Three variable SOS

asked 2013-07-22 05:00:22 -0500

sedddd gravatar image

Hi, suppose I have symmetric or cyclic expression in variables $a,b,c$ that is equal to $0$ when $a = b = c$. Can sage find the SOS form of the expression? I.e. write it in form $$(a - b)^2 \cdot S_c + (b - c)^2 \cdot S_a + (c - a)^2 \cdot S_b$$ where $S_a$ is some expression in $a,b,c$ and $S_b$, $S_c$ are obtained by cyclic permutations. For example $$\frac{a}{b + c} + \frac{b}{c + a} + \frac{c}{a + b} - \frac{3}{2}$$ has SOS form $$\frac{(a - b)^2}{2(b + c)(c + a)} + \frac{(b - c)^2}{2(c + a)(a + b)} + \frac{(c - a)^2}{2(a + b)(b + c)}$$

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