library(name,R)
library(name,var)
This method contains a library of some interesting nonnegative forms.
The Motzkin polynomial is a ternary sextic that is nonnegative, but is not a sum of squares. It was the first such example found.
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The Robinson and Schmüdgen polynomials are also ternary sextics that are not sums of squares.
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The Lax-Lax and Choi-Lam polynomials are quaternary quartics that are not sums of squares.
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The Scheiderer polynomial is a sum of squares over the reals, but not over the rationals.
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The Harris polynomial is a ternary form of degree 10 with 30 projective zeros (the largest number known in August 2018).
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References: Some concrete aspects of Hilbert's 17th problem. B. Reznick. Contemporary mathematics (2000), 253, pp. 251-272.
The object library is a method function.
The source of this document is in SumsOfSquares/SOSdoc.m2:777:0.