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Re: small samples



Ron Whitney wrote:
> 
> Item 9 / fonts
> 
> TeX:                    {\bf R}, \mathbf R
> 
> Wolfram:                <b>R</b>
> 
> MINSE:
> Display-List (S):
> Display-List (MS):
> ISO 12083:              <bold>R</bold>

Assuming that what you are trying to represent here is the
set of real numbers, you'd write that in MINSE as 

    'Real

using the definitions that i'm currently working with.

I suppose that, if it is really absolutely necessary to add
a meaningless font-changing compound, one could simply do

    'bold(R)

or  'bf(R)

or somesuch.  Declaring "bf" as a unary prefix operator
would then make it possible to simply write

    .bf R

in the manner which you (Ron) refer to as "most natural".

Note that there is nothing in MINSE which prevents us
from adding more notational-oriented compounds rather
than semantic ones.  I choose to give the semantic
ones preference because they provide more flexibility
in rendering to different environments.

> 4. I do find the AMSTeX, unary prefix operator, style of notation
>    most natural since it accords with other operator-style methods of
>    embellishing objects. Can this be done in the Wolfram approach?

The flexibility of being able to make operator declarations
lets us choose more "natural" ways of expression.  Another
argument for extensibility...

> 5. Suppose for the moment we have a paper in which the author uses
>    emboldening to indicate vectors. Suppose also that the style for
>    indicating the reals and complexes is to embolden the "R" and "C".
...
>    How do we envision type-theoretic information being attached to
>    all the various kinds of vectors?

By declaring more vector-type compounds, up to the level of
detail we wish to achieve.  By this question i assume you
mean distinguishing between, say, a vector "v" in R^2 and
another vector "v" in C^3?
 
> ---------------------------------------------------------
> Item 10 / primes
> 
> TeX:                    x', x^\prime, x^{\prime\prime}
> 
> Wolfram:
> MINSE:
> Display-List (S):
> Display-List (MS):
> ISO 12083:
 
Priming is usually a form of qualifying to produce a new
symbol name.  The documents on the MINSE site (which have
now not been updated in a little while) reflect my thoughts
at the time, which were to designate a special character
to represent the "prime" qualifier.  Thus,

    x:!

This requires the assumption that the prime mark always
appear in the same place.  But this is not so with the
asterisk, which could be wanted anywhere.

Since the asterisk and prime mark are non-alphanumerics,
they need to be represented with symbols; thus you'd need
something like

    x:?star?

or  x .upqual ?star?

If this grew tedious to write, you could simply assign
this to a macro (say "xs") and write @xs instead.

> 3. For concreteness, how might some person or program associate
>    differentiation to priming within a paper?
 
Use the differentiation compound.  If the author wants
differentiation to be displayed, on paper, using a prime
mark, she can say so in the style definition.

> ---------------------------------------------------------
> Item 11 / overlines
> 
> TeX:                    \overline s, \overline{s+t}
> 
> Wolfram:
> MINSE:
> Display-List (S):
> Display-List (MS):
> ISO 12083:              <overline>s</overline>,
>                         <overline>s+t</overline>

I don't really see how you would expect this kind of
thing to be read aloud or understood by a symbolic
manipulation program.

The graphical renderer can currently produce overlines
using an "enclosure" primitive, which is used by the
current "image" style definition for compounds like
"line segment" and so on.  But the possibilities include

    'not(P .or Q)
    'cconj(x+y)
    'line(AB)

... and so on.

> Notes:
> 1. The `line' of the ISO overline can come in many styles (single,
>    double, triple, dash, dot, bold, etc.). TeX has to stand on its head
>    to get many of these. "\overline" and "\bar" are two related
>    embellishment forms, the first `stretchy', the second not.

The current rendering program could be extended to handle more
interesting enclosure shapes and styles.
 
> ---------------------------------------------------------
> Item 12 / overbar with subscript
> 
> TeX:                    \bar x_1
> 
> Wolfram:                x^^&bar;_1
> 
> MINSE:
> Display-List (S):       <mscript>
>                           <moverscript>x<mc>&bar;</moverscript>
>                           <mc><mc>1
>                         </mscript>
> 
> Display-List (MS):
> ISO 12083:              x<top>&bar;</top><inf>1</inf>
> 
> Notes:
> 1. This is a simple example, but it brings up a couple of points.
>    If the overbar signifies conjugation, it's probably most likely that
>    the proper "expression" (and, in any case, a possible expression) is
>    one signifying the conjugate of the object "x_1".

If it does signify conjugation, then you should simply be writing

    'cconj(x;1)

Having to ask the question belies that you would really have
to know in the first place what you are trying to say!

> 3. And as with prime notation, how would a person or software specify
>    that barring is to be read as conjugation? Does it come to individual
>    interpretational annotations (semantical markup embedded within the
>    mathematical text) or a declaration outside the body of a paper?

Simply use the appropriate compound.


Ping


References: