MapleV Emacs Mode 2.37

MapleV

MapleV is a GNU Emacs major mode for developing source code for Maple, a computer algebra system (CAS) from Waterloo Maple Inc. MapleV is written entirely in Emacs-Lisp and is distributed under the GNU General Public License.

This manual is for MapleV version 2.37.

Copyright © 2011, Joseph S. Riel

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, with no Front-Cover texts, and with no Back-Cover Texts. A copy of the license is included in the section entitled “GNU Free Documentation License.”

Editing

Processes

Appendices

Indices

 — The Detailed Node Listing —

Introduction

Indentation

Indentation Tricks

Shortcuts

Abbreviations

Miscellaneous features

Configuration

Mint

Maple

Help pages

Viewing

Installation

Evolution

1 Introduction

1.1 Summary

Following is a brief tour of MapleV’s major features.

1.1.1 Indentation

Maple source code is grammatically indented, either as you enter it or all at once. Customizable variables permit a limited control of the indentation style. The default settings produce a result that is very close to the pretty printed output of Maple.

1.1.2 Font Lock

Maple reserved words, special words, initial variables, built-in functions, and top-level procedure assignments are font locked. Comments and quotes are syntactically highlighted. The amount of “decoration” can be customized.

1.1.3 Comments

Commands are provided for inserting and aligning Maple comments. Auto-filling can be enabled so that comments automatically wrap.

1.1.4 Shortcuts

Abbreviations for common Maple words are defined and automatically expanded, if enabled. A blank procedure template, including your copyright statement, can be inserted into the source. It queries for the name of the procedure, optional arguments, and a description.

1.1.5 Mint interface

All or portions of the buffer can be sent to mint, Maple’s syntax checker. The output is displayed in a buffer with a mode that highlights and activates warnings and error messages. Clicking on the activated text either moves the cursor to the appropriate point in the source code or queries to automatically correct the error.

1.1.6 Maple interface

All or portions of the buffer can be sent to the command line version of Maple, which is run in its own buffer. You can work directly in that buffer to exercise the source code.

1.1.7 Online help

Help pages from Maple help databases can be called up and displayed in a buffer. The buffer has a mode that font locks section headings and provides commands for viewing other help pages and recalling previously visited pages.

1.1.8 Viewing library code

Modules and procedures from Maple libraries can be displayed in a buffer. They are font-locked the same as in a MapleV buffer. A history provides a convenient means to return to previously displayed code.

1.2 Requirements

MapleV has been used with Maple version from 4 to 2015, with GNU Emacs 22 to 24, and on Linux, Mac, and Windows machines.

2 Basics

For MapleV to properly locate, fontify, and index top-level procedures, that is, non-nested procedure assignments, the procedure name must be flush left. Indenting the buffer moves top-level procedures to the left margin.

There are a few exceptional cases in which what should be top-level procedures are, in fact, not. The primary example is a Maple script in which procedures are conditionally assigned. See Preventing indentation, for an illustration and a method to automatically indent these procedures to the left column.

Most of the higher-level MapleV functions, those that do more than edit text, are available on the menu-bar.

3 Indentation

Maple source code is indented according to its grammar. The indentation can occur either as you enter the code or all at once; the latter action is useful when working with non-indented source code. A grammatical error, typically an out-of-place keyword or parenthesis, generates an error and moves the cursor to the place where the error was detected.

3.1 Commands

TAB

Indent the current line (maplev-electric-tab).

C-j

Indent the current line, insert a new line, and indent that line (maplev-indent-newline).

C-c TAB TAB

C-c TAB b

Indent the buffer (maplev-indent-buffer).

C-c TAB k

Clear the indentation information (maplev-indent-clear-info). To increase speed, MapleV’s indentation algorithm stores the last valid indentation point. Moving the point may occasionally cause indentation errors; use this procedure to recompute the indentation point.

C-c TAB p

Indent a procedure (maplev-indent-procedure). The smallest procedure, or module, at point is indented.

C-c TAB r

Indent the region (maplev-indent-region). The selected region is indented.

3.2 Customizing

The following variables affect indentation:

maplev-indent-level

The amount a subblock is indented. The default is 4.

maplev-indent-tabs-mode

Non-nil means tabs may be used to indent. The default is nil.

maplev-indent-declaration-level

This value is used to initialize the buffer-local variable maplev-indent-declaration, which sets the amount Maple procedure declarations (local, global, option, and description) are indented. The default is 0.

maplev-dont-indent-re

A regular expression or nil. If non-nil then lines that begin with a match are not indented. The default, ‘"#"’, prevents flush left comment lines from being indented.

maplev-tab-width

This integer value is used to initialize the value of tab-width.

maplev-get-tab-width-function

If assigned, this function is called, with the filename of the current buffer, when maplev-mode is executed. It should return the desired value of tab-width. If not assigned, maplev-tab-width is used as the value.

