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

The print_ranking command prints a message describing the ranking defined on a differential polynomial ring R set up with the differential_ring command.

The ranking of a differential polynomial ring R is a total ordering over the set of all the derivatives of the differential indeterminates of R that is compatible with derivation (see ranking)

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

In lists, leftmost elements are greater than rightmost ones.
The derivatives of [u, v] are ordered by grlexA:
_U [tau] > _V [phi] when
    |tau| > |phi| or
    |tau| = |phi| and _U > _V w.r.t. the list of indeterminates or
    |tau| = |phi| and _U = _V and tau > phi w.r.t. [x, y]

In lists, leftmost elements are greater than rightmost ones.
The derivatives of [u, v] are ordered by grlexB:
_U [tau] > _V [phi] when
    |tau| > |phi| or
    |tau| = |phi| and tau > phi w.r.t. [x, y] or
    tau = phi and _U > _V w.r.t. the list of indeterminates

In lists, leftmost elements are greater than rightmost ones.
The derivatives of [u, v] are ordered by lex:
_U [tau] > _V [phi] when
    tau > phi for the lex. order [x, y] or
    tau = phi and _U > _V w.r.t. the list of indeterminates

In lists, leftmost elements are greater than rightmost ones.
The derivatives of [u, v] are ordered by weights:
Weights are [u = 3, v = 0, x = 3, y = 1]
_U [tau] > _V [phi] when
    weight (_U [tau]) > weight (_V [phi]) or
    weights are equal and _U > _V w.r.t. the list of indeterminates or
    weights and indeterminates are equal and
        tau > phi for the lex. order [x, y]