This strategy implements a numerical-symbolic hybrid algorithm for computing Noetherian operators. The output is symbolic. `"Hybrid"` supports computing Noetherian operators of either primary ideals (noetherianOperators(Ideal)), or primary components of unmixed ideals (noetherianOperators(Ideal,Ideal)).

The `"Hybrid"` strategy finds a point on the variety of the component of interest, and computes a set of specialized Noetherian operators (see specializedNoetherianOperators). Using this numerical data is then used as a starting point for the symbolic computation of Noetherian operators, which in many cases lead to significant performance improvements over the fully symbolic methods.

The strategy accepts the following optional arguments:

`Sampler => f`, where `f` is a function taking a primary ideal and returning a single point on the variety. The default sampler uses a combination of bertiniSample and bertiniPosDimSolve. The user can supply a point to used by using a dummy sampler, as in the example below:

i1 : R = QQ[x,y,t]; |

i2 : I = ideal(x^2, y^2-x*t); o2 : Ideal of R |

i3 : p = point{{0_CC,0, 3}}; |

i4 : noetherianOperators(I, Strategy => "Hybrid", Sampler => I -> p) -- warning: experimental computation over inexact field begun -- results not reliable (one warning given per session) o4 = {| 1 |, | dy |, | tdy^2+2dx |, | tdy^3+6dxdy |} o4 : List |

`Tolerance => ...`: takes a positive real number. This specifies the numerical precision when computing the specialized Noetherian operators. The default value is `1e-6`. See See Tolerance (NoetherianOperators).

`DependentSet =>...`: takes a list of variables. For details, see DependentSet.

- Strategy => "PunctualQuot" -- strategy for computing Noetherian operators
- Strategy => "MacaulayMatrix" -- strategy for computing Noetherian operators