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RE: Re: Readability confuses mathematica? - Notation Package

Hi Jason,

I would like to put some comments in here concerning the Notation package. I
think the package tackles a very useful and a very complicated problem. I
doubt if there are many people who could carry out what you have done.

Still I find severe problems with the package. It is difficult to put my
finger accurately on them but I will make an attempt. I have, on a number of
occasions, spent many hours and even days trying to use the package and have
always given up in frustration. Perhaps my intellectual capability just
isn't up to it.

User interface and documentation are very important for a package.

Let's talk about user interface first. The first thing that will happen when
a user is trying to learn a package like this is that he will make mistakes.
You can count on it. But there appears to be no easy method to undo the
mistakes. If a specific notation or Symbol has been entered incorrectly,
there doesn't seem to be any good way to get rid of it without killing the
kernel and starting over. When I tried to use RemoveNotation or RemoveSymbol
it did not get rid of the underlying built_up symbols so errors or warning
messages were generated when I tried again to define a notation. One should
be able to easily undo one's mistakes and continue on.

It would be very helpful if one did not have to use the palette to enter a
notation or symbol. People do seem to have trouble in selecting the correct
box. It might be better if one could type in the command to establish a
notation and perhaps use Headers to distinguish special input.

Much of the Mathematica pattern capability appears to be lost in the
Notations package. Or else it isn't very clear how to use it. Can we use the
general patterns, for example multiple arguments, arguments with specified
heads, or conditional patterns when establishing Symbols and Notations? Can
we use Rule based programming with entities established with Symbolize or
Notation? Without the use of general patterns I think that Notations is too
severely limited. I'm hoping that you will tell me that I am wrong here and
one can make general use of patterns! But it should be as easy as using
general patterns in regular Mathematica.

The modification of the notebook style sheet may be necessary and harmless
but it certainly does raise eyebrows with the user. It probably needs more
explanation in the documentation. Does it add a style sheet to the notebook
or does it modify the underlying style sheet? This is why I still question
if the palette is the best method for entering notations.

I still think that the documentation is not good enough. The very first
thing that a new user might try is the first example under Symbolize. I defy
anyone to freshly type that example in, and not just evaluate the example in
the Help notebook. It is definitely not What You See Is What You Type! If a
user can't get beyond that example what chance does he have?

As you explain below, the user has to be instructed about the use of the
underlying cell expressions. And once these are brought in the Notations
package is not quite the shortcut that users might have been hoping for. It
may be all right but it has to be explained and there have to be numerous
and COMMON examples.

In summary
1) I would like to see a better user interface and usability.
2) This is a difficulty subject and requires extra good documentation.
3) We need to know how to use general patterns and rule based programming
with notations.

I would dearly love to be able to use Notations. Renan Cabrera,
Jean-Francois Gouyet and I have a Tensorial package where we use Format
statements to format tensor output, and a number of other things such as
absolute derivatives, Lie derivatives or colored indices. It looks nice and
works, but the output cannot be copied and pasted. I was able to write some
MakeBoxes and MakeExpression statements that did allow the copying of output
and tab entry on indices, but it was delicate and version dependent so we
didn't include it in the package.  It would be very nice to make Notations
work on something like this.

David Park
djmp at

From: Jason Harris [mailto:jasonh at]
To: mathgroup at

Hi Andrzej,

[Notation example snipped]

>  On my system this example just fails miserabley (the
>  definiton of transmissionCoefficient does not parse) although it once
>  used to work. (Actually, I would like to hear from other people,
>  because either the Notation package is no longer working or something
>  is wrong with my installation).

I know these things can appear frustrating at times, but the Notation
package is working fine. In the example you have given, you have
managed to include the box wrapper twice in your Symbolize statement.
(You likely did this through copying the k subscript including box
wrapper and pasted it into a new Symbolize statement.)

>  Anyway, if this works on your system than the problem is solved. You
>  can symbolize subscripted variables and use them as if they were
>  symbols. On the other hand, in the past, when this package used to work
>  on my system, I got myself into a huge mess when I tried to evaluate
>  again a notebook that had previously worked correctly.

If there is some notebook corruption going on then we definitely want
to know about this. In the example you have given it is extremely
likely that you inadvertently caused the error with a copy and paste
from one symbolize statement to another. (I know notation statements
can be tricky and it is not all that hard to "hang yourself".)

>  Because of that I finally decided that relying on a package like this is
>  just too risky if you are doing any serious work.

Hmm... Actually I personally think its just the opposite. If you are
really doing serious work you need to know about typesetting and how
to enter expressions in notations which are familiar to
Mathematicians, physicists, and other users and have these notations
function correctly.

First a general comment:
When you are troubleshooting problems with setting up notations it is
often necessary to look at the underlying boxes representing the
typeset expression. You can do this through either the command key
shortcut of cmd-shift-E (OSX) and I think cntrl-shift-E (Win), or
through the menu item "Format" -> "Show Expression..."

Looking at the underlying boxes shows you how the typeset expression
is represented. As a Mathematica programmer you no doubt use FullForm
at times to examine how a certain pattern is structured. Its really
not too different with typesetting in that Mathematica functions through
MakeBoxes and MakeExpression which operate on these box structures. If
you don't have the correct structures, the boxes will not be
interpreted as they should be.

In a Symbolize statement waiting to be filled in the underlying
structure is

     RowBox[{"Symbolize", "[",
         TagStyle->"NotationTemplateStyle"], "]"}]], "Input"]

To see this load the notation package, type Esc-symb-Esc and then show
the underlying expression. The box structure to be symbolized must be
the first argument of this TagBox.

The tag box wrapper, NotationBoxTag, is necessary so you can enter
typeset expressions into Mathematica that are not currently
syntactically valid. Then once the Notation package gets a hold of
them, it compiles / translates these into corresponding rules for
MakeExpression and MakeBoxes that do what you instructed. The tag box
wrapper inertizes the box structure so it becomes syntactically valid
Mathematica input.

You can see this by copying out the box wrapper into a new cell and
entering some syntactically invalid input into the wrapper, say "x"
followed by "*", and then viewing how it is interpreted by
Mathematica. E.g. after loading the notation package paste the
following cell into Mathematica and interpret it:

       RowBox[{"x", "*"}],
       TagStyle->"NotationTemplateStyle"]], "Input"]

Then evaluate this interpreted cell. Then start a new cell and
evaluate FullForm[%]. The answer will be

NotationBoxTag[RowBox[List["x", "*"]]]

Thus the TagBox wrapper, NotationBoxTag, has allowed us to enter
something that is syntactically invalid and get the box structure into
the kernel. (Incidentally you can programmatically create symbolize
and notation statements this way.) The TagBox wrapper NotationBoxTag
can do this miraculous feat because it itself has a corresponding
notation. (The TagStyle option is set so you can get some visual
indication of where these tag box wrappers occur.)

So anyway getting back to your example if you look at the underlying
boxes you will see that instead of having

     RowBox[{"Symbolize", "[",
         SubscriptBox["k", "_"],
         TagStyle->"NotationTemplateStyle"], "]"}]], "Input"]

You had

     RowBox[{"Symbolize", "[",
           SubscriptBox["k", "_"],
         TagStyle->"NotationTemplateStyle"], "]"}]], "Input"]

i.e. the wrapper was in there twice. Fixing this mistake resolves your


Jason Harris
Wolfram Research

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