A Demonstration of Calc
=======================

This section will show some typical small problems being solved with
Calc.  The focus is more on demonstration than explanation, but
everything you see here will be covered more thoroughly in the
Tutorial.

To begin, start Emacs if necessary (usually the command `emacs' does
this), and type `M-# c' (or `ESC # c') to start the Calculator.
(See Starting Calc, if this doesn't work for you.)

Be sure to type all the sample input exactly, especially noting the
difference between lower-case and upper-case letters.  Remember,
`RET', `TAB', `DEL', and `SPC' are the Return, Tab, Delete, and Space
keys.

*RPN calculation.*  In RPN, you type the input number(s) first,
then the command to operate on the numbers.

Type `2 RET 3 + Q' to compute the square root of 2+3, which is
2.2360679775.

Type `P 2 ^' to compute the value of `pi' squared, 9.86960440109.

Type `TAB' to exchange the order of these two results.

Type `- I H S' to subtract these results and compute the Inverse
Hyperbolic sine of the difference, 2.72996136574.

Type `DEL' to erase this result.

*Algebraic calculation.*  You can also enter calculations using
conventional "algebraic" notation.  To enter an algebraic formula, use
the apostrophe key.

Type `' sqrt(2+3) RET' to compute the square root of 2+3.

Type `' pi^2 RET' to enter `pi' squared.  To evaluate this symbolic
formula as a number, type `='.

Type `' arcsinh($ - $$) RET' to subtract the second-most-recent result
from the most-recent and compute the Inverse Hyperbolic sine.

*Keypad mode.*  If you are using the X window system, press
`M-# k' to get Keypad mode.  (If you don't use X, skip to
the next section.)

Click on the 2, ENTER, 3, +, and SQRT "buttons" using your left mouse
button.

Click on PI, 2, and y^x.

Click on INV, then ENTER to swap the two results.

Click on -, INV, HYP, and SIN.

Click on <- to erase the result, then click OFF to turn the Keypad
Calculator off.

*Grabbing data.*  Type `M-# x' if necessary to exit Calc.
Now select the following numbers as an Emacs region:  "Mark" the
front of the list by typing control-`SPC' or control-`@' there,
then move to the other end of the list.  (Either get this list from
the on-line copy of this manual, accessed by `M-# i', or just
type these numbers into a scratch file.)  Now type `M-# g' to
"grab" these numbers into Calc.

     1.23  1.97
     1.6   2
     1.19  1.08

The result `[1.23, 1.97, 1.6, 2, 1.19, 1.08]' is a Calc "vector."
Type `V R +' to compute the sum of these numbers.

Type `U' to Undo this command, then type `V R *' to compute the
product of the numbers.

You can also grab data as a rectangular matrix.  Place the cursor on
the upper-leftmost `1' and set the mark, then move to just after the
lower-right `8' and press `M-# r'.

Type `v t' to transpose this 3x2 matrix into a 2x3 matrix.  Type
`v u' to unpack the rows into two separate vectors.  Now type
`V R + TAB V R +' to compute the sums of the two original columns.
(There is also a special grab-and-sum-columns command, `M-# :'.)

*Units conversion.*  Units are entered algebraically.
Type `' 43 mi/hr RET' to enter the quantity 43 miles-per-hour.
Type `u c km/hr RET'.  Type `u c m/s RET'.

*Date arithmetic.*  Type `t N' to get the current date and
time.  Type `90 +' to find the date 90 days from now.  Type `' <25 dec
87> RET' to enter a date, then `- 7 /' to see how many weeks have
passed since then.

*Algebra.*  Algebraic entries can also include formulas
or equations involving variables.  Type `' [x + y = a, x y = 1] RET'
to enter a pair of equations involving three variables.  (Note the
leading apostrophe in this example; also, note that the space between
`x y' is required.)  Type `a S x,y RET' to solve these equations for
the variables `x' and `y'.

Type `d B' to view the solutions in more readable notation.
Type `d C' to view them in C language notation, and `d T'
to view them in the notation for the TeX typesetting system.
Type `d N' to return to normal notation.

Type `7.5', then `s l a RET' to let `a = 7.5' in these formulas.
(That's a letter `l', not a numeral `1'.)

*Help functions.*  You can read about any command in the on-line
manual.  Remember to type the letter `l', then `M-# c', to
return here after each of these commands: `h k t N' to read
about the `t N' command, `h f sqrt RET' to read about the
`sqrt' function, and `h s' to read the Calc summary.

Press `DEL' repeatedly to remove any leftover results from the stack.
To exit from Calc, press `q' or `M-# c' again.