A saddle point is a point on the surface of a graph where the slope (or derivative) is zero in multiple dimensions, but is not a local extremum (i.e., not a local maximum or minimum). It occurs in both single-variable and multivariable calculus, although the characteristics can differ slightly based on the context.
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For a holomorphic phase , a saddle point is a critical point with . At a simple saddle, , and the quadratic Taylor term determines the local descent directions.
