returns the separant of a differential polynomial
Separant(ideal, v, opts)
Separant(p, v, R, opts)
Separant(L, v, R, opts)
a differential ideal
a differential polynomial
a list or a set of differential polynomials
a differential polynomial ring
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 Separant(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 Separant(p,v,R) returns the separant of p regarded as a univariate polynomial in v, that is the partial derivative of p with respect to v. The differential polynomial p is assumed to be non-numeric.
The function call Separant(L,v,R) returns the list or the set of the separants of the elements of L with respect to v.
If ideal is a regular differential chain, the function call Separant(ideal,v) returns the list of the separants of the chain elements. If ideal is a list of regular differential chains, the function call Separant(ideal,v) returns a list of lists of separants.
When the parameter v is omitted, it is understood to be the leading derivative of the processed differential polynomial with respect to the ranking of R, or the one of its embedding polynomial ring, if R is an ideal.
This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form Separant(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[Tools][Separant](...).
R ≔ DifferentialRing⁡derivations=x,y,blocks=v,u,p,parameters=p
ideal ≔ RosenfeldGroebner⁡ux2−4⁢u,ux,y⁢vy−u+p,vx,x−ux,R
The separants, in the usual sense.
The separant with respect to ux,y
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