Another way to create a new Calculator command uses algebraic formulas.
The Z F (calc-user-define-formula) command stores the
formula at the top of the stack as the definition for a key. This
command prompts for five things: The key, the command name, the function
name, the argument list, and the behavior of the command when given
non-numeric arguments.
For example, suppose we type ' a+2b RET to push the formula
`a + 2*b' onto the stack. We now type Z F m to define this
formula on the z m key sequence. The next prompt is for a command
name, beginning with `calc-', which should be the long (M-x) form
for the new command. If you simply press RET, a default name like
calc-User-m will be constructed. In our example, suppose we enter
spam RET to define the new command as calc-spam.
If you want to give the formula a long-style name only, you can press SPC or RET when asked which single key to use. For example Z F RET spam RET defines the new command as M-x calc-spam, with no keyboard equivalent.
The third prompt is for a function name. The default is to use the same name as the command name but with `calcFunc-' in place of `calc-'. This is the name you will use if you want to enter your new function in an algebraic formula. Suppose we enter yow RET. Then the new function can be invoked by pushing two numbers on the stack and typing z m or x spam, or by entering the algebraic formula `yow(x,y)'.
The fourth prompt is for the function's argument list. This is used to associate values on the stack with the variables that appear in the formula. The default is a list of all variables which appear in the formula, sorted into alphabetical order. In our case, the default would be `(a b)'. This means that, when the user types z m, the Calculator will remove two numbers from the stack, substitute these numbers for `a' and `b' (respectively) in the formula, then simplify the formula and push the result on the stack. In other words, 10 RET 100 z m would replace the 10 and 100 on the stack with the number 210, which is a + 2 b with a=10 and b=100. Likewise, the formula `yow(10, 100)' will be evaluated by substituting a=10 and b=100 in the definition.
You can rearrange the order of the names before pressing RET to control which stack positions go to which variables in the formula. If you remove a variable from the argument list, that variable will be left in symbolic form by the command. Thus using an argument list of `(b)' for our function would cause 10 z m to replace the 10 on the stack with the formula `a + 20'. If we had used an argument list of `(b a)', the result with inputs 10 and 100 would have been 120.
You can also put a nameless function on the stack instead of just a formula, as in `<a, b : a + 2 b>'. See section Specifying Operators. In this example, the command will be defined by the formula `a + 2 b' using the argument list `(a b)'.
The final prompt is a y-or-n question concerning what to do if symbolic arguments are given to your function. If you answer y, then executing z m (using the original argument list `(a b)') with arguments 10 and x will leave the function in symbolic form, i.e., `yow(10,x)'. On the other hand, if you answer n, then the formula will always be expanded, even for non-constant arguments: `10 + 2 x'. If you never plan to feed algebraic formulas to your new function, it doesn't matter how you answer this question.
If you answered y to this question you can still cause a function
call to be expanded by typing a " (calc-expand-formula).
Also, Calc will expand the function if necessary when you take a
derivative or integral or solve an equation involving the function.
Once you have defined a formula on a key, you can retrieve this formula
with the Z G (calc-user-define-get-defn) command. Press a
key, and this command pushes the formula that was used to define that
key onto the stack. Actually, it pushes a nameless function that
specifies both the argument list and the defining formula. You will get
an error message if the key is undefined, or if the key was not defined
by a Z F command.
The Z E (calc-user-define-edit) command on a key that has
been defined by a formula uses a variant of the calc-edit command
to edit the defining formula. Press M-# M-# to finish editing and
store the new formula back in the definition, or M-# x to
cancel the edit. (The argument list and other properties of the
definition are unchanged; to adjust the argument list, you can use
Z G to grab the function onto the stack, edit with `, and
then re-execute the Z F command.)
As usual, the Z P command records your definition permanently. In this case it will permanently record all three of the relevant definitions: the key, the command, and the function.
You may find it useful to turn off the default simplifications with
m O (calc-no-simplify-mode) when entering a formula to be
used as a function definition. For example, the formula `deriv(a^2,v)'
which might be used to define a new function `dsqr(a,v)' will be
"simplified" to 0 immediately upon entry since deriv considers
a to be constant with respect to v. Turning off
default simplifications cures this problem: The definition will be stored
in symbolic form without ever activating the deriv function. Press
m D to turn the default simplifications back on afterwards.