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 © 2002–2024 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.”
Table of Contents
Next: Quick Tutorial, Previous: SES: Simple Emacs Spreadsheet, Up: SES: Simple Emacs Spreadsheet [Contents][Index]
1 Sales Pitch
- Create and edit simple spreadsheets with a minimum of fuss.
- Full undo/redo/autosave.
- Immune to viruses in spreadsheet files.
- Cell formulas are straight Emacs Lisp.
- Printer functions for control of cell appearance.
- Intuitive keystroke commands: C-o = insert row, M-o = insert column, etc.
- “Spillover” of lengthy cell values into following blank cells.
- Header line shows column letters or a selected row.
- Completing-read for entering symbols as cell values.
- Cut, copy, and paste can transfer formulas and printer functions.
- Import and export of tab-separated values or tab-separated formulas.
- Plaintext, easily-hacked file format.
Next: The Basics, Previous: Sales Pitch, Up: SES: Simple Emacs Spreadsheet [Contents][Index]
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.)
Alternatively you can use the !
modifier of ses-range
to
remove blank cells from the returned list, which allows to use
+
instead of ses+
:
(apply '+ (ses-range A2 A5 !))
Next: Advanced Features, Previous: Quick Tutorial, Up: SES: Simple Emacs Spreadsheet [Contents][Index]
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
). Unless the cell is a renamed cell, the identifier is case-insensitive. A prefix argument n move to cell with coordinates (n\div R, n \% C) for a spreadsheet of R rows and C columns, and A1 being of coordinates (0,0). The way the identifier or the command prefix argument are interpreted can be customized through variablesses-jump-cell-name-function
andses-jump-prefix-function
.
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
).
- Cell formulas
- Resizing the spreadsheet
- Printer functions
- Clearing cells
- Copy, cut, and paste
- Customizing SES
Next: Resizing the spreadsheet, Up: The Basics [Contents][Index]
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 the following keys:- M-TAB
to complete symbol names, and
- C-h C-n
to list the named cells symbols in a help buffer.
- ' (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
).
Next: Printer functions, Previous: Cell formulas, Up: The Basics [Contents][Index]
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)
).
Next: Clearing cells, Previous: Resizing the spreadsheet, Up: The Basics [Contents][Index]
3.3 Printer functions
Printer functions convert binary cell values into the print forms that Emacs will display on the screen.
- Various kinds of printer functions
- Configuring what printer function applies
- Standard printer functions
- Local printer functions
- Writing a lambda printer function
3.3.1 Various kinds of printer functions
When configuring what printer function applies (see Configuring what printer function applies), you can enter a printer function as one of the following:
- 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, the result of which is
a string (right-aligned) or list of one string (left-aligned). Such a
function can be in turn configured as:
- A lambda expression, for instance:
(lambda (x) (cond ((null x) "") ((numberp x) (format "%.2f" x)) (t (ses-center-span x ?# 'ses-prin1))))
While typing in a lambda, you can use M-TAB to complete the names of symbols.
- A symbol referring to a standard printer function (see Standard printer functions).
- A symbol referring to a local printer function (see Local printer functions).
- A lambda expression, for instance:
Next: Standard printer functions, Previous: Various kinds of printer functions, Up: Printer functions [Contents][Index]
3.3.2 Configuring what printer function applies
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
allows the following commands during editing:
- arrow-up
- arrow-down
To browse history: 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 (see Standard printer functions) and the local printers (see Local printer functions).- TAB
To complete the local printer symbols, and
- C-h C-p
To list the local printers in a help buffer.
Next: Local printer functions, Previous: Configuring what printer function applies, Up: Printer functions [Contents][Index]
3.3.3 Standard printer functions
Except for ses-prin1
, the other 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.
ses-prin1
¶This is the fallback printer, used when calling the configured printer throws some error.
Next: Writing a lambda printer function, Previous: Standard printer functions, Up: Printer functions [Contents][Index]
3.3.4 Local printer functions
You can define printer function local to a sheet with the command
ses-define-local-printer
. For instance, define a printer
‘foo’ to "%.2f"
, and then use symbol ‘foo’ as a
printer function. Then, if you call again
ses-define-local-printer
on ‘foo’ to redefine it as
"%.3f"
, all the cells using printer ‘foo’ will be
reprinted accordingly.
