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

The command denote converts the differential polynomial q given in the notation  defined on R to the notation code.

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

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

$R≔\mathrm{differential\_ring}\left(\mathrm{derivations}=\left[t\right]\,\mathrm{ranking}=\left[u\right]\right)$

$R≔\mathrm{ODE\_ring}$

$p≔{u\left[t\right]}^2-4u\left[\right]$

$p≔u_t^2-4u\left[\right]$

$\mathrm{denote}\left(p\,\mathrm{diff}\,R\right)$

${\left(\frac{\ⅆ}{\ⅆt}u\left(t\right)\right)}^2-4u\left(t\right)$

$Q≔\mathrm{differential\_ring}\left(\mathrm{derivations}=\left[t\right]\,\mathrm{ranking}=\left[u\right]\,\mathrm{notation}=\mathrm{diff}\right)$

$Q≔\mathrm{ODE\_ring}$

$q≔\mathrm{diff}\left(u\left(t\right)\,t\,t\right)-tu\left(t\right)+{\mathrm{diff}\left(u\left(t\right)\,t\right)}^2$

$q≔\frac{{\ⅆ}^2}{\ⅆt^2}u\left(t\right)-tu\left(t\right)+{\left(\frac{\ⅆ}{\ⅆt}u\left(t\right)\right)}^2$

$\mathrm{denote}\left(q\,\mathrm{jet}\,Q\right)$

$-tu\left[\right]+u_t^2+u_{t,t}$