differentiates a differential rational fraction - Maple Help

Home : Support : Online Help : Mathematics : Differential Equations : Differential Algebra : Tools : DifferentialAlgebra/Tools/Differentiate

DifferentialAlgebra[Tools][Differentiate] - differentiates a differential rational fraction

 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

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

 > $\mathrm{with}\left(\mathrm{DifferentialAlgebra}\right):$$\mathrm{with}\left(\mathrm{Tools}\right):$
 > $R:=\mathrm{DifferentialRing}\left(\mathrm{derivations}=\left[t\right],\mathrm{blocks}=\left[u\right]\right)$
 ${R}{:=}{\mathrm{differential_ring}}$ (1)
 > $\mathrm{Differentiate}\left({u}_{t}^{2}-4u,t,R\right)$
 ${2}{}{{u}}_{{t}}{}{{u}}_{{t}{,}{t}}{-}{4}{}{{u}}_{{t}}$ (2)
 > $\mathrm{Differentiate}\left(\left[u,\frac{1}{u}\right],{t}^{2},R\right)$
 $\left[{{u}}_{{t}{,}{t}}{,}\frac{{-}{{u}}^{{2}}{}{{u}}_{{t}{,}{t}}{+}{2}{}{u}{}{{u}}_{{t}}^{{2}}}{{{u}}^{{4}}}\right]$ (3)

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

 > $\mathrm{Differentiate}\left({u}_{t}^{2}-4u,\mathrm{notation}=\mathrm{diff},R\right)$
 ${\left(\frac{{ⅆ}}{{ⅆ}{t}}{}{u}{}\left({t}\right)\right)}^{{2}}{-}{4}{}{u}{}\left({t}\right)$ (4)