Published Paper
Inserted: 16 mar 2018
Last Updated: 13 may 2020
Journal: Discrete Comput Geom
Volume: 51
Pages: 559–568
Year: 2014
Doi: https://doi.org/10.1007/s00454-014-9588-3
Abstract:
In 1888 Hilbert showed that every nonnegative homogeneous polynomial with real coefficients of degree $2d$ in $n$ variables is a sum of squares if and only if $d=1$ (quadratic forms), $n=2$ (binary forms) or $(n,d)=(3,2)$ (ternary quartics). In these cases, it is interesting to compute canonical expressions for these decompositions. Starting from Carath\'eodory's Theorem, we compute the Carath\'eodory number of Hilbert cones of nonnegative quadratic and binary forms.