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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

• 

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.

Examples

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

withdiffalg:

p:=ux,y+vx,x;q:=vx+vy,y

p:=ux,y+vx,x

q:=vx+vy,y

(1)

Q:=differential_ringderivations=x,y,ranking=grlexAu,v:

print_rankingQ

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]

leaderp,Q,leaderq,Q

ux,y,vy,y

(2)

R:=differential_ringderivations=x,y,ranking=grlexBu,v

R:=PDE_ring

(3)

print_rankingR

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

leaderp,R,leaderq,R

vx,x,vy,y

(4)

S:=differential_ringderivations=x,y,ranking=lexu,v

S:=PDE_ring

(5)

print_rankingS

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

leaderp,S,leaderq,S

vx,x,vx

(6)

T:=differential_ringderivations=x,y,indeterminates=u,v,leaders_ofp,q=ux,y,vx

T:=PDE_ring

(7)

print_rankingT

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]

See Also

diffalg(deprecated), diffalg(deprecated)/differential_algebra, diffalg(deprecated)/differential_ring, diffalg(deprecated)[leader], DifferentialAlgebra[Tools][Display]


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