diffalg(deprecated)/print_ranking - Help

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.

 > $\mathrm{with}\left(\mathrm{diffalg}\right):$
 > $p≔{u}_{x,y}+{v}_{x,x};$$q≔{v}_{x}+{v}_{y,y}$
 ${p}{:=}{{u}}_{{x}{,}{y}}{+}{{v}}_{{x}{,}{x}}$
 ${q}{:=}{{v}}_{{x}}{+}{{v}}_{{y}{,}{y}}$ (1)
 > $Q≔\mathrm{differential_ring}\left(\mathrm{derivations}=\left[x,y\right],\mathrm{ranking}=\left[{\mathrm{grlexA}}_{u,v}\right]\right):$
 > $\mathrm{print_ranking}\left(Q\right)$
 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]
 > $\mathrm{leader}\left(p,Q\right),\mathrm{leader}\left(q,Q\right)$
 ${{u}}_{{x}{,}{y}}{,}{{v}}_{{y}{,}{y}}$ (2)
 > $R≔\mathrm{differential_ring}\left(\mathrm{derivations}=\left[x,y\right],\mathrm{ranking}=\left[{\mathrm{grlexB}}_{u,v}\right]\right)$
 ${R}{:=}{\mathrm{PDE_ring}}$ (3)
 > $\mathrm{print_ranking}\left(R\right)$
 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
 > $\mathrm{leader}\left(p,R\right),\mathrm{leader}\left(q,R\right)$
 ${{v}}_{{x}{,}{x}}{,}{{v}}_{{y}{,}{y}}$ (4)
 > $S≔\mathrm{differential_ring}\left(\mathrm{derivations}=\left[x,y\right],\mathrm{ranking}=\left[{\mathrm{lex}}_{u,v}\right]\right)$
 ${S}{:=}{\mathrm{PDE_ring}}$ (5)
 > $\mathrm{print_ranking}\left(S\right)$
 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
 > $\mathrm{leader}\left(p,S\right),\mathrm{leader}\left(q,S\right)$
 ${{v}}_{{x}{,}{x}}{,}{{v}}_{{x}}$ (6)
 > $T≔\mathrm{differential_ring}\left(\mathrm{derivations}=\left[x,y\right],\mathrm{indeterminates}=\left\{u,v\right\},\mathrm{leaders_of}\left(\left[p,q\right]\right)=\left[{u}_{x,y},{v}_{x}\right]\right)$
 ${T}{:=}{\mathrm{PDE_ring}}$ (7)
 > $\mathrm{print_ranking}\left(T\right)$
 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]