SES: Simple Emacs Spreadsheet

     SES is a major mode for GNU Emacs to edit spreadsheet files, which
     contain a rectangular grid of cells.  The cells' values are specified
     by formulas that can refer to the values of other cells.

To report bugs, use M-x report-emacs-bug.

This file documents SES: the Simple Emacs Spreadsheet.

Copyright © 2002–2014 Free Software Foundation, Inc.

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 the Front-Cover Texts being “A GNU Manual,” and with the Back-Cover Texts as in (a) below. A copy of the license is included in the section entitled “GNU Free Documentation License.”

(a) The FSF's Back-Cover Text is: “You have the freedom to copy and modify this GNU manual.”

Sales Pitch Why use SES?
Quick Tutorial A quick introduction
The Basics Basic spreadsheet commands
Advanced Features Want to know more?
For Gurus Want to know even more?
Index Concept, Function and Variable Index
Acknowledgments Acknowledgments
GNU Free Documentation License The license for this documentation.

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1 Sales Pitch

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2 Quick Tutorial

If you want to get started quickly and think that you know what to expect from a simple spreadsheet, this chapter may be all that you need.

First, visit a new file with the .ses extension. Emacs presents you with an empty spreadsheet containing a single cell.

Begin by inserting a headline: "Income"<RET>. The double quotes indicate that this is a text cell. (Notice that Emacs automatically inserts the closing quotation mark.)

To insert your first income value, you must first resize the spreadsheet. Press <TAB> to add a new cell and navigate back up to it. Enter a number, such as ‘2.23’. Then proceed to add a few more income entries, e.g.:

     A
      Income
        2.23
        0.02
       15.76
       -4.00

To add up the values, enter a Lisp expression:

     (+ A2 A3 A4 A5)

Perhaps you want to add a cell to the right of cell A4 to explain why you have a negative entry. Pressing TAB in that cell adds an entire new column ‘B’, where you can add such a note.

The column is fairly narrow by default, but pressing w allows you to resize it as needed. Make it 20 characters wide. You can now add descriptive legends for all the entries, e.g.:

     A       B
      Income
        2.23       Consulting fee
        0.02     Informed opinion
       15.76       Lemonade stand
          -4          Loan to Joe
       14.01                Total

By default, the labels in column B are right-justified. To change that, you can enter a printer function for the whole column, using e.g., M-p ("%s"). You can override a column's printer function in any individual cell using p.

If Joe pays back his loan, you might blank that entry; e.g., by positioning the cursor in cell A5 and pressing C-d twice. If you do that, the total cell will display ‘######’. That is because the regular + operator does not handle a range that contains some empty cells. Instead of emptying the cell, you could enter a literal ‘0’, or delete the entire row using C-k. An alternative is to use the special function ses+ instead of the regular +:

     (ses+ A2 A3 A4 A5)

To make a formula robust against changes in the spreadsheet geometry, you can use the ses-range macro to refer to a range of cells by the end-points, e.g.:

     (apply 'ses+ (ses-range A2 A5))

(The apply is necessary because ses-range produces a list of values. This allows for more complex possibilities.)

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3 The Basics

To create a new spreadsheet, visit a nonexistent file whose name ends with ".ses". For example, C-x C-f test.ses RET.

A cell identifier is a symbol with a column letter and a row number. Cell B7 is the 2nd column of the 7th row. For very wide spreadsheets, there are two column letters: cell AB7 is the 28th column of the 7th row. Super wide spreadsheets get AAA1, etc. You move around with the regular Emacs movement commands.

j
Moves point to cell, specified by identifier (ses-jump).

Point is always at the left edge of a cell, or at the empty endline. When mark is inactive, the current cell is underlined. When mark is active, the range is the highlighted rectangle of cells (SES always uses transient mark mode). Drag the mouse from A1 to A3 to create the range A1-A2. Many SES commands operate only on single cells, not ranges.

