## Scaling of mixed volume

General discussion on polymake goes here.
Fabian91
Posts: 2
Joined: 13 Aug 2021, 23:07

### Scaling of mixed volume

Hi,
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,
F&M

joswig
Main Author
Posts: 269
Joined: 24 Dec 2010, 11:10

### Re: Scaling of mixed volume

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.