ec-af.html

    <div class="titlepage">
      <div>
        <div>
          <h2 class="title"><a name="_tutorial"></a>Addition formula</h2>
        </div>
      </div>
    </div>

<p>
Consider $P_1(x_1,y_1)$ and $P_2(x_2,y_2) \in E_K$. Then we define $$P_3=P_1+P_2$$, where
$$x_3=\lambda^2 -x_1 -x_2$$

$$y_3=(x_2-x_1)\lambda - y_1$$

with $$ \lambda = \frac{y_2-y_1}{x_2-x_1}, when \color{red}{x_1 \neq x_2}$$ and 
$$ \lambda = \frac{3x_1^2+A}{2y_1}, when \color{red}{x_1 = x_2}$$

</p>