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 $\mathrm{\Delta }$-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 $\mathrm{\Delta }$-polynomials.

The numeric coefficients of the returned $\mathrm{\Delta }$-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](...).

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

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

$R≔\mathrm{differential\_ring}$

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

$v_y$

$\mathrm{DeltaPolynomial}\left({u\left[x\right]}^2-4u\,u\left[x,x\right]\,R\right)$

$u_x$