3.3 Indentation Tricks

The indentation algorithm is not perfect. It can fail to indent code that should be indented or it may indent code that should not be indented. The following sections give examples and demonstrate workarounds.

3.3.1 Forcing indentation

MapleV’s indentation algorithm does not (currently) handle continued expressions. It aligns continuations with the left most character in the preceding line. In an assignment it is preferable to align with the right side of the assignment.

Problem

Indenting the following code causes the continued line to be left aligned with the preceding line, as the following illustrates:

---------- Buffer: foo ----------
y := a + ( ... ) 
     + b;∗
---------- Buffer: foo ----------

TAB
   ⇒
---------- Buffer: foo ----------
y := a + ( ... ) 
+ b;∗
---------- Buffer: foo ----------        

Solution

Use extra parentheses to prevent the continuation line from being aligned with the opening column:

---------- Buffer: foo ----------
y := ( a + ( ... ) 
       + b );
---------- Buffer: foo ----------

3.3.2 Preventing indentation

Problem

Consider an installation script in which the procedures ‘foo1’ and ‘foo2’ are assigned only when the flag assign_procs is ‘true’. The following example shows what happens when the buffer is indented.

---------- Buffer: foo ----------
if assign_procs then
foo1 := proc() ... end:
foo2 := proc() ... end:
fi:
---------- Buffer: foo ----------

M-x maplev-indent-buffer
   ⇒
---------- Buffer: foo ----------
if assign_procs then
    foo1 := proc() ... end:
    foo2 := proc() ... end:
fi:
---------- Buffer: foo ----------

Because foo1 and foo2 are no longer flush left they are not recognized as top-level procedures. Their names are not properly font locked and MapleV commands that operate on top-level procedures do not work on them.

Solution

Because MapleV ignores comment continuations that Maple respects (Comments), we can use the following technique to prevent ‘foo1’ and ‘foo2’ from being indented.

---------- Buffer: foo ----------
if assign_procs then       #\
fi                         # Maple does not see this line
foo1 := proc() ... end:
foo2 := proc() ... end:
#\
if then                    # Maple does not see this line
fi:
---------- Buffer: foo ----------

MapleV ignores the comment continuations and determines that each if statement is completed on the following line. The procedures foo1 and foo2 are not indented. Maple, however, continues the comments and so matches the initial if to the final fi; it ignores the dummy statements.

3.4 Indentation Details

A grammar table (maplev--grammar-alist) defines the grammar used to indent Maple code.

MapleV parses the source to compute the appropriate indentation for each line. To speed this process, information from the last parse is saved and reused. This method allows it to indent entire buffers reasonably quickly; the largest file in the Maple R5 share library (gdev.mpl, 160K, by Bruno Salvy) took twelve seconds to indent on a PC running NTEmacs. During editing, if the buffer is modified above the last indentation location then the indentation information is lost; consequently, you may occasionally notice small delays as the source is reparsed.

4 Font Lock

The amount of syntactical highlighting, or “decoration”, is controlled by the global variable font-lock-maximum-decoration, which you may set in your .emacs file. See (emacs)Font Lock, for information. MapleV mode provides three levels of decoration:

1. Comments, quotes, top-level procedure names and Maple reserved works are highlighted.
2. Everything in level 1 plus Maple special words, initial variables, and the ditto operators are highlighted.
3. Everything in level 2 plus Maple built-in functions are highlighted.

Execute M-x maplev-reset-font-lock RET LEVEL RET or use the menubar, MapleV -> Setup -> Decoration, to change the decoration in a MapleV buffer. LEVEL is an integer from 1 to 3.

5 Comments

MapleV uses standard Emacs commands to enter, align and fill Maple comments. See (emacs)Comments. The commands are reproduced here for convenience.

M-;

Insert or align an inline comment (indent-for-comment). The comment character is inserted at column comment-column.

C-x ;

Set comment column (set-comment-column).

C-u - C-x ;

Kill comment on current line (kill-comment ).

M-q

Fill a comment (fill-paragraph). Wrap lines at column fill-column and insert new comment characters, aligned with the original comment character.

