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Minor fixes for chapters 6, 7 and 8 #109

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@Vindaar Vindaar commented Jun 27, 2024

Hey!

First of all thanks for the great resource! Really valuable and well explained.

I went through chapters 6, 7 and 8 over the last few days. I only realized halfway through 6 that the TeX source of the document is public. After I realized that, I fixed several minor issues when I encountered them.

Mostly it's typos and some (imo) stylistic improvements. In the Groth16 chapter I also added a few more equation references, because I found it very helpful to quickly glance back and forth and in some instances that was missing (evince's preview is useful for that!).

If desired I can add some screenshots for what the changed things look like (i.e. typesetting the Malbolge in \text{} for the 'Malbolge language').

Personally, I would probably also typeset other things (e.g. true / false) in \text when used inside math mode (the letter spacing is not ideal when just writing in math mode). If wanted, I can do that one of these days.

In one commit I forgot to disable auto-fill-mode in emacs, so the paragraphs are short there. I can fix that up (or line break everything to a sensible level, if that was desired).

Anyway, if you don't want to include one or more of the commits, just let me know and I'll kill them!

It should be W_4, same as in the previous (referenced) examples.
As far as I understand in the JS 'Circom 1' this was supported. But at
this point, I suppose it's more sensible to have code that is valid
for Circom 2.
Instance variables and witness variables in the previous part always
individually start from index 1. This rule is broken in the first
fixed circuit.

In the second one this is also broken and in addition in the
simplified circuit we should rename the witnesses to go from 1 to 3
instead of having {1, 3, 4}.
Note: I also changed the

0 \leq j < m

to

0 \leq j \leq m

because I first didn't realize the second operator was not a less than
equal, but a real less than.
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