diffalg[print_ranking] - print a message describing the ranking of a differential polynomial ring.
|
Calling Sequence
|
|
print_ranking (R)
|
|
Parameters
|
|
R
|
-
|
differential polynomial ring
|
|
|
|
|
Description
|
|
•
|
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.
|
|
|
Examples
|
|
Important: The diffalg package has been deprecated. Use the superseding package DifferentialAlgebra instead.
>
|
|
>
|
|
| (1) |
>
|
|
>
|
|
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]
| |
>
|
|
| (2) |
>
|
|
| (3) |
>
|
|
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
| |
>
|
|
| (4) |
>
|
|
| (5) |
>
|
|
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
| |
>
|
|
| (6) |
>
|
|
| (7) |
>
|
|
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]
| |
|
|
Download Help Document
Was this information helpful?