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

Let fp and fq denote the leaders of p and q. The function delta_leader returns a sequence, if it exists, of derivations s such that fp = differentiate (fq, s, R).

The function returns FAIL if p or q belongs to the ground field of R or if fp and fq are derivatives of different differential indeterminates.

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

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

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

$R≔\mathrm{PDE\_ring}$

$p≔{u\left[x,x,y\right]}^2-4u\left[\right]$

$p≔u_{x,x,y}^2-4u\left[\right]$

$q≔u\left[x\right]$

$q≔u_x$

$\mathrm{delta\_leader}\left(p\,q\,R\right)$

$x,y$