Sometimes there are local printers that you want to define or
re-define automatically every time you open a sheet. For instance
imagine that you want to define/re-define automatically a local
printer euro
to display a number like an amount of euros, that
is to say number 3.1
would be displayed as
3.10€
. To do so in any non read-only SES buffer,
you can add some code like this to your .emacs init file:
(defun my-ses-mode-hook () (unless buffer-read-only (ses-define-local-printer 'euro (lambda (x) (cond ((null x) "") ((numberp x) (format "%.2f€" x)) (t (ses-center-span x ?# 'ses-prin1))))))) (add-hook 'ses-mode-hook 'my-ses-mode-hook)
If you replace command ses-define-local-printer
by function
ses-define-if-new-local-printer
the definition will occur only if a local printer with the same name
in not already defined.
Previous: Local printer functions, Up: Printer functions [Contents][Index]
3.3.5 Writing a lambda printer function
You can write a printer function with a lambda expression taking one argument in two cases:
- when you configure the printer function applying to a cell or column, or
- when you define a local printer function with command
ses-define-local-printer
.
When doing so, please take care that the returned value is a string, or a list containing a string, even when the input argument has an unexpected value. Here is an example:
(lambda (val) (cond ((null val) "") ((and (numberp val) (>= val 0)) (format "%.1f" val)) (t (ses-center-span val ?# 'ses-prin1))))
This example will:
- When the cell is empty (ie. when
val
isnil
), print an empty string""
- When the cell value is a non negative number, format the value in fixed-point notation with one decimal after point
- Otherwise, handle the value as erroneous by printing it as an
s-expression (using
ses-prin1
), centered and surrounded by#
filling.
Another precaution to take is to avoid stack overflow due to a
printer function calling itself indefinitely. This mistake can
happen when you use a local printer as a column printer,
and this local printer implicitly calls the current column printer, so it
will call itself recursively. Imagine for instance that you want to
create some local printer =fill
that would center the content
of a cell and surround it by equal signs =
, and you do it this
way:
(lambda (x) (cond ((null x) "") (t (ses-center x 0 ?=))))
Because =fill
uses the standard printer ses-center
without
explicitly passing any printer to it, ses-center
will call the
current column printer if any, or the spreadsheet default printer
otherwise. So using =fill
as a column printer will result in a
stack overflow in this column. SES does not check for that;
you just have to be careful. For instance, re-write =fill
like
this:
(lambda (x) (cond ((null x) "") ((stringp x) (ses-center x 0 ?= " %s ")) (t (ses-center-span x ?# 'ses-prin1))))
The code above applies the =
filling only to strings; it also
surrounds the string by one space on each side before filling with
=
signs. So the string ‘Foo’ will be displayed like ‘=== Foo ===’ in an 11 character wide column. Anything other than an empty cell
or a non-string is displayed as an error by using #
filling.
Next: Copy, cut, and paste, Previous: Printer functions, Up: The Basics [Contents][Index]
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
).
Next: Customizing SES, Previous: Clearing cells, Up: The Basics [Contents][Index]
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 usesundo
to delete the old yank. This doesn’t make any difference?
Previous: Copy, cut, and paste, Up: The Basics [Contents][Index]
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-jump-cell-name-function
is a customizable variable by
default set to the upcase
function. This function is called
when you pass a cell name to the ses-jump
command (j),
it changes the entered cell name to that where to jump. The default
setting upcase
allows you to enter the cell name in low
case. Another use of ses-jump-cell-name-function
could be some
internationalization to convert non latin characters into latin
equivalents to name the cell. Instead of a cell name, the function may
return cell coordinates in the form of a cons, for instance (0
. 0)
for cell A1
, (1 . 0)
for cell A2
, etc.
ses-jump-prefix-function
is a customizable variable by default
set to the ses-jump-prefix
function. This function is called
when you give a prefix argument to the ses-jump
command
(j). It returns a cell name or cell coordinates corresponding to
the prefix argument. Cell coordinates are in the form of a cons, for
instance (1 . 0)
for cell A2
. The default setting
ses-jump-prefix
will number cells left to right and then top
down, so assuming a 4x3 spreadsheet prefix argument 0 jumps to cell
A1, prefix argument 2 jumps to C1, prefix argument 3 jumps to A2, etc.
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!
Next: For Gurus, Previous: The Basics, Up: SES: Simple Emacs Spreadsheet [Contents][Index]
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 that can be a valid local variable name (See also Nonrelocatable references).
- 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
- The print area
- Ranges in formulas
- Sorting by column
- Standard formula functions
- More on cell printing
- Import and export
- Virus protection
- Spreadsheets with details and summary
Next: Ranges in formulas, Up: Advanced Features [Contents][Index]
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
).
