Let $D=k [x_1,\ldots, x_n, \partial_1,\ldots, \partial_n] $ be the nth Weyl algebra over the characteristic zero field $k $. Set $\theta_i=x_i\partial_i $. Let $I $ be a left ideal in $D $. Is there a known algorithm to compute (a generating set of) the intersection $I\cap k [\theta_1,\ldots,\theta_n] $?

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