22.214.171.124 User-Defined Compositions
The `Z C' (`calc-user-define-composition') command lets you define the
display format for any algebraic function. You provide a formula
containing a certain number of argument variables on the stack. Any
time Calc formats a call to the specified function in the current
language mode and with that number of arguments, Calc effectively
replaces the function call with that formula with the arguments
Calc builds the default argument list by sorting all the variable
names that appear in the formula into alphabetical order. You can edit
this argument list before pressing <RET> if you wish. Any variables in
the formula that do not appear in the argument list will be displayed
literally; any arguments that do not appear in the formula will not
affect the display at all.
You can define formats for built-in functions, for functions you have
defined with `Z F' (Note: Algebraic Definitions), or for functions
which have no definitions but are being used as purely syntactic
objects. You can define different formats for each language mode, and
for each number of arguments, using a succession of `Z C' commands.
When Calc formats a function call, it first searches for a format
defined for the current language mode (and number of arguments); if
there is none, it uses the format defined for the Normal language mode.
If neither format exists, Calc uses its built-in standard format for
that function (usually just `FUNC(ARGS)').
If you execute `Z C' with the number 0 on the stack instead of a
formula, any defined formats for the function in the current language
mode will be removed. The function will revert to its standard format.
For example, the default format for the binomial coefficient function
`choose(n, m)' in the Big language mode is
You might prefer the notation,
To define this notation, first make sure you are in Big mode, then put
choriz([cvert([cvspace(1), n]), C, cvert([cvspace(1), m])])
on the stack and type `Z C'. Answer the first prompt with `choose'.
The second prompt will be the default argument list of `(C m n)'. Edit
this list to be `(n m)' and press <RET>. Now, try it out: For
example, turn simplification off with `m O' and enter `choose(a,b) +
choose(7,3)' as an algebraic entry.
C + C
a b 7 3
As another example, let's define the usual notation for Stirling
numbers of the first kind, `stir1(n, m)'. This is just like the
regular format for binomial coefficients but with square brackets
instead of parentheses.
choriz([string("["), cvert([n, cbase(cvspace(1)), m]), string("]")])
Now type `Z C stir1 <RET>', edit the argument list to `(n m)', and
The formula provided to `Z C' usually will involve composition
functions, but it doesn't have to. Putting the formula `a + b + c'
onto the stack and typing `Z C foo <RET> <RET>' would define the
function `foo(x,y,z)' to display like `x + y + z'. This "sum" will act
exactly like a real sum for all formatting purposes (it will be
parenthesized the same, and so on). However it will be computationally
unrelated to a sum. For example, the formula `2 * foo(1, 2, 3)' will
display as `2 (1 + 2 + 3)'. Operator precedences have caused the "sum"
to be written in parentheses, but the arguments have not actually been
summed. (Generally a display format like this would be undesirable,
since it can easily be confused with a real sum.)
The special function `eval' can be used inside a `Z C' composition
formula to cause all or part of the formula to be evaluated at display
time. For example, if the formula is `a + eval(b + c)', then `foo(1,
2, 3)' will be displayed as `1 + 5'. Evaluation will use the default
simplifications, regardless of the current simplification mode. There
are also `evalsimp' and `evalextsimp' which simplify as if by `a s' and
`a e' (respectively). Note that these "functions" operate only in the
context of composition formulas (and also in rewrite rules, where they
serve a similar purpose; Note: Rewrite Rules). On the stack, a call
to `eval' will be left in symbolic form.
It is not a good idea to use `eval' except as a last resort. It can
cause the display of formulas to be extremely slow. For example, while
`eval(a + b)' might seem quite fast and simple, there are several
situations where it could be slow. For example, `a' and/or `b' could
be polar complex numbers, in which case doing the sum requires
trigonometry. Or, `a' could be the factorial `fact(100)' which is
unevaluated because you have typed `m O'; `eval' will evaluate it
anyway to produce a large, unwieldy integer.
You can save your display formats permanently using the `Z P'
command (Note: Creating User Keys).
automatically generated by info2www version 126.96.36.199