The opts arguments may contain one or more of the options below.

fullset = boolean. In the case of the function call Initial(ideal), 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 Initial(p,R) returns the initial of p with respect to the ranking of R, or of its embedding polynomial ring, if R is an ideal. It is assumed that p is non-numeric.

The function call Initial(L,R) returns the list or the set of the initials of the elements of L with respect to the ranking of R.

If ideal is a regular differential chain, the function call Initial(ideal) returns the list of the initials of the chain elements. If ideal is a list of regular differential chains, the function call Initial(ideal) returns a list of lists of initials.

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

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

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

$R≔\mathrm{differential\_ring}$

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

$v_y$

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

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

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

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

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

$\left[1\,4u\,1\,1\right]$