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DifferentialAlgebra[Tools]

  

Differentiate

  

differentiates a differential rational fraction

 

Calling Sequence

Parameters

Options

Description

Examples

Calling Sequence

Differentiate(p, theta, R, opts)

Differentiate(L, theta, R, opts)

Differentiate(ideal, theta, opts)

Parameters

p

-

a differential rational fraction

L

-

a list or a set of differential polynomials or rational fractions

theta

-

a sequence of derivation operators

R

-

a differential polynomial ring or ideal

ideal

-

a differential ideal

opts (optional)

-

a sequence of options

Options

• 

The opts arguments may contain one or more of the options below.

• 

fullset = boolean. In the case of the function call Differentiate(ideal,theta), applies the function also over the differential polynomials which state that the derivatives of the parameters are zero. Default value is false.

• 

notation = jet, tjet, diff or Diff. Specifies the notation used for the result of the function call. If not specified, the notation of p is used.

• 

memout = nonnegative. Specifies a memory limit, in MB, for the computation. Default is zero (no memory out).

Description

• 

The function call Differentiate(p, theta, R) returns the derivative of p with respect to theta. The parameter p is regarded as a differential polynomial or a differential rational fraction of R, or of its embedding ring if R is an ideal.

• 

The parameter theta is a possibly empty sequence of differential operators. See DifferentialAlgebra for more details.

• 

The function call Differentiate(L, theta, R) returns the list or the set of the derivatives of the elements of L with respect to theta.

• 

If ideal is a regular differential chain, the function call Differentiate(ideal, theta) returns the list of the derivatives of the chain elements. If ideal is a list of regular differential chains, the function call returns a list of lists of derivatives.

• 

This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form Differentiate(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[Tools][Differentiate](...).

Examples

withDifferentialAlgebra:withTools:

RDifferentialRingderivations=t,blocks=u

R:=differential_ring

(1)

Differentiateut24u,t,R

2utut,t4ut

(2)

Differentiateu,1u,t2,R

ut,t,u2ut,t+2uut2u4

(3)

No differential operator is provided. The function acts as the identity.

Differentiateut24u,notation=diff,R

ⅆⅆtut24ut

(4)

See Also

DifferentialAlgebra

FactorDerivative

 


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