returns the initial of a differential polynomial
Initial(p, R, opts)
Initial(L, 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 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](...).
with (DifferentialAlgebra): with(Tools):
R := DifferentialRing (derivations=[x,y], blocks=[[v,u],p], parameters=[p]);
Initial (u[x,y]*v[y]-u+p, R);
ideal := RosenfeldGroebner ([u[x]^2-4*u, u[x,y]*v[y]-u+p, v[x,x]-u[x]], R);
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