p-a differential polynomialL-a list or a set of differential polynomialsF-a field descriptionR-a differential ring or idealopts (optional)-a sequence of options

<Text-field style="Heading 2" layout="Heading 2" bookmark="bkmrk1">Options</Text-field>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).
<Text-field style="Heading 2" layout="Heading 2" bookmark="info">Description</Text-field>The function call FieldElement (p,F,R) returns true if the differential polynomial p belongs to the differential field NiNJImtHNiI= 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 NiNJImtHNiI= presented by the list of derivatives G and the regular differential chain regchain. The field NiNJImtHNiI= contains the rational numbers. Its set of generators is made of the independent variables, plus all the dependent variables occurring in G or in the differential polynomials of regchain. Every polynomial expression belonging to the differential ideal defined by regchain, is zero in NiNJImtHNiI=. Every other polynomial expression between the generators of NiNJImtHNiI=, is invertible in NiNJImtHNiI=. Notes:Any of the arguments generators = G, and, relations = regchain can be omitted.It is required that the generators of NiNJImtHNiI= appear at the bottom of the ranking of R, and, that any block which involves a generator of NiNJImtHNiI=, purely consists of generators of NiNJImtHNiI=.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](...).
<Text-field style="Heading 2" layout="Heading 2" bookmark="examples">Examples</Text-field>with (DifferentialAlgebra): with(Tools):R := DifferentialRing (derivations = [t], blocks = [u,v,w]);With no arguments, the field NiNJImtHNiI= is the smallest field involving the rational numbers and the independent variables.FieldElement ([1, t, u], field (), R);In this example, the field NiNJImtHNiI= is the smallest differential field involving the rational numbers, the independent variables, and, the derivatives of NiNJInZHNiI= and NiNJIndHNiI=. FieldElement ([u/v[t], w[t,t], 1/(v+w)], field (generators = [v,w]), R);In this example, the field NiNJImtHNiI= is presented by generators and relations. The expression NiMsJiZJInZHNiI2JEkidEdGJkYoIiIiISIjRik= is NiMiIiE= in NiNJImtHNiI=.fieldrels := PretendRegularDifferentialChain ([v[t]^2-4*v], R);NormalForm (v[t,t]-2, fieldrels);FieldElement ((v[t,t]-2)*u+w[t]+1, field (relations = fieldrels, generators = [v,w]), R);See AlsoDifferentialAlgebraRosenfeldGroebner