Succinctly Describe Common Types of Matrices

[NV-Codes]

MathCAT Version

MathCAT-0.6.8 RC 2 (NVDA Add-On)

Description

It would be helpful for MathCAT to recognize

• identity matrices.
  • Example: "The four by four identity matrix"
• zero matrices.
  • Example: "The three by one zero matrix"
• diagonal matrices.
  • Example: "The two by two diagonal matrix, row 1 column 1, h-bar over two, row 2 column 2, negative h-bar over two"

The identity matrix is a special kind of diagonal matrix whose verbalization rule should override that of the general diagonal matrix.

It seems reasonably safe to employ these shorthand descriptions in all relevant cases in ClearSpeak and SimpleSpeak and to leave the current behavior in LiteralSpeak. Perhaps there are other considerations.

[NSoiffer]

I've thought about doing that for years (including back when I worked on MathPlayer). Thanks for adding this issue. It's a bit lower priority. I think xpath will allow me to recognize those cases (certainly the zero matrix), but I need to think about it.

Implementation maybe a couple of months away due to many high priority issues, including helping with pending translations, that I need to do first.

[NV-Codes]

Sounds good!

[NSoiffer]

[updated with correct patterns]

Just to save this somewhere, I think I can use the following patterns (not tested):

• zero matrix (check first): not( */*/*[not(self::m:mn and .= 0)] )
• identity matrix (check second): count(*) = count(*[1]/*) and not( */*/*[not(self::m:mn and .= 0)][count(../preceding-sibling::*)!=count(../../preceding-sibling::*) or .!= 1] )
• symmetric matrix: count(*) = count(*[1]/*) and not( */*/*[not(self::m:mn and .= 0)][count(../preceding-sibling::*)!=count(../../preceding-sibling::*) )

[NSoiffer]

@NV-Codes: I was editing some of the code related to speaking tables and decided I'd go ahead and add these also. For diagonal matrices, I was planning to have a Terse version that only said row numbers, not row and column since they are always the same. In doing the implementation, I found that without significantly more work, I can only get column numbers to speak. So "the 3 by 3 diagonal matrix; column 1; 2; column 2; 1; column 3; x squared;". I hope that is ok, at for now.

[NV-Codes]

Great, that works!

[NV-Codes]

This seems to work perfectly in MathCAT-0.6.8 RC 6!

Identity Matrix

$$\begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{bmatrix}$$

Speech: "the 4 by 4 identity matrix"

Zero Matrix

$$\begin{bmatrix} 0 \\ 0 \\ 0 \end{bmatrix}$$

Speech: "the 3 by 1 zero matrix"

Diagonal Matrix

$$\begin{bmatrix} \frac{\hbar}{2} & 0 \\ 0 & -\frac{\hbar}{2} \end{bmatrix}$$

Speech: "the 2 by 2 diagonal matrix; column 1; h bar over 2,; column 2; negative h bar over 2"