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](...).

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).