Typos in the paper

[DanShaders]

It seems that there should be no "= \varnothing" at the beginning of the second column on page 10. And no "-s" in "ingredients", likewise no "-o" in "computationo".

As we are already talking about the article, how is this fact at the very end of the first column on page 9 being used later in the proof?

[jk-jeon]

It seems that there should be no "= \varnothing" at the beginning of the second column on page 10. And no "-s" in "ingredients", likewise no "-o" in "computationo".

Thanks, I'll upload the fixed manuscript.

As we are already talking about the article, how is this fact at the very end of the first column on page 9 being used later in the proof?

I'm assuming you are asking how that is used for the proof of Theorem 4.4, part 2. This inequality is used in the last part of the proof, for the case when

$$ \frac{n{1}p{}}{q_{}} - \left\lfloor\frac{n{1}p{}}{q_{}}\right\rfloor = \frac{n{2}p{}}{q_{}} - \left\lfloor\frac{n{2}p{}}{q_{}}\right\rfloor. $$

The claim "Clearly, in this case we should have $n{1} < n{2}$..." follows from the said inequality.

(It seems markdown doesn't like the stars in the latex equations...)

Thanks a lot!

[DanShaders]

The claim "Clearly, in this case we should have n1<n2..." follows from the said inequality.

Got it. I cannot say it is that "clear" then)

Thank you!

[DanShaders]

Oops

[jk-jeon]

Uploaded the fixed one.

Got it. I cannot say it is that "clear" then)

Also made this really clear :)