deletions | additions       diff --git a/Sketchy Generation.tex b/Sketchy Generation.tex  index cd8ee52..95c73dc 100644  --- a/Sketchy Generation.tex  +++ b/Sketchy Generation.tex 
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\end{equation}  As the divergence operator maps a vecotr field to a scalar field it must be a row vector. As the divergence of any curl is zero it must result in 0 under the left operation. This gives a likely form \begin{equation}  \begin{bmatrix} \partial_z^{-1}\partial_y^{-1} \partial_x  & \partial_z^{-1}\partial_x^{-1} \partial_y  & \partial_y^{-1}\partial_x^{-1} \partial_z  \end{bmatrix} \begin{bmatrix}  0 & -\partial_z & \partial_y \\  \partial_z & 0 & -\partial_x \\  -\partial_y & \partial_x & 0  \end{bmatrix}  =\begin{bmatrix}\partial_x^{-1}-\partial_x^{-1}&\partial_y^{-1}-\partial_y^{-1}&\partial_z^{-1}-\partial_z^{-1}\end{bmatrix} =\begin{bmatrix}0&0&0\end{bmatrix}  \end{equation}  Knowing this we require the gradient operator to be a column vector such that when it left operates on the divergence row operator we may create the matrix form above. This gives the form \begin{equation}  \begin{bmatrix} \partial_x^2\partial_y\partial_z \partial_x  \\ \partial_x\partial_y^2\partial_z \partial_y  \\ \partial_x\partial_y\partial_z^2 \partial_z  \end{bmatrix} \begin{bmatrix} \partial_z^{-1}\partial_y^{-1} \partial_x  & \partial_z^{-1}\partial_x^{-1} \partial_y  & \partial_y^{-1}\partial_x^{-1} \partial_z  \end{bmatrix} =  \begin{bmatrix}  \partial_x^2 & \partial_y\partial_x & \partial_z\partial_x \\