diffOp(Matrix) -- create a differential operator

Synopsis

Function: diffOp
Usage:

diffOp M
Inputs:
- M, a matrix, consisting of a single column, or a ring element.
Outputs:
- a differential operator,

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

Ways to use this method: