Displayed systems of equations with identifying numbers and complex matrices

[rsherwood12]

Hello! The Numerical Analysis chapter I'm working on has several systems of equations, with identifying numbers in parentheses at the right margin. There are also lots of matrices, some of which have dots in vertical and diagonal patterns.

Starting with example 1 in the attached: Where would I place the identifier at the right in print (6.1) in relation to the Nemeth Code switch indicators and required blank lines?

Are the equations in this example considered aligned by term? They do not fit across the width of the braille page, so I am unsure how to align the terms if I have to divide each equation before the equals sign.

Is it alright to treat the vertical ellipses as a new "equation" at the displayed margin of cell 3? I am beginning to think as I read the chapter that the placement of the vertical ellipses may have meaning.

I am not familiar with this form of math. Do you think the space before the colon is significant, or can I remove the space and use the punctuation indicator before the colon?

Normally the Nemeth Code terminator would come before the period ending the sentence, but in this case, should it come after the period, and a blank line? Would the next sentence begin right after the Nemeth Code terminator, or does it have to be on a line by itself? I have put my attempt at brailling the first example in the attached document.

In example 2: For the four equations labeled (6.2), many of the same questions apply. These terms are clearly aligned in print. I think I have it aligned properly, but I wanted to get a double check.

In example 3: The vertical ellipses start to look like their placement is intentional because the book is introducing matrices containing dots, both vertical, horizontal and diagonal. In the first system here, would you change them to regular ellipses and align them beneath ⠁⠆⠆⠭⠆ and ⠨⠅? Once we get to matrices with vertical lines of dots between columns, does it make sense to make these tactile graphics?

Example 4 shows a matrix with diagonal lines of dots. I think for sure this should be a tactile, yes?

Thanks for your expertise!
Rebecca

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[kdejute]

G'day, Rebecca!

Thank you for the questions.

1. Labels for displayed mathematical items should be included in the Nemeth "bubble" for the math item(s). In Example 1, I would place the opening Nemeth Code indicator after the end of text. Then I would insert the blank line and then the label, followed by the system of equations (with no blank line between the label and the system of equations).
2. It does seem that Example 1's and Example 2's equations' terms are aligned in print. In Example 1, the way you've aligned the first parts of each equation and then run over before the equals is what I would do.
3. I believe your treatment of print's vertical ellipsis in Example 1 is appropriate and will not mislead the student.
4. Your treatment of the colon is appropriate. "E sub 1", "E sub 2", and "E sub n" seem to be labels for "Equation 1:", "Equation 2:", and "Equation n:".
5. I wouldn't change a thing about your placement of the Nemeth Code terminator and the period at the end of "E sub n" in Example 1. The Guidance does say that the terminator must be placed on a line by itself.
6. Your alignment of the system of equations in Example 2 is almost perfect; the "x sub 4" in the first equation needs to be moved four cells to the right.
7. In Example 3, the first pair of vertical ellipses (in the system of equations) seems just to be print getting fancy and trying to foreshadow the ellipses in the matrices that follow. I would transcribe this pair of vertical ellipses as you transcribed the ellipsis in Example 1 (a series of three dot threes beginning in the cell for displayed material).
8. Example 3's vertical dotted line does seem to be a great candidate for a tactile graphic. I do not believe it is a mathematical sign at all.
9. I think the diagonal dotted lines (all consisting of more than the three dots of an ellipsis) are also not so much mathematical as gestural and so would be best represented with tactile lines.

Again, thank you for your questions. Please do let me know if you have concerns following on this.

Cheers!
–Kyle

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