The function call FieldElement (p,F,R) returns true if the differential polynomial p belongs to the differential field  defined F and R, else it returns false. The differential polynomial p is regarded as a differential polynomial of R, if R is a differential ring, or, of the embedding ring of R, if R is an ideal.

The argument F has the form field (generators = G, relations = regchain). It defines a differential field  presented by the list of derivatives G and the regular differential chain regchain. The field  contains the rational numbers. Its set of generators is made of the independent variables, plus all the dependent variables occuring in G or in the differential polynomials of regchain. Every polynomial expression belonging to the differential ideal defined by regchain, is zero in . Every other polynomial expression between the generators of , is invertible in . Notes:

Any of the arguments generators = G, and, relations = regchain can be omitted.

It is required that the generators of  appear at the bottom of the ranking of R, and, that any block which involves a generator of , purely consists of generators of .

The function call FieldElement (L,F,R) returns a list or a set of boolean.

This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form FieldElement(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[Tools][FieldElement](...).

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 the first argument is used.

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