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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

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