Next: Sorting by column, Previous: The print area, Up: Advanced Features [Contents][Index]
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 symbolsnil
or*skip*
. For instance(ses-range A1 A4 !)
will do the same as(list A1 A3)
when cellsA2
andA4
are empty._
Empty cell values are replaced by the argument following flag
_
, or0
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 cellsA2
andA4
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 GNU Emacs Calc Manual). 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.
Next: Standard formula functions, Previous: Ranges in formulas, Up: Advanced Features [Contents][Index]
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.
Next: More on cell printing, Previous: Sorting by column, Up: Advanced Features [Contents][Index]
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. Order of args is reverted. Please note thatses-range
has a!
modifier that allows to remove blanks, so it is possible to write:(ses-range A1 A5 !)
instead of
(apply 'ses-delete-blanks (ses-range A1 A5 <))
(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
.
Next: Import and export, Previous: Standard formula functions, Up: Advanced Features [Contents][Index]
4.5 More on cell printing
Special cell values:
- nil prints the same as "", but allows previous cell to spill over.
- ’*skip* replaces nil when the previous cell actually does spill over; nothing is printed for it.
- ’*error* indicates that the formula signaled an error instead of producing a value: the print cell is filled with hash marks (#).
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
ses-prin1
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”.
Next: Virus protection, Previous: More on cell printing, Up: Advanced Features [Contents][Index]
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.
Next: Spreadsheets with details and summary, Previous: Import and export, Up: Advanced Features [Contents][Index]
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.
Previous: Virus protection, Up: Advanced Features [Contents][Index]
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.
Next: Index, Previous: Advanced Features, Up: SES: Simple Emacs Spreadsheet [Contents][Index]
5 For Gurus
- Deferred updates
- Nonrelocatable references
- The data area
- Buffer-local variables in spreadsheets
- Uses of defadvice in SES
Next: Nonrelocatable references, Up: For Gurus [Contents][Index]
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.
Next: The data area, Previous: Deferred updates, Up: For Gurus [Contents][Index]
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?
The best way is to rename cells that you do not want to be relocatable
by using ses-rename-cell
.
Cells that do not have an A1-like name style are not relocated on
yank. Using this method, the concerned cells won’t be relocated
whatever formula they appear in. Please note however that when a
formula contains some range (ses-range cell1 cell2)
then in the yanked formula each range bound cell1 and
cell2 are relocated, or not, independently, depending on whether
they are A1-like or renamed.
An alternative method is to 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, this is why using
ses-rename-cell
is most of the time preferable.
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.
Next: Buffer-local variables in spreadsheets, Previous: Nonrelocatable references, Up: For Gurus [Contents][Index]
5.3 The data area
Begins with an 014 character, followed by sets of cell-definition macros for each row, followed by the set of local printer definitions, followed by column-widths, column-printers, default-printer, and header-row. Then there’s the global parameters (file-format ID, row count, column count, local printer count) and the local variables (specifying SES mode for the buffer, etc.).
When a SES file is loaded, first the global parameters are
loaded, then the entire data area is eval
ed, 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
).
Next: Uses of defadvice in SES, Previous: The data area, Up: For Gurus [Contents][Index]
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)
Previous: Buffer-local variables in spreadsheets, Up: For Gurus [Contents][Index]
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.
Next: Acknowledgments, Previous: For Gurus, Up: SES: Simple Emacs Spreadsheet [Contents][Index]
Index
Jump to: | *
A B C D E F I K M N P R S T U V W Y |
---|
Jump to: | *
A B C D E F I K M N P R S T U V W Y |
---|
Next: GNU Free Documentation License, Previous: Index, Up: SES: Simple Emacs Spreadsheet [Contents][Index]
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
Previous: Acknowledgments, Up: SES: Simple Emacs Spreadsheet [Contents][Index]
Appendix A GNU Free Documentation License
Copyright © 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc. https://fsf.org/ Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.
- 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.
- 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.
- 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.
- 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.
- 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:
- 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.
- 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.
- State on the Title page the name of the publisher of the Modified Version, as the publisher.
- Preserve all the copyright notices of the Document.
- Add an appropriate copyright notice for your modifications adjacent to the other copyright notices.
- 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.
- Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document’s license notice.
- Include an unaltered copy of this License.
- 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.
- 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.
- 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.
- 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.
- Delete any section Entitled “Endorsements”. Such a section may not be included in the Modified Version.
- Do not retitle any existing section to be Entitled “Endorsements” or to conflict in title with any Invariant Section.
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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.
- 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.”
- 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.
- 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.
- 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.
- 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.
- 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 https://www.gnu.org/licenses/.
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.
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“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:
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If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation.
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