The following variables affect comments:

maplev-auto-fill-comment-flag

A boolean flag. If non-nil, the default, comment lines wrap as they are typed. Wrapping, however, does not automatically start in an inline comment; it must be invoked with fill-paragraph.

maplev-comment-string

String variable inserted by indent-for-comment. The default is ‘# ’.

maplev-comment-column

Initial value of comment-column. The default is 40.

maplev-comment-fill-column

Initial value of fill-column. The default is 79.

Maple comment lines can be continued to the next line by ending them with a backslash. MapleV does not recognize this continuation and interprets the following line as code. This can fool the MapleV indentation grammar; however, it can also be used to achieve certain effects. See Preventing indentation, for an example.

6 Shortcuts

6.1 Abbreviations

Abbreviations are available for common or lengthy Maple keywords. They are expanded whenever abbrev-mode is active. See (emacs)Abbrevs. The command maplev-abbrev-help displays a list of the available abbreviations.

The following variables affect the expansion of abbreviations:

maplev-initial-abbrev-mode-flag

If non-nil abbrev-mode is activated when MapleV is started. The default is ‘t’.

maplev-expand-abbrevs-in-comments-and-strings-flag

If non-nil then the Maple abbreviations are expanded in comments and strings. The default is ‘nil’.

6.1.1 Customizing Abbreviations

The predefined MapleV abbreviations are stored in the abbreviation table maplev-mode-abbrev-table. The following code may be added to your .emacs file to assign ‘simp’ as an abbreviation for ‘simplify’.

(define-abbrev maplev-mode-abbrev-table 
        "simp" "simplify" 'maplev--abbrev-hook)

The function ‘'maplev--abbrev-hook’ prevents the abbreviation from being expanded inside a comment or quote.

To remove an abbreviation from the table assign it nil. For example, to prevent ‘lib’ from expanding to ‘libname’, add the following to emacs:

(define-abbrev maplev-mode-abbrev-table "lib" nil nil)

6.2 Templates

C-c C-p

Insert a procedure template (maplev-template-proc). The user is queried for the name, arguments, and a description of the procedure. Any of the entries can be left blank. If the name is blank then an anonymous procedure is inserted, otherwise an assignment is inserted with the procedure assigned to the given name. Backquotes are added automatically to procedure names if required by Maple.

C-;

Insert an assignment operator at the end of the current line (maplev-insert-assignment-operator).

The following variables affect the shortcuts:

maplev-insert-copyright-flag

If non-nil then a copyright notice is inserted in the option declaration of the procedure template. The default is t.

maplev-copyright-owner

String inserted as the copyright owner.

maplev-comment-end-flag

If non-nil then the name of the procedure is inserted as a comment to the right of the closing end statement.

maplev-assignment-operator

The string inserted by maplev-insert-assignment-operator. The default value is ‘ := ’.

7 Imenu support

Executing maplev-add-imenu or selecting MapleV -> Add Index from the menubar creates an indexed menu of the top-level Maple procedures, global variables, and macro assignments. The menu appears under the ‘Index’ heading in the menubar. Clicking on an item in the menu moves point to the assignment of that item.

The assignments must be flush left to be indexed. Only the first macro in a macro assignment is indexed.

8 Miscellaneous features

8.1 Include statements

Maple include statements, such as $include <somefile>, are font-locked and active. Clicking on them, or typing C-c C-o, calls maplev-find-include-file-at-point, which searches for the file and, if successful, opens it. If the path exists, but the file does not, the user is asked whether to create the file.

The include path can be assigned, as a list of strings, to the variable maplev-include-path. The paths are searched in the order of occurrence in the list.

The customizable variable maplev-include-file-other-window-flag determines whether the file is opened in the current window or another window.

8.2 Indent trace output

The Maple trace command causes Maple to print the assignments that occur in selected procedures. The following commands can be used to hierarchically indent the resulting output in an Emacs buffer. To be sensible, the output should be created with interface(prettyprint=0).

maplev-trace-indent-buffer

Hierarchically indent all Maple trace output in the buffer.

maplev-trace-indent-region

Hierarchically indent selected region in the buffer.

maplev-trace-indent

Emacs variable that sets the indentation level for trace output. The default is four spaces.

9 Configuration

When Maplev-mode is called, a search is made for a .maplev file if the flag maplev-load-config-file-flag is non-nil. The search begins in default-directory, which is typically the directory associated with the current buffer, and moves upward through the file hierarchy, stopping when the file is found or root is reached. If the file is found, it is loaded as an Emacs lisp file.

