returns the leading coefficient of a differential polynomial
LeadingCoefficient(ideal, v, opts)
LeadingCoefficient(p, v, R, opts)
LeadingCoefficient(L, v, R, opts)
a differential ideal
a differential polynomial
a list or a set of differential polynomials
a differential polynomial ring or ideal
a sequence of options
The opts arguments may contain one or more of the options below.
fullset = boolean. In the case of the function call LeadingCoefficient(ideal,v), 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 the first argument is used.
memout = nonnegative. Specifies a memory limit, in MB, for the computation. Default is zero (no memory out).
The function call LeadingCoefficient(p,v,R) returns the leading coefficient of p regarded as a univariate polynomial in v. If p does not depend on v then the function call returns p.
The function call LeadingCoefficient(L,v,R) returns the list or the set of the leading coefficients of the elements of L with respect to v.
If ideal is a regular differential chain, the function call LeadingCoefficient(ideal,v) returns the list of the leading coefficients of the chain elements. If ideal is a list of regular differential chains, the function call LeadingCoefficient(ideal,v) returns a list of lists of leading coefficients.
When the parameter v is omitted, it is understood to be the leading derivative of each processed differential polynomial. In that case, the function behaves as the Initial function.
This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form LeadingCoefficient(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[Tools][LeadingCoefficient](...).
R := DifferentialRing(derivations=[x,y], blocks=[[v,u],p], parameters=[p]);
ideal := RosenfeldGroebner([u[x]^2-4*u, u[x,y]*v[y]-u+p, v[x,x]-u[x]], R);
The leading coefficients of the chain polynomials, with respect to ux
The derivative is not specified. The initial is returned.
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