C-<SPC>
C-@
Set mark at point (set-mark-command).
C-g
Turn off the mark (keyboard-quit).
M-h
Highlight current row (ses-mark-row).
S-M-h
Highlight current column (ses-mark-column).
C-x h
Highlight all cells (mark-whole-buffer).

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3.1 Cell formulas

To insert a value into a cell, simply type a numeric expression, ‘"double-quoted text"’, or a Lisp expression.

0..9
Self-insert a digit (ses-read-cell).
-
Self-insert a negative number (ses-read-cell).
.
Self-insert a fractional number (ses-read-cell).
"
Self-insert a quoted string. The ending double-quote is inserted for you (ses-read-cell).
(
Self-insert an expression. The right-parenthesis is inserted for you (ses-read-cell). To access another cell's value, just use its identifier in your expression. Whenever the other cell is changed, this cell's formula will be reevaluated. While typing in the expression, you can use M-<TAB> to complete symbol names.
' (apostrophe)
Enter a symbol (ses-read-symbol). SES remembers all symbols that have been used as formulas, so you can type just the beginning of a symbol and use <SPC>, <TAB>, and ? to complete it.

To enter something else (e.g., a vector), begin with a digit, then erase the digit and type whatever you want.

RET
Edit the existing formula in the current cell (ses-edit-cell).
C-c C-c
Force recalculation of the current cell or range (ses-recalculate-cell).
C-c C-l
Recalculate the entire spreadsheet (ses-recalculate-all).

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3.2 Resizing the spreadsheet

Basic commands:

C-o
(ses-insert-row)
M-o
(ses-insert-column)
C-k
(ses-delete-row)
M-k
(ses-delete-column)
w
(ses-set-column-width)
TAB
Moves point to the next rightward cell, or inserts a new column if already at last cell on line, or inserts a new row if at endline (ses-forward-or-insert).
C-j
Linefeed inserts below the current row and moves to column A (ses-append-row-jump-first-column).

Resizing the spreadsheet (unless you're just changing a column width) relocates all the cell-references in formulas so they still refer to the same cells. If a formula mentioned B1 and you insert a new first row, the formula will now mention B2.

If you delete a cell that a formula refers to, the cell-symbol is deleted from the formula, so (+ A1 B1 C1) after deleting the third column becomes (+ A1 B1). In case this is not what you wanted:

C-_
C-x u
Undo previous action ((undo)).

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3.3 Printer functions

Printer functions convert binary cell values into the print forms that Emacs will display on the screen.

A printer can be a format string, like ‘"$%.2f"’. The result string is right-aligned within the print cell. To get left-alignment, use parentheses: ‘("$%.2f")’. A printer can also be a one-argument function (a symbol or a lambda), whose result is a string (right-aligned) or list of one string (left-aligned). While typing in a lambda, you can use M-<TAB> to complete the names of symbols.

Each cell has a printer. If nil, the column-printer for the cell's column is used. If that is also nil, the default-printer for the spreadsheet is used.

p
Enter a printer for current cell or range (ses-read-cell-printer).
M-p
Enter a printer for the current column (ses-read-column-printer).
C-c C-p
Enter the default printer for the spreadsheet (ses-read-default-printer).

The ses-read-XXX-printer commands have their own minibuffer history, which is preloaded with the set of all printers used in this spreadsheet, plus the standard printers.

The standard printers are suitable only for cells, not columns or default, because they format the value using the column-printer (or default-printer if nil) and then center the result:

ses-center
Just centering.
ses-center-span
Centering with spill-over to following blank cells.
ses-dashfill
Centering using dashes (-) instead of spaces.
ses-dashfill-span
Centering with dashes and spill-over.
ses-tildefill-span
Centering with tildes (~) and spill-over.

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3.4 Clearing cells

These commands set both formula and printer to nil:

DEL
Clear cell and move left (ses-clear-cell-backward).
C-d
Clear cell and move right (ses-clear-cell-forward).