The maplev-config function can be used in the .maplev file to create an object that configures MapleV on a per-project basis.

9.1 Configuration Object

The function maplev-config constructs an eieio object of class maplev-config-class and assigns it to the eponymous buffer-local variable maplev-config. For details about objects, see The EIEIO Manual. The following fields are defined.

:compile

Shell command to build and install a Maple archive. If assigned, the string is assigned to the Emacs lisp variable compile-command, which is then made buffer-local. Executing the Emacs function compile in a MapleV buffer that uses this configuration runs the assigned shell command. Typically assigned to a make command. See Configuration Example.

:include-path

A string or list of strings of directories to search for files specified with $include statements in Maple source files. Used by mint, Maple’s syntax checker, by hyperlinked $include statements, and by the mpldoc tester, see the :tester entry, below.

:maple

Shell command to execute tty (command-line) Maple. The default is ‘maple’. See Maple.

:mapledir

The path to the installation of Maple. If left nil, the default, this field is automatically assigned by the function maplev-config.

:maple-options

A string of options to pass to maple. The default is ‘-B -A2 -e2’. See the Maple help page for maple for a description of the available options.

:mint

Shell command to execute Mint, the Maple syntax-checker. The default is ‘mint’. See Mint.

:mint-options

A string of options to pass to mint. The default is ‘-i2 -q -v -w 100’. The use of the verbose option, ‘-v’, is necessary so that mint output for include files shows the path to the file; the information is used to jump to the source location of a mint warning. Maplesoft developers: be aware that smint use ‘-V’ for the verbose option. See the Maple help page for mint for a description of the available options.

:tester

Shell command to execute Maplesoft tester. Used by mpldoc-test-run-tester, which is part of the mpldoc package. See Testing in The Mpldoc Manual. Use of this requires access to Maplesoft’s tester facility.

:tester-options

A string of options to pass to tester. See above. The default is the empty string.

9.2 Configuration Example

Following is a typical example of the content of a .maplev file, for a Maple package/project named Bark.

(let ((proj-root (concat (getenv "HOME") "/maple/Bark")))
  (maplev-config
   :maple-options "-B -A2 -e2"  ; configure libname and error/warning levels of Maple 
   :mint-options "-l"           ; ignore leading underscore
   :include-path proj-root      ; add proj-root to the include path for Maple and Mint
   :compile (format "make -C %s mla-install" proj-root)))

The :compile value in this example is a shell command that passes the mla-install target to a project-specific Makefile. The associated rule in the Makefile presumably builds and installs the Maple library archive, Bark.mla.

10 Mint

Mint is Maple’s syntax checker. It analyzes a Maple program and produces a report about the syntax and variable usage. MapleV can run mint on the entire buffer or a portion of it. The output of mint is displayed in a buffer with a special mode, mint-mode, that provides a convenient means for locating and correcting syntax errors.

To allow Emacs to run mint, the :mint and :mint-options fields of maplev-config must be properly configured. See Configuration.

10.1 Running mint

The following commands send source code in the buffer to mint:

C-c RET b

Run mint on the buffer (mint-buffer).

C-c RET p

Run mint on the current procedure (mint-procedure).

C-c RET r

Run mint on the marked region (mint-region).

C-c RET RET

Rerun the previous mint command (mint-rerun).

These commands are available through the menubar, MapleV -> Mint. The following variables affect the output of mint:

mint-info-level

An integer from 0 to 4 that selects the amount of information displayed by mint. 0 displays no information, 4 displays the most. The default value is 3. This value can be set through the menubar, Maplev -> Mint -> Mint level.

mint-coding-system

Symbol that defines the coding system used by mint. The default value is undecided-dos.

10.2 Mint mode

Mint mode is applied to mint’s output buffer. Warnings and errors are font locked and activated. Moving the mouse pointer over active text highlights it; clicking it (mouse-1) either moves the cursor to the appropriate point in the source code or queries to automatically correct an error.

The following commands are available:

s

Incremental forward search (isearch-forward).

r

Incremental backward search (isearch-backward).

RET

Re-execute the previous mint command (mint-rerun).

DEL

Scroll down (scroll-down).

SPC

Scroll up (scroll-up).

mouse-1

Goto location in source, or fix error, depending on the active text.

The following variables set the display faces for the highlighted text in the mint buffer:

mint-proc-face

Face for procedure names.

mint-warning-face

Face for warnings.

mint-error-face

Face for errors.

mint-note-face

Face for notes (usually ‘on line’).

