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](...).

with(DifferentialAlgebra): with(Tools):

R := DifferentialRing(derivations=[x,y], blocks=[[v,u],p], parameters=[p]);

$R≔\mathrm{differential\_ring}$

theta, indep := FactorDerivative(u[x,y], R);

$\mathrm{\theta },\mathrm{indep}≔xy,u$

Differentiate(indep, theta, R);

$u_{x,y}$

FactorDerivative(u, R);

$1,u$

FactorDerivative(diff(u(x,y),x), R, notation=diff);

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