Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.

The function derivatives returns the set of the derivatives occurring in the differential polynomial p.

If the third parameter is present, the function returns the list of the derivatives, sorted increasingly or decreasingly, with respect to the ranking of R.

The command with(diffalg,derivatives) allows the use of the abbreviated form of this command.

$\mathrm{with}\left(\mathrm{diffalg}\right)\:$

$K≔\mathrm{field\_extension}\left(\mathrm{transcendental\_elements}=\left[u\left[t\right]\right]\right)\:$

$R≔\mathrm{differential\_ring}\left(\mathrm{field\_of\_constants}=K\,\mathrm{derivations}=\left[x\,y\right]\,\mathrm{ranking}=\left[\mathrm{lex}\left[u\right]\right]\right)$

$R≔\mathrm{PDE\_ring}$

$p≔u\left[x\right]u\left[t\right]+u\left[x,x\right]+{u\left[x,x\right]}^2+x{u\left[x,y,y\right]}^2+1$

$p≔x{u}_{x,y,y}^2+u_x{u}_t+u_{x,x}^2+u_{x,x}+1$

$\mathrm{derivatives}\left(p\,R\,'\mathrm{increasingly}'\right)$

$\left[u_x\,u_{x,y,y}\,u_{x,x}\right]$