11 Maple

The command line version of Maple can be started in a buffer. All or portions of the code in the MapleV buffer can be passed directly to the Maple process. Maple commands can be directly executed in the buffer.

11.1 Running Maple

The following commands in the MapleV buffer affect the Maple engine:

C-c C-c b

Send the entire buffer to the Maple engine (cmaplev-send-buffer).

C-c C-c p

Send the current procedure to the Maple engine (cmaplev-send-procedure).

C-c C-c r

Send the marked region to the Maple engine (cmaplev-send-region).

C-c C-c g

Goto the Maple buffer (cmaplev-goto-buffer).

C-c C-c i

Interrupt the Maple engine (cmaplev-interrupt).

C-c C-c k

Kill the Maple engine (cmaplev-kill).

These commands are available through the menubar, MapleV -> Maple.

11.2 Cmaple mode

The command line version of Maple is run in a buffer with the mode cmaple-process-mode that is based on comint-mode. See (emacs)Shell Mode for more information. In addition to the normal comint commands, the following commands are available:

?

C-?

Display a Maple help topic (see Help pages).

M-?

Display a Maple expression (see Viewing).

12 Help pages

Help pages can be read from the Maple help databases and displayed in a buffer with major mode maplev-help-mode. Text in the buffer is highlighted and cross references are activated.

12.1 Displaying help pages

The following commands display Maple help pages:

C-?

Query for a help topic, using the word at point as a default. Display the help page in a buffer (maplev-help-at-point).

S-mouse-2

Display the Maple help page for the topic at the click (maplev-help-follow-mouse).

Help pages are displayed in a buffer with major mode maplev-help-mode.

12.2 MapleV help mode

The major mode maplev-help-mode is active in the buffer that displays Maple help pages. Section headers are font locked and text in the ‘See Also’ section is activated so that clicking on it opens the help page for the topic. The following commands are available:

s

Incremental forward search (isearch-forward).

p

Previous help topic (maplev-prev-item).

n

Next help topic (maplev-next-item).

P

Parent help topic (maplev-help-parent).

r

Redraw help page (maple-redo-item).

?

C-?

RTN

Query for a help topic (maplev-help-at-point).

M-?

Query for a procedure (maplev-proc-at-point).

SPC

Scroll down.

DEL

Scroll up.

MapleV help mode keeps a history of the help topics displayed. Use the command maplev-clear-history to erase the history.

The help page for a chosen topic is displayed by sending the string ‘?TOPIC’ to the Maple engine and capturing the output. If the Maple engine is busy an error message, ‘Maple busy’, is displayed in the message window.

13 Viewing

Maple code for modules and procedures stored in Maple libraries, or otherwise known to Maple, can be displayed in a buffer with major mode maplev-view-mode. The code is font-locked the same as in MapleV mode.

13.1 Displaying procedures

The following commands display Maple procedures:

M-?

Query for a procedure name, using the word at point as the default. Read the procedure from the Maple library and display it in a buffer (maplev-view-at-point).

M-S-mouse-2

Read the procedure at the click from the library and display it in a buffer (maplev-view-follow-point).

Procedures are displayed in a buffer with major mode maplev-view-mode.

13.2 MapleV view mode

The major mode maplev-view-mode is active in the buffer that displays Maple modules and procedures read from a Maple library. It font-locks the code, highlighting keywords the same as MapleV mode does. Clicking on a name in the buffer displays its source code or opens a help page for them. A history mechanism stores the previously displayed procedure.

The following commands are available:

s

Incremental forward search (isearch-forward).

p

Previous procedure (maplev-prev-item).

n

Next procedure (maplev-next-item).

r

Redraw procedure (maple-redo-item).

?

C-?

RTN

Query for a help topic (maplev-help-at-point).

M-?

Query for a procedure (maplev-view-at-point).

SPC

Scroll down.

DEL

Scroll up.

MapleV help mode keeps a history of the help topics displayed. Use the command maplev-clear-history to erase the history.

A procedure is read from a library and displayed by using the Maple procedure ‘maplev_print’ that is assigned when the Maple engine is started. If the Maple engine is busy an error message, ‘Maple busy’, is displayed in the message window.

Appendix A Installation

This section describes how to install MapleV into GNU Emacs.

A.1 Emacs Files

Install the Emacs lisp files, those with extension .el, into the directory ~/.emacs.d/maple. The tilde, ~, corresponds to your home directory.

