# diffOp(Matrix) -- create a differential operator

## Synopsis

• Function: diffOp
• Usage:
diffOp M
• Inputs:
• Outputs:

## Description

Creates a differential operator from a vector of polynomials in $S = \mathbb{K}[x_1,\dotsc,x_n][dx_1,\dotsc,dx_n]$. The ring $S$ is obtained from the ring $R = \mathbb{K}[x_1,\dotsc,x_n]$ by using diffOpRing.

 i1 : R = QQ[x_1,x_2] o1 = R o1 : PolynomialRing i2 : S = diffOpRing R o2 = S o2 : PolynomialRing i3 : diffOp matrix {{(x_1 * x_2 + 3)*dx_1*dx_2^2}, {dx_2^2}} o3 = | (x_1x_2+3)dx_1dx_2^2 | | dx_2^2 | 2 o3 : DiffOp in S

A ring element can be used instead of a $1 \times 1$ matrix.

 i4 : diffOp (x_1^2*dx_1^2) o4 = | x_1^2dx_1^2 | 1 o4 : DiffOp in S