Add examples for all SFR gadgets about book_about_quadratization HOT 2 OPEN

I have added examples with n=4 and k=2, which just fit within one line.

from book_about_quadratization.

Very well done!

• For consistency with other examples like Eq. 11, 25, 38, etc. it is preferable that we go from highest degree to lowest degree, so the 6b1b2b3b4 can go first and the quadratic terms can go last.
• I appreciate the brackets around S_2, S_3 and S_4 which helps to recognize how the terms can be grouped together. I'd prefer to remove the brackets around the S_2 though since it takes up less space, and is not really needed. If it didn't take up so much space I'd also prefer to remove the brackets from the S_3, but then we would need to add the coefficient "3" for each term, and it might no longer fit on one line without making the font size inconsistent.

Apart from these 2 points, I think you have made smart choices in every regard. Maybe the (N choose 2) functions can be expanded a bit so that they look more like quadratizations that people are used to seeing (not a FULL expansion, but as a product of polynomials).

from book_about_quadratization.