Comments on linear transformation- x2^2-x1x3.mw worksheet:

Reducing quadratic form to the format x_2^2-x_1x_3 is a sequence of elementary algebraic transformations. 

1. Given a point on the curve, we make a linear transformation to get [0,0,1]. Then, we intersect the curve with a couple of lines to get more pts. Now, [1,0,0], [0,1,0], [0,0,1] are on the curve. 

2. We then do simple linear transformations to eliminate certain terms. We do this for a couple of times. So, we're looking at ..x1x2 + ..x1x3 + ..x2x3 and all of those coefficients are non-zero.

3. Finally, we do some linear transformations to get x_2^2-x_1x_3.