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](...).

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

$R≔\mathrm{DifferentialRing}\left(\mathrm{derivations}=\left[x\,y\right]\,\mathrm{blocks}=\left[\left[v\,u\right]\,p\right]\,\mathrm{parameters}=\left[p\right]\right)$

$R≔\mathrm{differential\_ring}$

$\mathrm{ideal}≔\mathrm{RosenfeldGroebner}\left(\left[{u\left[x\right]}^2-4u\,u\left[x,y\right]v\left[y\right]-u+p\,v\left[x,x\right]-u\left[x\right]\right]\,R\right)$

$\mathrm{ideal}≔\left[\mathrm{regular\_differential\_chain}\,\mathrm{regular\_differential\_chain}\right]$

$\mathrm{Equations}\left(\mathrm{ideal}\left[1\right]\right)$

$\left[v_{x,x}-u_x\,p{u}_x{u}_y-u{u}_x{u}_y+4u{v}_y\,u_x^2-4u\,u_y^2-2u\right]$

$\mathrm{LeadingCoefficient}\left(\mathrm{ideal}\left[1\right]\,u\left[x\right]\right)$

$\left[\mathrm{-1}\,p{u}_y-u{u}_y\,1\,u_y^2-2u\right]$

$\mathrm{LeadingCoefficient}\left(u\left[x,y\right]v\left[y\right]-u+p\,R\right)$

$v_y$