returns a Delta-polynomial
DeltaPolynomial (p, q, R,opts)
a differential polynomial
a differential polynomial ring or ideal
a sequence of options
The opts arguments may contain one or more of the options below.
notation = jet, tjet, diff or Diff. Specifies the notation used for the result of the function call. If not specified, the notation of R or of ideal is used.
memout = nonnegative. Specifies a memory limit, in MB, for the computation. Default is zero (no memory out).
The function call DeltaPolynomial (p, q, R) returns the Δ-polynomial generated by p and q, which are regarded as differential polynomials of R, or, of its embedding ring, if R is an ideal. See DifferentialAlgebra for the definition of Δ-polynomials.
The numeric coefficients of the returned Δ-polynomial are normalized: their gcd is equal to 1, and, the leading one is positive. It is required that the leading derivatives of p and q are derivatives of some same dependent variable.
This command is part of the DifferentialAlgebra:-Tools package. It can be called using the form DeltaPolynomial(...) after executing the command with(DifferentialAlgebra:-Tools). It can also be directly called using the form DifferentialAlgebra[Tools][DeltaPolynomial](...).
R ≔ DifferentialRing⁡derivations=x,y,blocks=u,v
The triangular case: the least common derivative of the two leading derivatives is different from both of them.
The non-triangular case: the leading derivative of the second argument is a derivative of the leading derivative of the first one.
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