Embedded Mode (Overview)
------------------------

"Embedded Mode" is a way to use Calc directly from inside an editing
buffer.  Suppose you have a formula written as part of a document like
this:

     The derivative of

                                        ln(ln(x))

     is

and you wish to have Calc compute and format the derivative for you
and store this derivative in the buffer automatically.  To do this
with Embedded Mode, first copy the formula down to where you want the
result to be:

     The derivative of

                                        ln(ln(x))

     is

                                        ln(ln(x))

Now, move the cursor onto this new formula and press `M-# e'.  Calc
will read the formula (using the surrounding blank lines to tell how
much text to read), then push this formula (invisibly) onto the Calc
stack.  The cursor will stay on the formula in the editing buffer, but
the buffer's mode line will change to look like the Calc mode line
(with mode indicators like `12 Deg' and so on).  Even though you are
still in your editing buffer, the keyboard now acts like the Calc
keyboard, and any new result you get is copied from the stack back
into the buffer.  To take the derivative, you would type `a d x RET'.

     The derivative of

                                        ln(ln(x))

     is

     1 / ln(x) x

To make this look nicer, you might want to press `d =' to center the
formula, and even `d B' to use "big" display mode.

     The derivative of

                                        ln(ln(x))

     is
     % [calc-mode: justify: center]
     % [calc-mode: language: big]

                                            1
                                         -------
                                         ln(x) x

Calc has added annotations to the file to help it remember the modes
that were used for this formula.  They are formatted like comments in
the TeX typesetting language, just in case you are using TeX.  (In
this example TeX is not being used, so you might want to move these
comments up to the top of the file or otherwise put them out of the
way.)

As an extra flourish, we can add an equation number using a righthand
label: Type `d } (1) RET'.

     % [calc-mode: justify: center]
     % [calc-mode: language: big]
     % [calc-mode: right-label: " (1)"]

                                            1
                                         -------                      (1)
                                         ln(x) x

To leave Embedded Mode, type `M-# e' again.  The mode line and
keyboard will revert to the way they were before.  (If you have
actually been trying this as you read along, you'll want to press `M-#
0' [with the digit zero] now to reset the modes you changed.)

The related command `M-# w' operates on a single word, which generally
means a single number, inside text.  It uses any non-numeric
characters rather than blank lines to delimit the formula it reads.
Here's an example of its use:

     A slope of one-third corresponds to an angle of 1 degrees.

Place the cursor on the `1', then type `M-# w' to enable
Embedded Mode on that number.  Now type `3 /' (to get one-third),
and `I T' (the Inverse Tangent converts a slope into an angle),
then `M-# w' again to exit Embedded mode.

     A slope of one-third corresponds to an angle of 18.4349488229 degrees.

See Embedded Mode, for full details.