Byte-compile them from Emacs with the command

C-u 0 M-x byte-recompile-directory RET ~/emacs.d/maple RET

Add the following line to your .emacs file

(add-to-list 'load-path (concat user-emacs-directory "maple"))
(autoload 'maplev-mode "maplev" "Maple editing mode" 'interactive)

To have Emacs auto-magically start in MapleV mode when editing Maple source, add the following to your .emacs file, modifying the regular expression as needed.

(setq auto-mode-alist 
      (cons `("\\.mpl\\'" . maplev-mode) auto-mode-alist))

A.2 Maple Files

A Maple archive file, maplev.mla, containing code used by maplev-view, is provided with the distribution. If desired it can be rebuilt from source by removing the existing file and executing

maple maple/maplev.mpl

The file maplev.mla should be installed at ~/maple/toolbox/emacs/lib.

A.3 Customizing

Some of MapleV’s default settings must be customized for your installation. Most significantly, you must specify the locations of the executable files for mint and maple, the command-line version of Maple. Multiple versions of mint and maple can be assigned and selected. The easiest method is to invoke customize using the following commands:

M-x load-library RET maplev RET
M-x customize-group RET maplev RET

Select the MapleV Executables subgroup and customize maplev-executable-alist. It is a list of sublists. Each sublist contains four items: an identifier, the path to the Maple tty executable, the path to the a Maple initialization file, and the path to the mint executable. An example of a sublist is

("maple17" "/usr/local/maple17/bin/maple" nil "/usr/local/maple17/bin/mint")

The identifier is arbitrary. To determine the name and path to the maple and mint executables, launch maple and execute kernelopts(mapledir), that returns the directory in which Maple is installed.

On Linux or Mac, the shell commands are locate in the bin subdirectory of the installed directory and are named maple and mint.

On Windows the shell commands are usually in the bin.wnt subdirectory of the installed directory and are named cmapleXXXX.exe and mintXXXX.exe, where XXXX is the Maple release. When entering the path to the binaries, use forward slashes (/) as the directory separators.

After setting the values, click the ‘Apply and Save’ button.

A.4 Info documentation

Install the included maplev.info file to a directory in the Info load path and then edit the dir to point to it. I add the following menu item to my dir file:

* MapleV: (maplev).       MapleV reference manual.

Appendix B Evolution

B.1 Bugs

If you encounter a bug in this package, wish to suggest an enhancement, or want to make a smart remark, then send an email to me:

Joseph S. Riel (Joe Riel) jriel@maplesoft.com

B.2 Acknowledgements

I’d like to thank a number of people who have contributed, either directly or indirectly, to this package.

Bruno Salvy

For writing maple-mode, a small but useful Emacs mode for editing Maple code.

Michael Smith

For writing Gap-mode and Gap-process. These gave me the idea, and showed me how, to display help pages. Displaying source code from the Maple libraries was a natural extension. Gap is a CAS specialized for group theory.

Nicholas Thiéry

For writing Maple-mode, another Emacs mode for editing Maple code. It introduced the idea of using a grammar to indent Maple source code.

Bob Glickstein

For writing Writing GNU Emacs Extensions. It allowed me, a novice Elisp programmer, to put it all together.

Christian Pomar

For courageously agreeing to test a series of alpha versions of this package. He found numerous errors and suggested many improvements.

Erik Postma

For providing useful feedback and suggested enhancements.

Key Index

Function Index

Variable Index

Concept Index

Appendix C GNU Free Documentation License

Copyright © 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc.
http://fsf.org/

Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.

1. PREAMBLE

   The purpose of this License is to make a manual, textbook, or other functional and useful document free in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others.

   This License is a kind of “copyleft”, which means that derivative works of the document must themselves be free in the same sense. It complements the GNU General Public License, which is a copyleft license designed for free software.

   We have designed this License in order to use it for manuals for free software, because free software needs free documentation: a free program should come with manuals providing the same freedoms that the software does. But this License is not limited to software manuals; it can be used for any textual work, regardless of subject matter or whether it is published as a printed book. We recommend this License principally for works whose purpose is instruction or reference.

2. APPLICABILITY AND DEFINITIONS

   This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions stated herein. The “Document”, below, refers to any such manual or work. Any member of the public is a licensee, and is addressed as “you”. You accept the license if you copy, modify or distribute the work in a way requiring permission under copyright law.

   A “Modified Version” of the Document means any work containing the Document or a portion of it, either copied verbatim, or with modifications and/or translated into another language.

