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).

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](...).

$\mathrm{with}\left(\mathrm{DifferentialAlgebra}\right)\:$$\mathrm{with}\left(\mathrm{Tools}\right)\:$

$R≔\mathrm{DifferentialRing}\left(\mathrm{derivations}\=\left[x\,y\right]\,\mathrm{blocks}\=\left[\left[v\,u\right]\,p\right]\,\mathrm{parameters}\=\left[p\right]\right)$

$R≔\mathrm{differential\_ring}$

$\mathrm{\θ}\,\mathrm{indep}≔\mathrm{FactorDerivative}\left(u_{x\,y}\,R\right)$

$\mathrm{\θ}\,\mathrm{indep}≔xy\,u$

$\mathrm{Differentiate}\left(\mathrm{indep}\,\mathrm{\θ}\,R\right)$

$u_{x\,y}$

$\mathrm{FactorDerivative}\left(u\,R\right)$

$1\,u$

$\mathrm{FactorDerivative}\left(\frac{\partial }{\partial x}u\left(x\,y\right)\,R\,\mathrm{notation}\=\mathrm{diff}\right)$

$x\,u\left(x\,y\right)$