FactorDerivative - Maple Help

DifferentialAlgebra[Tools]

 FactorDerivative
 extracts the derivation operator of a derivative

 Calling Sequence FactorDerivative(v, R, opts)

Parameters

 v - a derivative R - a differential polynomial ring or ideal opts (optional) - a sequence of options

Options

 • The opts arguments may contain one or more of the options below.
 • notation = jet, tjet, diff or Diff. Specifies the notation used for the result of the function call. If not specified, the notation of v is used.
 • memout = nonnegative. Specifies a memory limit, in MB, for the computation. Default is zero (no memory out).

Description

 • The function call FactorDerivative(v,R) returns a sequence $\mathrm{\theta }$, $u$ such that $\mathrm{\theta }$ is the derivation operator, and, u is the dependent variable, associated to $u$ (see DifferentialAlgebra). The argument v must be a derivative of R, or of its embedding ring if R is an ideal.
 • This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form FactorDerivative(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[Tools][FactorDerivative](...).

Examples

 > $\mathrm{with}\left(\mathrm{DifferentialAlgebra}\right):$$\mathrm{with}\left(\mathrm{Tools}\right):$
 > $R≔\mathrm{DifferentialRing}\left(\mathrm{derivations}=\left[x,y\right],\mathrm{blocks}=\left[\left[v,u\right],p\right],\mathrm{parameters}=\left[p\right]\right)$
 ${R}{≔}{\mathrm{differential_ring}}$ (1)
 > $\mathrm{\theta },\mathrm{indep}≔\mathrm{FactorDerivative}\left(u\left[x,y\right],R\right)$
 ${\mathrm{\theta }}{,}{\mathrm{indep}}{≔}{x}{}{y}{,}{u}$ (2)
 > $\mathrm{Differentiate}\left(\mathrm{indep},\mathrm{\theta },R\right)$
 ${{u}}_{{x}{,}{y}}$ (3)
 > $\mathrm{FactorDerivative}\left(u,R\right)$
 ${1}{,}{u}$ (4)
 > $\mathrm{FactorDerivative}\left(\mathrm{diff}\left(u\left(x,y\right),x\right),R,\mathrm{notation}=\mathrm{diff}\right)$
 ${x}{,}{u}{}\left({x}{,}{y}\right)$ (5)