The opts arguments may contain one or more of the options below.

fullset = boolean. In the case of the function call Differentiate(ideal,theta), applies the function also over the differential polynomials which state that the derivatives of the parameters are zero. Default value is false.

notation = jet, tjet, diff or Diff. Specifies the notation used for the result of the function call. If not specified, the notation of p is used.

memout = nonnegative. Specifies a memory limit, in MB, for the computation. Default is zero (no memory out).

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](...).

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

$R≔\mathrm{DifferentialRing}\left(\mathrm{derivations}=\left[t\right]\,\mathrm{blocks}=\left[u\right]\right)$

$R≔\mathrm{differential\_ring}$

$\mathrm{Differentiate}\left({u\left[t\right]}^2-4u\,t\,R\right)$

$2u_t{u}_{t,t}-4u_t$

$\mathrm{Differentiate}\left(\left[u\,\frac{1}{u}\right]\,t^2\,R\right)$

$\left[u_{t,t}\,\frac{-u^2{u}_{t,t}+2u{u}_t^2}{u^4}\right]$

$\mathrm{Differentiate}\left({u\left[t\right]}^2-4u\,\mathrm{notation}=\mathrm{diff}\,R\right)$

${\left(\frac{\ⅆ}{\ⅆt}u\left(t\right)\right)}^2-4u\left(t\right)$