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3.5 Copy, cut, and paste

The copy functions work on rectangular regions of cells. You can paste the copies into non-SES buffers to export the print text.

M-w
[copy]
[C-insert]
Copy the highlighted cells to kill ring and primary clipboard (kill-ring-save).
[drag-mouse-1]
Mark a region and copy it to kill ring and primary clipboard (mouse-set-region).
[M-drag-mouse-1]
Mark a region and copy it to kill ring and secondary clipboard (mouse-set-secondary).
C-w
[cut]
[S-delete]
The cut functions do not actually delete rows or columns—they copy and then clear (ses-kill-override).
C-y
[S-insert]
Paste from kill ring (yank). The paste functions behave differently depending on the format of the text being inserted:
  • When pasting cells that were cut from a SES buffer, the print text is ignored and only the attached formula and printer are inserted; cell references in the formula are relocated unless you use C-u.
  • The pasted text overwrites a rectangle of cells whose top left corner is the current cell. If part of the rectangle is beyond the edges of the spreadsheet, you must confirm the increase in spreadsheet size.
  • Non-SES text is usually inserted as a replacement formula for the current cell. If the formula would be a symbol, it's treated as a string unless you use C-u. Pasted formulas with syntax errors are always treated as strings.

[paste]
Paste from primary clipboard or kill ring (clipboard-yank).
[mouse-2]
Set point and paste from primary clipboard (mouse-yank-at-click).
[M-mouse-2]
Set point and paste from secondary clipboard (mouse-yank-secondary).
M-y
Immediately after a paste, you can replace the text with a preceding element from the kill ring (ses-yank-pop). Unlike the standard Emacs yank-pop, the SES version uses undo to delete the old yank. This doesn't make any difference?

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3.6 Customizing SES

By default, a newly-created spreadsheet has 1 row and 1 column. The column width is 7 and the default printer is ‘"%.7g"’. Each of these can be customized. Look in group “ses”.

After entering a cell value, point normally moves right to the next cell. You can customize ses-after-entry-functions to move left or up or down. For diagonal movement, select two functions from the list.

ses-mode-hook is a normal mode hook (list of functions to execute when starting SES mode for a buffer).

The variable safe-functions is a list of possibly-unsafe functions to be treated as safe when analyzing formulas and printers. See Virus protection. Before customizing safe-functions, think about how much you trust the person who's suggesting this change. The value t turns off all anti-virus protection. A list-of-functions value might enable a “gee whiz” spreadsheet, but it also creates trapdoors in your anti-virus armor. In order for virus protection to work, you must always press n when presented with a virus warning, unless you understand what the questionable code is trying to do. Do not listen to those who tell you to customize enable-local-eval—this variable is for people who don't wear safety belts!

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4 Advanced Features

C-c M-C-h
(ses-set-header-row). The header line at the top of the SES window normally shows the column letter for each column. You can set it to show a copy of some row, such as a row of column titles, so that row will always be visible. Default is to set the current row as the header; use C-u to prompt for header row. Set the header to row 0 to show column letters again.
[header-line mouse-3]
Pops up a menu to set the current row as the header, or revert to column letters.
M-x ses-rename-cell
Rename a cell from a standard A1-like name to any string.
M-x ses-repair-cell-reference-all
When you interrupt a cell formula update by clicking C-g, then the cell reference link may be broken, which will jeopardize automatic cell update when any other cell on which it depends is changed. To repair that use function ses-repair-cell-reference-all

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4.1 The print area

A SES file consists of a print area and a data area. Normally the buffer is narrowed to show only the print area. The print area is read-only except for special SES commands; it contains cell values formatted by printer functions. The data area records the formula and printer functions, etc.

C-x n w
Show print and data areas (widen).
C-c C-n
Show only print area (ses-renarrow-buffer).
S-C-l
M-C-l
Recreate print area by reevaluating printer functions for all cells (ses-reprint-all).

