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Results tagged with symmetric-polynomials
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user 135040
3
votes
Representing a symmetric polynomial as a conical sum of squares
For four variables $a$, $b$ $c$ and $d$ we'll use the following natation.
$$\sum_{sym}a=6(a+b+c+d),$$
$$\sum_{sym}ab=4(ab+ac+bc+ad+bd+cd),$$
$$\sum_{sym}a^2b=2\sum_{cyc}a^2(b+c+d).$$
Number of addends …
- 1,054
6
votes
Polynomial inequality of sixth degree
I have found the following identity, which solves my problem for $k=\frac{13}{5}.$
$$4\prod_{cyc}(a+b)^2\left(\sum_{cyc}\frac{2a^2+bc}{(b+c)^2}-\frac{9}{4}\right)=\frac{1}{3}\left(\sum_{cyc}(2a^3-a^2b …
- 1,054