diffalg(deprecated)/leader - Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : diffalg(deprecated)/leader

diffalg

  

leader

  

return the leader of a differential polynomial

  

rank

  

return the rank of a differential polynomial

  

initial

  

return the initial of a differential polynomial

  

separant

  

return the separant of a differential polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

leader (q, R)

rank (q, R)

initial (q, R)

separant (q, R)

Parameters

q

-

differential polynomial

R

-

differential polynomial ring

Description

• 

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

• 

The leader of a differential polynomial q is the greatest derivative occurring in q with respect to the ranking of R.

• 

The rank of q is the leader of q raised to the degree of q with respect to its leader.

• 

The initial of q is the leading coefficient of q with respect to its leader.

• 

The separant of q is the partial derivative of q with respect to its leader. It is also the initial of any proper derivative of q.

• 

If q belongs to the ground field R, then leader, rank, initial and separant return an error message.

• 

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

• 

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

• 

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

• 

The command with(diffalg,separant) 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:

Rdifferential_ringderivations=t,ranking=u

R:=ODE_ring

(1)

put1ut,t2+ut,t+ut2+tu[]

p:=ut1ut,t2+ut,t+ut2+tu[]

(2)

leaderp,R

ut,t

(3)

rankp,R

ut,t2

(4)

initialp,R

ut1

(5)

separantp,R

2utut,t2ut,t+1

(6)

 

Kfield_extensiontranscendental_elements=a,b:

Rdifferential_ringfield_of_constants=K,derivations=t,ranking=u

R:=ODE_ring

(7)

p2utbut,t2+u[]ut,t2a+ut

p:=2utbut,t2+u[]ut,t2a+ut

(8)

initialp,R

2abut+u[]a

(9)

leaderp,R

ut,t

(10)

rankp,R

ut,t2

(11)

initialp,R

2abut+u[]a

(12)

separantp,R

4abutut,t+2u[]ut,ta

(13)

 

pux,yvx,y,y2+ux,x2+ux

p:=ux,yvx,y,y2+ux,x2+ux

(14)

R1differential_ringderivations=x,y,ranking=u,v

R1:=PDE_ring

(15)

leaderp,R1

ux,x

(16)

rankp,R1

ux,x2

(17)

initialp,R1

1

(18)

separantp,R1

2ux,x

(19)

initialdifferentiatep,x,x,R1,R1

2ux,x

(20)

R2differential_ringderivations=x,y,ranking=u,v

R2:=PDE_ring

(21)

leaderp,R2

vx,y,y

(22)

rankp,R2

vx,y,y2

(23)

initialp,R2

ux,y

(24)

separantp,R2

2vx,y,yux,y

(25)

initialdifferentiatep,x,x,R2,R2

2vx,y,yux,y

(26)

See Also

diffalg(deprecated)

diffalg(deprecated)/differential_algebra

diffalg(deprecated)/differential_ring

diffalg(deprecated)/field_extension

diffalg(deprecated)[differentiate]

DifferentialAlgebra[Tools][Get]

DifferentialAlgebra[Tools][Initial]

DifferentialAlgebra[Tools][LeadingCoefficient]

DifferentialAlgebra[Tools][LeadingDerivative]

DifferentialAlgebra[Tools][LeadingRank]

DifferentialAlgebra[Tools][Separant]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam