Erroneous truncated output from MathML with <mmultiscripts>

[nsoiffer]

Erroneous truncated output from MathML with

from mathcat.

[NSoiffer]

Seems like AT is batting 0% on this one. It's a tensor notation and the position of the indices matter. I'm not sure what the semantic speech should be, but it is probably something like

cap R with indices lower i, upper j, lower k, lower l

I'm going to need to some digging about what is appropriate in braille. Tensor notation is way above what UEB covers in their instructions/examples. I don't remember seeing it in the Nemeth book either. The problem is that the pairs matter (each pair is like matrix entry), and a singleton index is accessing the row/col (depending on whether it is a sub/superscript). Because of this, you can't say the k is a subscript of expression that precedes it -- it is sort of a continuation of the preceding scripts.

If you see something in Nemeth or UEB that seems like it might cover this, please me know.

[brichwin]

I'm not sure if the following adds anything, I tried creating a LaTeX equivalent:

R_i{}^j{}_k{}_l

In the MathCAT demo, the LaTeX snip created a similar visual rendering and provided the following text and braille:

• Clearspeak: R sub i, with 3 prescripts, none j k none l none
• Nemeth braille: ⠠⠗⠰⠊⠘⠚⠐

In the MathML 3 spec, section 3.4.7.1 it says:

The argument sequence consists of the base followed by zero or more pairs of vertically-aligned subscripts and superscripts (in that order) that represent all of the postscripts.

I'm out of my depth here! It seems MathCAT/Clearspeak recognized the multiscript nature and I'm guessing it is incorrect in using "prescripts" instead of "postscripts"; And, isn't the i part of the postscripts?. Assuming I understand that model, I would have expected R with 4 postscripts, i none, none j, k none, l none (adding commas to aid in perceiving postscript pairs).

I'm guessing the indication of "none" for missing scripts is useful - However, your suggested speech of "cap R with indices lower i, upper j, lower k, lower l" seems easier to listen to.

The braille output appears to be truncated again... it looks like it attempted to add a back to base indicator after the superscript k and then stopped for some reason. I'm a member of the National Braille Association, so I can post in their forums. I'll ask there if anyone knows how to handle multiscripts (assuming I can craft the question correctly).

[brichwin]

Mary Stores pointed out to me that Nemeth Rule XIII Section 82 describes both Simultaneous as well as Non-Simultaneous superscripts and subscripts (page 96) - The non-simultaneous examples appears to describe Nemeth braille for prescripts and postscripts similar to the tensor indices notation:

I've posted a question to the Nemeth forum on the National Braille Authority, but it still has not cleared moderation...

[NSoiffer]

I'm getting close to getting mmultiscripts right.

The Duxbury output is not correct: ⠠⠗⠰⠊⠅⠇⠘⠚ in ascii braille is ,r;ikl^j. In that form, it is easy to see that the order of the indices has been lost. According to 82.b (above) a baseline indicator (dot 5) is needed between the scripts, and there are none in the Duxbury output, so that's another mistake.

Once I get all the tests working, I'd be curious to know how many of the mmultiscripts tests I have have bugs in Duxbury's translator. Would you be able to run 10 tests or so?

[brichwin]

Certainly - Mary and I could run tests through Duxbury, if that's what you mean.

[NSoiffer]

I'm very curious to know how well MathCAT stacks up against Duxbury, so the more tests you are willing to run, the better.

Here's what MathCAT now produces (Nemeth and ASCII braille):

⠠⠗⠰⠊⠐⠘⠚⠐⠰⠅⠐⠰⠇
,r;i"^j";k";l

Does this look right?

I need to fix the UEB next.

[brichwin]

I received feedback on the post I made on the National Braille Association's Nemeth Code for Math and Science forum. My original post was eaten by their SPAM filter due to the links I put in it. Here is Lindy Walton's reply:
From: https://www.nationalbraille.org/forums/topic/missing-post-nemeth-for-tensor-indices-notation-multiscripts/#post-39442

[brichwin]

Well, Duxbury doesn't do well with this:

The ASCII and Unicode versions:
,r;ikl^j
⠠⠗⠰⠊⠅⠇⠘⠚

I might write this up and send it to Duxbury as an issue as well.

[NSoiffer]

@brichwin: could you check with Lindy about the translation. I don't think she realized that the k and the l are in separate subscripts. Lindy's Nemeth translation places them in the same subscript. That is mathematically wrong because it would imply the last tensor index is "k times l" whereas there are actually four of them and the 'k' and 'l' are not (implied) multiplication. With that correction (and knowing that MathCAT leaves it up the to caller to add the Nemeth switch indicators), ⠠⠗⠰⠊⠐⠘⠚⠐⠰⠅⠐⠰⠇ as the correct MathCAT generates appears correct.

[brichwin]

@brichwin: could you check with Lindy about the translation... With that correction (and knowing that MathCAT leaves it up the to caller to add the Nemeth switch indicators), ⠠⠗⠰⠊⠐⠘⠚⠐⠰⠅⠐⠰⠇ as the correct MathCAT generates appears correct.

Here is Lindy Walton's reply:

Hi Brian.

I am unfamiliar with MathCAT or with the topic of tensor indices and multiscripts. As a transcriber, I look at the print and translate it to Nemeth according to what I have learned about print-to-braille transcription. The possibility of having side-by-side letters at the same subscript level yet meaning two different "multiscripts" is not something I am familiar with mathematically. Insertion of the dot 5 before letter "l" does indeed separate it from letter "k" in a similar manner that it functions as a separator between subscript "i" and superscript "j". I see nothing wrong with this transcription.

Lindy

[NSoiffer]

@brichwin: thanks for checking.