Timeline for area of triangle from coefficients of its cubic?

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Nov 23, 2011 at 12:08	comment	added	kassabov		you can simplify the computations even further by reducing to the case $a=0$ and $c=1$, but then you cna not expect the answer to be algebraic in $b$, but it should be algebraic in $Re b$ and $Im b$
Nov 23, 2011 at 11:51	comment	added	Wadim Zudilin		This was already in Igor's comments. No secrets from you: My choice was $a=\log(2)$, $b=\exp(1)$ and $c=\pi\sqrt{-1}$. Believe you or not, but the zeroes were all unreal. Even more, I also tried the case $a=0$, $b=\exp(1)$ and $c=\pi\sqrt{-1}$ (which is mentioned in your post) and still no result in degree less than 7.
Nov 23, 2011 at 11:44	comment	added	kassabov		This is not very likely to work since if you take $a,b,c$ to be reals umbers you are likely to get $3$ real roots and the area will be zero, which will not be usefull. Of course if you take the real parts of $a,b,c$ and the imaginary paorts of $a,b,c$ to be algebraicly independant you can do it, but the number of variables is getting too big.
Nov 23, 2011 at 10:41	history	answered	Wadim Zudilin	CC BY-SA 3.0