   A “Secondary Section” is a named appendix or a front-matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document’s overall subject (or to related matters) and contains nothing that could fall directly within that overall subject. (Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain any mathematics.) The relationship could be a matter of historical connection with the subject or with related matters, or of legal, commercial, philosophical, ethical or political position regarding them.

   The “Invariant Sections” are certain Secondary Sections whose titles are designated, as being those of Invariant Sections, in the notice that says that the Document is released under this License. If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant. The Document may contain zero Invariant Sections. If the Document does not identify any Invariant Sections then there are none.

   The “Cover Texts” are certain short passages of text that are listed, as Front-Cover Texts or Back-Cover Texts, in the notice that says that the Document is released under this License. A Front-Cover Text may be at most 5 words, and a Back-Cover Text may be at most 25 words.

   A “Transparent” copy of the Document means a machine-readable copy, represented in a format whose specification is available to the general public, that is suitable for revising the document straightforwardly with generic text editors or (for images composed of pixels) generic paint programs or (for drawings) some widely available drawing editor, and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters. A copy made in an otherwise Transparent file format whose markup, or absence of markup, has been arranged to thwart or discourage subsequent modification by readers is not Transparent. An image format is not Transparent if used for any substantial amount of text. A copy that is not “Transparent” is called “Opaque”.

   Examples of suitable formats for Transparent copies include plain ASCII without markup, Texinfo input format, LaTeX input format, SGML or XML using a publicly available DTD, and standard-conforming simple HTML, PostScript or PDF designed for human modification. Examples of transparent image formats include PNG, XCF and JPG. Opaque formats include proprietary formats that can be read and edited only by proprietary word processors, SGML or XML for which the DTD and/or processing tools are not generally available, and the machine-generated HTML, PostScript or PDF produced by some word processors for output purposes only.

   The “Title Page” means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License requires to appear in the title page. For works in formats which do not have any title page as such, “Title Page” means the text near the most prominent appearance of the work’s title, preceding the beginning of the body of the text.

   The “publisher” means any person or entity that distributes copies of the Document to the public.

   A section “Entitled XYZ” means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language. (Here XYZ stands for a specific section name mentioned below, such as “Acknowledgements”, “Dedications”, “Endorsements”, or “History”.) To “Preserve the Title” of such a section when you modify the Document means that it remains a section “Entitled XYZ” according to this definition.

   The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document. These Warranty Disclaimers are considered to be included by reference in this License, but only as regards disclaiming warranties: any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License.

3. VERBATIM COPYING

   You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices, and the license notice saying this License applies to the Document are reproduced in all copies, and that you add no other conditions whatsoever to those of this License. You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute. However, you may accept compensation in exchange for copies. If you distribute a large enough number of copies you must also follow the conditions in section 3.

   You may also lend copies, under the same conditions stated above, and you may publicly display copies.

4. COPYING IN QUANTITY

   If you publish printed copies (or copies in media that commonly have printed covers) of the Document, numbering more than 100, and the Document’s license notice requires Cover Texts, you must enclose the copies in covers that carry, clearly and legibly, all these Cover Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on the back cover. Both covers must also clearly and legibly identify you as the publisher of these copies. The front cover must present the full title with all words of the title equally prominent and visible. You may add other material on the covers in addition. Copying with changes limited to the covers, as long as they preserve the title of the Document and satisfy these conditions, can be treated as verbatim copying in other respects.

   If the required texts for either cover are too voluminous to fit legibly, you should put the first ones listed (as many as fit reasonably) on the actual cover, and continue the rest onto adjacent pages.

   If you publish or distribute Opaque copies of the Document numbering more than 100, you must either include a machine-readable Transparent copy along with each Opaque copy, or state in or with each Opaque copy a computer-network location from which the general network-using public has access to download using public-standard network protocols a complete Transparent copy of the Document, free of added material. If you use the latter option, you must take reasonably prudent steps, when you begin distribution of Opaque copies in quantity, to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy (directly or through your agents or retailers) of that edition to the public.

   It is requested, but not required, that you contact the authors of the Document well before redistributing any large number of copies, to give them a chance to provide you with an updated version of the Document.

