finding multiple minima



On Tue, 11 May 2010, Barton Willis wrote:

> In general, the answer to your question is no. Even for a R --> R
> function, there is no Maxima function that will find all the local
> minima (either symbolically or approximately). For example, find all
> local minima for the function x |--> bessel_j(0,x). Maxima doesn't
> even have an effective way to represent nonfinite sets.

But I guess for many cases, one can use

diff() to find the grad of a multivariate function,

to_poly_solve() to find roots of that grad (stationary points),

diff() again to construct the Hessian, and

eigenvalues() to diagonalize the Hessian and find out whether the
stationary points are maxima, minima, or saddles

-- 

Regards,

Dan