sline(2,-1)&&\sline(2,1)&&\sline(2,-1)\cr \l{u}\bullet&&&&\bullet&&&&\bullet\r{v}\cr &\sline(2,-1)&&\sline(2,1)&&\sline(2,-1)&&\sline(2,1)\cr &&\bullet&&&&\bullet\cr &&u\cap V&&&&U\cap v\cr}$$ Again, the construction of this diagram requires careful choices for the arrow lengths and is facilitated by the introduction of the ad hoc macros `\cross', `\r', and `\l'. Note also that superscripts were used to adjust the position of the vertices u(U intersection v) and (u intersection V)v. Many diagrams may be typeset with the predefined macros that appear here; however, ingenuity is often required to handle special cases. File: eplain.info, Node: Commutative diagram parameters, Prev: Construction of commutative diagrams, Up: Commutative diagrams Commutative diagram parameters ------------------------------ The following is a list describing the parameters used in the commutative diagram macros. These dimensions may be changed globally or locally. `\harrowlength' (Default: 60 pt) The length of right or left arrows. `\varrowlength' (Default: 0.618`\harrowlength') The length of up or down arrows. `\sarrowlength' (Default: 60 pt) The horizontal length of slanted arrows. `\hmorphposn' (Default: 0 pt) The horizontal position of the morphism with respect to its default position. There are also the dimensions `\hmorphposnup', `\hmorphposndn', `\hmorphposnrt', and `\hmorphposnlft' for `^'/`_' or `\lft'/`\rt' constructions. `\vmorphposn' (Default: 0 pt) The vertical position of the morphism with respect to its default position. There are also the dimensions `\vmorphposnup', `\vmorphposndn', `\vmorphposnrt', and `\vmorphposnlft' for `^'/`_' or `\lft'/`\rt' constructions. `\morphdist' (Default: 4 pt) The distance of morphisms from slanted lines or arrows. `\channelwidth' (Default: 3 pt) The distance between double lines or arrows. `\hchannel, \vchannel' (Defaults: 0 pt) Overrides `\channelwidth'. The horizontal and vertical shifts between double lines or arrows. `\commdiagbaselines' (Default: `\baselineskip=15pt \lineskip=3pt \lineskiplimit=3pt ') The parameters used by `\commdiag' for setting interline glue. `\hgrid' (Default: 15 pt) The horizontal spacing of the grid used by `\gridcommdiag'. `\vgrid' (Default: 15 pt) The vertical spacing of the grid used by `\gridcommdiag'. File: eplain.info, Node: Programming definitions, Next: Copying, Prev: Arrow theoretic diagrams, Up: Top Programming definitions *********************** The definitions in this section are only likely to be useful when you are writing nontrivial macros, not when writing a document. * Menu: * Category codes:: Changing category codes. * Allocation macros:: Non-outer versions of \newcount et al. * Iteration:: Doing `for' loops in TeX. * Macro arguments:: Reading and ignoring them. * Converting to characters:: Normalizing control sequences and spaces. * Expansion:: Controlling expansion. * Obeying spaces:: Making whitespace count anywhere. * Writing out numbers:: Making `1' into `one'. * Mode-specific penalties:: * Auxiliary files:: Testing for their existence. File: eplain.info, Node: Category codes, Next: Allocation macros, Up: Programming definitions Category codes ============== Plain TeX defines `\active' (as the number 13) for use in changing category codes. Although the author of `The TeXbook' has "intentionally kept the category codes numeric", two other categories are commonly used: letters (category code 11) and others (12). Therefore, Eplain defines `\letter' and `\other'. Sometimes it is cleaner to make a character active without actually writing a `\catcode' command. The `\makeactive' command takes a character as an argument to make active (and ignores following spaces). For example, here are two commands which both make `\' active: \makeactive`\\ \makeactive92 Usually, when you give a definition to an active character, you have to do so inside a group where you temporarily make the character active, and then give it a global definition (cf. the definition of `\obeyspaces' in `The TeXbook'). This is inconvenient if you are writing a long macro, or if the character already has a global definition you do not wish to transcend. Eplain provides `\letreturn', which defines the usual end-of-line character to be the argument. For example: \def\mymacro{... \letreturn\myreturn ... } \mymacro hello there The end-of-line between `hello' and `there' causes `\myreturn' to be expanded. `The TeXbook' describes `\uncatcodespecials', which makes all characters which are normally "special" into "other" characters, but the definition never made it into plain TeX. Eplain therefore defines Finally, `\percentchar' expands into a literal `%' character. This is useful when you `\write' TeX output to a file, and want to avoid spurious spaces. For example, Eplain writes a `\percentchar' after the definition of cross-references. The macros `\lbracechar' and `\rbracechar' expand similarly.