5. MODIFICATIONS

   You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified Version under precisely this License, with the Modified Version filling the role of the Document, thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it. In addition, you must do these things in the Modified Version:

   1. Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, and from those of previous versions (which should, if there were any, be listed in the History section of the Document). You may use the same title as a previous version if the original publisher of that version gives permission.
   2. List on the Title Page, as authors, one or more persons or entities responsible for authorship of the modifications in the Modified Version, together with at least five of the principal authors of the Document (all of its principal authors, if it has fewer than five), unless they release you from this requirement.
   3. State on the Title page the name of the publisher of the Modified Version, as the publisher.
   4. Preserve all the copyright notices of the Document.
   5. Add an appropriate copyright notice for your modifications adjacent to the other copyright notices.
   6. Include, immediately after the copyright notices, a license notice giving the public permission to use the Modified Version under the terms of this License, in the form shown in the Addendum below.
   7. Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document’s license notice.
   8. Include an unaltered copy of this License.
   9. Preserve the section Entitled “History”, Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the Modified Version as given on the Title Page. If there is no section Entitled “History” in the Document, create one stating the title, year, authors, and publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence.
   10. Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network locations given in the Document for previous versions it was based on. These may be placed in the “History” section. You may omit a network location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives permission.
   11. For any section Entitled “Acknowledgements” or “Dedications”, Preserve the Title of the section, and preserve in the section all the substance and tone of each of the contributor acknowledgements and/or dedications given therein.
   12. Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered part of the section titles.
   13. Delete any section Entitled “Endorsements”. Such a section may not be included in the Modified Version.
   14. Do not retitle any existing section to be Entitled “Endorsements” or to conflict in title with any Invariant Section.
   15. Preserve any Warranty Disclaimers.

   If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the Modified Version’s license notice. These titles must be distinct from any other section titles.

   You may add a section Entitled “Endorsements”, provided it contains nothing but endorsements of your Modified Version by various parties—for example, statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard.

   You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the old one.

   The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version.

6. COMBINING DOCUMENTS

   You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers.

   The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work.

   In the combination, you must combine any sections Entitled “History” in the various original documents, forming one section Entitled “History”; likewise combine any sections Entitled “Acknowledgements”, and any sections Entitled “Dedications”. You must delete all sections Entitled “Endorsements.”

7. COLLECTIONS OF DOCUMENTS

   You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects.

   You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document.

8. AGGREGATION WITH INDEPENDENT WORKS

   A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an “aggregate” if the copyright resulting from the compilation is not used to limit the legal rights of the compilation’s users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document.

   If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document’s Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate.

9. TRANSLATION

   Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail.

   If a section in the Document is Entitled “Acknowledgements”, “Dedications”, or “History”, the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title.

10. TERMINATION

    You may not copy, modify, sublicense, or distribute the Document except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense, or distribute it is void, and will automatically terminate your rights under this License.

    However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation.

    Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice.

    Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, receipt of a copy of some or all of the same material does not give you any rights to use it.

11. FUTURE REVISIONS OF THIS LICENSE

    The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See http://www.gnu.org/copyleft/.

    Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License “or any later version” applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation. If the Document specifies that a proxy can decide which future versions of this License can be used, that proxy’s public statement of acceptance of a version permanently authorizes you to choose that version for the Document.

12. RELICENSING

    “Massive Multiauthor Collaboration Site” (or “MMC Site”) means any World Wide Web server that publishes copyrightable works and also provides prominent facilities for anybody to edit those works. A public wiki that anybody can edit is an example of such a server. A “Massive Multiauthor Collaboration” (or “MMC”) contained in the site means any set of copyrightable works thus published on the MMC site.

    “CC-BY-SA” means the Creative Commons Attribution-Share Alike 3.0 license published by Creative Commons Corporation, a not-for-profit corporation with a principal place of business in San Francisco, California, as well as future copyleft versions of that license published by that same organization.

    “Incorporate” means to publish or republish a Document, in whole or in part, as part of another Document.

    An MMC is “eligible for relicensing” if it is licensed under this License, and if all works that were first published under this License somewhere other than this MMC, and subsequently incorporated in whole or in part into the MMC, (1) had no cover texts or invariant sections, and (2) were thus incorporated prior to November 1, 2008.

    The operator of an MMC Site may republish an MMC contained in the site under CC-BY-SA on the same site at any time before August 1, 2009, provided the MMC is eligible for relicensing.

ADDENDUM: How to use this License for your documents

To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page:

  Copyright (C)  year  your name.
  Permission is granted to copy, distribute and/or modify this document
  under the terms of the GNU Free Documentation License, Version 1.3
  or any later version published by the Free Software Foundation;
  with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
  Texts.  A copy of the license is included in the section entitled ``GNU
  Free Documentation License''.

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the “with…Texts.” line with this:

    with the Invariant Sections being list their titles, with
    the Front-Cover Texts being list, and with the Back-Cover Texts
    being list.

If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.

If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.

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