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

The function greater returns true if the rank of p is greater than the one of q. Otherwise, false is returned.

p has greater rank than q if

(a)  q belongs to the ground field of R and p does not,

(b)  the leader of p is greater than the leader of q with respect to the ranking of R, or

(c)  p and q have the same leader  and the degree,  in  this common leader,  of  p is greater than the one of  q.

The function greater provides only a pre-order on R.

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

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

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

$R≔\mathrm{PDE\_ring}$

$\mathrm{greater}\left(u\left[x\right]\,u\left[y,y\right]\,R\right)$

$\mathrm{true}$

$\mathrm{greater}\left({u\left[x,x\right]}^2+u\left[y\right]\,{u\left[y,y\right]}^5{u\left[x,x\right]}^2+1\,R\right)$

$\mathrm{false}$