This is just a notational question, to see if there is a better way to write the following quantities:
- $ v_1 = (f_{y} + f_{z}, f_{x}+f_{z}, f_{x} + f_{y} )$
- $ v_2 = (f_{yy} + f_{zz}, f_{xx}+f_{zz}, f_{xx} + f_{yy} )$
- $ t_1 = f_{xy}f_xf_y + f_{xz}f_xf_z + f_{yz}f_yf_z $
where $f_i$ is the partial derivative with respect to $i$, for $f:\mathbb{R}^3\rightarrow \mathbb{R}$. So, $v_1(x,y,z),v_2(x,y,z)\in\mathbb{R}^3$ are vector fields, while $t_1(x,y,z)\in\mathbb{R}$ is a scalar field.
How can I write these with common operators on $f$ (e.g. $\nabla,\times,\cdot,\Delta,\nabla\cdot,\nabla\times,\otimes$ and so on) and/or are there some operators I am missing?