Scaling of mixed volume

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Joined: 13 Aug 2021, 23:07

Scaling of mixed volume

Postby Fabian91 » 25 Mar 2022, 17:38

We are interested in the application of mixed volume to estimate the number of zeros of differently sized systems coming from applications. In order to design feasible experiments, we would like to know the scaling of the mixed volume. More precisely, in our applications, the space dimensions scale as N^3 where N is the number of electrons. Thus it is crucial for us to know the runtime of ``mixed_volume'' with respect to the space dimensions.
Thank you,

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Re: Scaling of mixed volume

Postby joswig » 30 Mar 2022, 11:56

All known algorithms for computing the mixed volume are exponential in the dimension. Since even computing the volume is known to be #P-hard there is no hope for any improvement.

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