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4.2 Ranges in formulas

A formula like

     (+ A1 A2 A3)

is the sum of three specific cells. If you insert a new second row, the formula becomes

     (+ A1 A3 A4)

and the new row is not included in the sum.

The macro (ses-range from to) evaluates to a list of the values in a rectangle of cells. If your formula is

     (apply '+ (ses-range A1 A3))

and you insert a new second row, it becomes

     (apply '+ (ses-range A1 A4))

and the new row is included in the sum.

While entering or editing a formula in the minibuffer, you can select a range in the spreadsheet (using mouse or keyboard), then paste a representation of that range into your formula. Suppose you select A1-C1:

[S-mouse-3]
Inserts "A1 B1 C1" (ses-insert-range-click)
C-c C-r
Keyboard version (ses-insert-range).
[C-S-mouse-3]
Inserts "(ses-range A1 C1)" (ses-insert-ses-range-click).
C-c C-s
Keyboard version (ses-insert-ses-range).

If you delete the from or to cell for a range, the nearest still-existing cell is used instead. If you delete the entire range, the formula relocator will delete the ses-range from the formula.

If you insert a new row just beyond the end of a one-column range, or a new column just beyond a one-row range, the new cell is included in the range. New cells inserted just before a range are not included.

Flags can be added to ses-range immediately after the to cell.

!
Empty cells in range can be removed by adding the ! flag. An empty cell is a cell the value of which is one of symbols nil or *skip*. For instance (ses-range A1 A4 !) will do the same as (list A1 A3) when cells A2 and A4 are empty.
_
Empty cell values are replaced by the argument following flag _, or 0 when flag _ is last in argument list. For instance (ses-range A1 A4 _ "empty") will do the same as (list A1 "empty" A3 "empty") when cells A2 and A4 are empty. Similarly, (ses-range A1 A4 _ ) will do the same as (list A1 0 A3 0).
>v
When order matters, list cells by reading cells row-wise from top left to bottom right. This flag is provided for completeness only as it is the default reading order.
<v
List cells by reading cells row-wise from top right to bottom left.
v>
List cells by reading cells column-wise from top left to bottom right.
v<
List cells by reading cells column-wise from top right to bottom left.
v
A short hand for v>.
^
A short hand for ^>.
>
A short hand for >v.
<
A short hand for >^.
*
Instead of listing cells, it makes a Calc vector or matrix of it (see Top). If the range contains only one row or one column a vector is made, otherwise a matrix is made.
*2
Same as * except that a matrix is always made even when there is only one row or column in the range.
*1
Same as * except that a vector is always made even when there is only one row or column in the range, that is to say the corresponding matrix is flattened.

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4.3 Sorting by column

C-c M-C-s
Sort the cells of a range using one of the columns (ses-sort-column). The rows (or partial rows if the range doesn't include all columns) are rearranged so the chosen column will be in order.
[header-line mouse-2]
The easiest way to sort is to click mouse-2 on the chosen column's header row (ses-sort-column-click).

The sort comparison uses string<, which works well for right-justified numbers and left-justified strings.

With prefix arg, sort is in descending order.

Rows are moved one at a time, with relocation of formulas. This works well if formulas refer to other cells in their row, not so well for formulas that refer to other rows in the range or to cells outside the range.

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4.4 Standard formula functions

Oftentimes you want a calculation to exclude the blank cells. Here are some useful functions to call from your formulas:

(ses-delete-blanks &rest args)
Returns a list from which all blank cells (value is either nil or '*skip*) have been deleted.
(ses+ &rest args)
Sum of non-blank arguments.
(ses-average list)
Average of non-blank elements in list. Here the list is passed as a single argument, since you'll probably use it with ses-range.

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4.5 More on cell printing

Special cell values:

If the result from the printer function is too wide for the cell and the following cell is nil, the result will spill over into the following cell. Very wide results can spill over several cells. If the result is too wide for the available space (up to the end of the row or the next non-nil cell), the result is truncated if the cell's value is a string, or replaced with hash marks otherwise.

