# Finding trivial solutions, of the type 0 = 0, of an equation involving su(N) structure constants

so I have a bunch of equations $f_{abc} = f_{egd}m_{ae}m_{bg}m_{cd}$ (sum over repeated indices), where $f_{abc}$ are the structure constants of $su(N)$, for some $N$, and $m_{ab}$ are elements of some matrix. I want to find how many of the $(N^2 -1)\times(N^2 -1)\times(N^2 -1)$ equations above are trivial, meaning that we have 0 at both sides. I did this for $su(3)$ with the code below, and I got the expected answer (I basically used this code to build the struture constants). Firts I define B = 0 as the variable that will do the counting, then

For[i = 1, i <= 8, i++,
For[j = 1, j <= 8, j++,
For[k = 1, k <= 8, k++,
If[SU3f[i, j, k] == 0,
If[Sum[SU3f[l, r, n]*M[[i, l]]*M[[j, r]]*M[[k, n]], {l, 1, 8}, {r,
1, 8}, {n, 1, 8}] == 0, B = B + 1]]]]]


This gives B = 176 or something like that in the end. Now, when I do the same thing for $su(4)$ and $su(5)$, only changing the generators and dimensions, I end up with B = 0, no equations are trivial, which I find a bit odd. My question is, does my code looks like it does what I want it to do? Is this a good way to do what I described, or is there a better way? Thanks in advance.

• Almost never use For since Table is preferable. Never use upper-case letters at the beginning of a variable name (B, M, SU3f) as this may conflict with Mathematica's naming conventions. I suspect you're a C++ programmer and are quite unaware of the style and syntax of Mathematica. – David G. Stork Jan 17 '18 at 0:03
• You'll probably get better answers if you post the actual code you used. At a guess (which is all I can do without the code), I'd try using Simplify, PossibleZeroQ, or something like that, because sometimes complicated expressions don't get simplified all the way. – aardvark2012 Jan 17 '18 at 0:05
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• @DavidG.Stork Yes, I'm used to work with C/C++ only, and I'm new to Mathematica. Thanks for the tips. – l_xavier Jan 17 '18 at 13:25
• @aardvark2012 The code is just the one that I posted. The only missing part is the definition of the structure constants that is in the link I also posted. Thanks for the tips. – l_xavier Jan 17 '18 at 13:32