decorated characters

A previous thread cast expressions like  x'  as multi-character
variables.

I think that was the wrong way to think about it.  There can
be multi-character variables, but a separate and possibly more
common situation is "decorated" characters.

Examples, and the way I would pronounce them, are:

x prime
x double prime
x hat
x bar
x tilde
x check
x dot
x double dot
x star

Note that some of those have the decoration above the character,
and others have the decoration above and to the right (northeast)
of the character.

I would be happy to hear of examples where one pronounces the
decoration first and the variable second.

Suppose  J_0  is the 0th order Bessel function of the first kind.
Is the subscript a decoration?  It looks like one to me.  And I
pronounce it as  "J zero" not "J sub zero".

An intent like
     intent=decoration($1, $2)
or
     intent=decoration($2, $1)
indicating on the order of pronunciation, could tell AT how to
say the decorated character.  That intent also conveys the idea
that the decorated character is one mathematical object.

I say "decorated character" and not "decorated variable" because
the decoration might be on a function and not on a variable.
The derivative f', and Fourier transform \hat{f}, are common
examples of functions with decorations.

A flaw is that we have not conveyed the meaning, only the
pronunciation.  What if there were an (optional?) 3rd argument
to the decoration intent?  For example:

decoration(f, hat, fourier-transform)
decoration(f, prime, derivative)
decoration(x, dot, time-derivative)
decoration(x, bar, mean)
decoration(J, 0, bessel)
decoration(a, n, index)

The last one would appear in

    sum a_n x^n

because the "n" is an index (of summation), and I would pronounce
the "sub" in that case.

If x' is just a new variable and the prime has no meaning,
that could be a case to omit the 3rd argument to decoration.

All this assumes AT actually needs help pronouncing decorated characters
correctly.

Regards,

David

Received on Monday, 18 October 2021 13:34:56 UTC