SES could get confused by printer results that contain newlines or tabs, so these are replaced with question marks.

t
Confine a cell to its own column (ses-truncate-cell). This allows you to move point to a rightward cell that would otherwise be covered by a spill-over. If you don't change the rightward cell, the confined cell will spill over again the next time it is reprinted.
c
When applied to a single cell, this command displays in the echo area any formula error or printer error that occurred during recalculation/reprinting (ses-recalculate-cell). You can use this to undo the effect of t.

When a printer function signals an error, the fallback printer ‘"%s"’ is substituted. This is useful when your column printer is numeric-only and you use a string as a cell value. Note that the standard default printer is “%.7g” which is numeric-only, so cells that are empty of contain strings will use the fallback printer. c on such cells will display “Format specifier doesn't match argument type”.

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4.6 Import and export

x t
Export a range of cells as tab-separated values (ses-export-tsv).
x T
Export a range of cells as tab-separated formulas (ses-export-tsf).

The exported text goes to the kill ring; you can paste it into another buffer. Columns are separated by tabs, rows by newlines.

To import text, use any of the yank commands where the text to paste contains tabs and/or newlines. Imported formulas are not relocated.

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4.7 Virus protection

Whenever a formula or printer is read from a file or is pasted into the spreadsheet, it receives a “needs safety check” marking. Later, when the formula or printer is evaluated for the first time, it is checked for safety using the unsafep predicate; if found to be “possibly unsafe”, the questionable formula or printer is displayed and you must press Y to approve it or N to use a substitute. The substitute always signals an error.

Formulas or printers that you type in are checked immediately for safety. If found to be possibly unsafe and you press N to disapprove, the action is canceled and the old formula or printer will remain.

Besides viruses (which try to copy themselves to other files), unsafep can also detect all other kinds of Trojan horses, such as spreadsheets that delete files, send email, flood Web sites, alter your Emacs settings, etc.

Generally, spreadsheet formulas and printers are simple things that don't need to do any fancy computing, so all potentially-dangerous parts of the Emacs Lisp environment can be excluded without cramping your style as a formula-writer. See the documentation in unsafep.el for more info on how Lisp forms are classified as safe or unsafe.

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4.8 Spreadsheets with details and summary

A common organization for spreadsheets is to have a bunch of “detail” rows, each perhaps describing a transaction, and then a set of “summary” rows that each show reduced data for some subset of the details. SES supports this organization via the ses-select function.

(ses-select fromrange test torange)
Returns a subset of torange. For each member in fromrange that is equal to test, the corresponding member of torange is included in the result.

Example of use:

     (ses-average (ses-select (ses-range A1 A5) 'Smith (ses-range B1 B5)))

This computes the average of the B column values for those rows whose A column value is the symbol 'Smith.

Arguably one could specify only fromrange plus to-row-offset and to-column-offset. The torange is stated explicitly to ensure that the formula will be recalculated if any cell in either range is changed.

File etc/ses-example.el in the Emacs distribution is an example of a details-and-summary spreadsheet.

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5 For Gurus

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5.1 Deferred updates

To save time by avoiding redundant computations, cells that need recalculation due to changes in other cells are added to a set. At the end of the command, each cell in the set is recalculated once. This can create a new set of cells that need recalculation. The process is repeated until either the set is empty or it stops changing (due to circular references among the cells). In extreme cases, you might see progress messages of the form “Recalculating... (nnn cells left)”. If you interrupt the calculation using C-g, the spreadsheet will be left in an inconsistent state, so use C-_ or C-c C-l to fix it.

To save even more time by avoiding redundant writes, cells that have changes are added to a set instead of being written immediately to the data area. Each cell in the set is written once, at the end of the command. If you change vast quantities of cells, you might see a progress message of the form “Writing... (nnn cells left)”. These deferred cell-writes cannot be interrupted by C-g, so you'll just have to wait.

