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Definition: A singular point of an algebraic curve is a point where the curve has "nasty" behavior such as a cusp or a point of self-intersection (when the underlying field K is taken as the reals). More formally, a point (a,b) on a curve f(x,y)=0 is singular if the x and y partial derivatives of f are both zero at the point (a,b). (If the field K is not the reals or complex numbers, then the partial derivative is computed formally using the usual rules of calculus.)