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## Main Question or Discussion Point

Let V be the variety of the ideal (f)

a singular point is a point where all the partial derivatives of the f are zero.

I know you can find singular points by writing down all these partial derivatives and also that the points are zeros of f (such as all points on the variety) and solve that system of equations. These are generally very difficult systems to solve so I wondered if there was a more elegant method to find these singular points.

a singular point is a point where all the partial derivatives of the f are zero.

I know you can find singular points by writing down all these partial derivatives and also that the points are zeros of f (such as all points on the variety) and solve that system of equations. These are generally very difficult systems to solve so I wondered if there was a more elegant method to find these singular points.

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