SES uses run-with-idle-timer to move the cell underline when Emacs will be scrolling the buffer after the end of a command, and also to narrow and underline after C-x C-v. This is visible as a momentary glitch after C-x C-v and certain scrolling commands. You can type ahead without worrying about the glitch.

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5.2 Nonrelocatable references

C-y relocates all cell-references in a pasted formula, while C-u C-y relocates none of the cell-references. What about mixed cases?

You can use

     (symbol-value 'B3)

to make an absolute reference. The formula relocator skips over quoted things, so this will not be relocated when pasted or when rows/columns are inserted/deleted. However, B3 will not be recorded as a dependency of this cell, so this cell will not be updated automatically when B3 is changed.

The variables row and col are dynamically bound while a cell formula is being evaluated. You can use

     (ses-cell-value row 0)

to get the value from the leftmost column in the current row. This kind of dependency is also not recorded.

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5.3 The data area

Begins with an 014 character, followed by sets of cell-definition macros for each row, followed by column-widths, column-printers, default-printer, and header-row. Then there's the global parameters (file-format ID, numrows, numcols) and the local variables (specifying SES mode for the buffer, etc.).

When a SES file is loaded, first the numrows and numcols values are loaded, then the entire data area is evaled, and finally the local variables are processed.

You can edit the data area, but don't insert or delete any newlines except in the local-variables part, since SES locates things by counting newlines. Use C-x C-e at the end of a line to install your edits into the spreadsheet data structures (this does not update the print area, use, e.g., C-c C-l for that).

The data area is maintained as an image of spreadsheet data structures that area stored in buffer-local variables. If the data area gets messed up, you can try reconstructing the data area from the data structures:

C-c M-C-l
(ses-reconstruct-all).

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5.4 Buffer-local variables in spreadsheets

You can add additional local variables to the list at the bottom of the data area, such as hidden constants you want to refer to in your formulas.

You can override the variable ses--symbolic-formulas to be a list of symbols (as parenthesized strings) to show as completions for the ' command. This initial completions list is used instead of the actual set of symbols-as-formulas in the spreadsheet.

For an example of this, see file etc/ses-example.ses.

If (for some reason) you want your formulas or printers to save data into variables, you must declare these variables as buffer-locals in order to avoid a virus warning.

You can define functions by making them values for the fake local variable eval. Such functions can then be used in your formulas and printers, but usually each eval is presented to the user during file loading as a potential virus. This can get annoying.

You can define functions in your .emacs file. Other people can still read the print area of your spreadsheet, but they won't be able to recalculate or reprint anything that depends on your functions. To avoid virus warnings, each function used in a formula needs

     (put 'your-function-name 'safe-function t)

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5.5 Uses of defadvice in SES

undo-more
Defines a new undo element format (fun . args), which means “undo by applying fun to args”. For spreadsheet buffers, it allows undos in the data area even though that's outside the narrowing.
copy-region-as-kill
When copying from the print area of a spreadsheet, treat the region as a rectangle and attach each cell's formula and printer as 'ses properties.
yank
When yanking into the print area of a spreadsheet, first try to yank as cells (if the yank text has 'ses properties), then as tab-separated formulas, then (if all else fails) as a single formula for the current cell.

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Index

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Acknowledgments

Coding by:

Jonathan Yavner, Stefan Monnier, Shigeru Fukaya

Texinfo manual by:

Jonathan Yavner, Brad Collins

Ideas from:

Christoph Conrad, CyberBob, Syver Enstad, Ami Fischman, Thomas Gehrlein, Chris F.A. Johnson, Yusong Li, Juri Linkov, Harald Maier, Alan Nash, François Pinard, Pedro Pinto, Stefan Reichör, Oliver Scholz, Richard M. Stallman, Luc Teirlinck, J. Otto Tennant, Jean-Philippe Theberge

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Appendix A GNU Free Documentation License

Version 1.3, 3 November 2008
     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.