The ToJet and FromJet commands rewrite mathematical expressions back and forth using jet and function notation respectively.

For ToJet, the option notation can be used to select the jet notation. The possible values are jet and tjet, respectively corresponding to the notations jetvariables and jetvariableswithbrackets explained in the help page of the equivalent PDEtools[ToJet] command.

For FromJet, the option differentiationnotation can be used to select the notation used for derivatives.  The possible values are diff, Diff and D, explained in the help page of the equivalent PDEtools[FromJet] command.

$\mathrm{with}\left(\mathrm{DifferentialAlgebra}:-\mathrm{Tools}\,\mathrm{ToJet}\,\mathrm{FromJet}\right)$

$\left[\mathrm{ToJet}\,\mathrm{FromJet}\right]$

$\mathrm{DepVars}≔\left[u\left(x\,t\right)\,v\left(t\right)\,w\left(y\right)\right]$

$\mathrm{DepVars}≔\left[u\left(x\,t\right)\,v\left(t\right)\,w\left(y\right)\right]$

$\mathrm{PDE}≔\mathrm{diff}\left(u\left(x\,t\right)v\left(t\right)w\left(y\right)\,x\right)+\mathrm{diff}\left(u\left(x\,t\right)v\left(t\right)w\left(y\right)\,t\,y\right)$

$\mathrm{PDE}≔\left(\frac{\partial }{\partial x}u\left(x\,t\right)\right)v\left(t\right)w\left(y\right)+\left(\frac{\partial }{\partial t}u\left(x\,t\right)\right)v\left(t\right)\left(\frac{\ⅆ}{\ⅆy}w\left(y\right)\right)+u\left(x\,t\right)\left(\frac{\ⅆ}{\ⅆt}v\left(t\right)\right)\left(\frac{\ⅆ}{\ⅆy}w\left(y\right)\right)$

$\mathrm{jet\_PDE}≔\mathrm{ToJet}\left(\mathrm{PDE}\,\mathrm{DepVars}\right)$

$\mathrm{jet\_PDE}≔u{v}_t{w}_y+vw{u}_x+v{u}_t{w}_y$

$\mathrm{tjet\_PDE}≔\mathrm{ToJet}\left(\mathrm{PDE}\,\mathrm{DepVars}\,\mathrm{notation}=\mathrm{tjet}\right)$

$\mathrm{tjet\_PDE}≔u\left[\right]v_t{w}_y+u_{t}v\left[\right]w_y+u_{x}v\left[\right]w\left[\right]$

$\mathrm{FromJet}\left(\mathrm{jet\_PDE}\,\mathrm{DepVars}\right)$

$\left(\frac{\partial }{\partial x}u\left(x\,t\right)\right)v\left(t\right)w\left(y\right)+\left(\frac{\partial }{\partial t}u\left(x\,t\right)\right)v\left(t\right)\left(\frac{\ⅆ}{\ⅆy}w\left(y\right)\right)+u\left(x\,t\right)\left(\frac{\ⅆ}{\ⅆt}v\left(t\right)\right)\left(\frac{\ⅆ}{\ⅆy}w\left(y\right)\right)$

$\mathrm{FromJet}\left(\mathrm{jet\_PDE}\,\mathrm{DepVars}\,\mathrm{differentiationnotation}='\mathrm{Diff}'\right)$

$\left(\frac{\partial }{\partial x}u\left(x\,t\right)\right)v\left(t\right)w\left(y\right)+\left(\frac{\partial }{\partial t}u\left(x\,t\right)\right)v\left(t\right)\left(\frac{\ⅆ}{\ⅆy}w\left(y\right)\right)+u\left(x\,t\right)\left(\frac{\ⅆ}{\ⅆt}v\left(t\right)\right)\left(\frac{\ⅆ}{\ⅆy}w\left(y\right)\right)$

$\mathrm{FromJet}\left(\mathrm{jet\_PDE}\,\mathrm{DepVars}\,\mathrm{differentiationnotation}='\mathrm{D}'\right)$

${\mathrm{D}}_1\left(u\right)\left(x\,t\right)v\left(t\right)w\left(y\right)+{\mathrm{D}}_2\left(u\right)\left(x\,t\right)v\left(t\right)\mathrm{D}\left(w\right)\left(y\right)+u\left(x\,t\right)\mathrm{D}\left(v\right)\left(t\right)\mathrm{D}\left(w\right)\left(y\right)$