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Is there a way to check whether or not this is a floating point error?

I have the following functions defined:




Now, if I use the solve function:

sage: solve(AA(N,j,k)==0,N)

I get the output

[sin(4*pi*k/N) == (sin(8*pi/N)*sin(6*pi/N)*sin(4*pi/N)^3*sin(2*pi/N)^2*sin(-2*(pi
- pi*j)/N)*sin(-2*(pi - pi*k)/N) - sin(2*pi*j/N)*sin(12*pi/N)*sin(4*pi/N)^2*sin(2*pi/N)*sin(-2*(pi
- pi*k)/N) - (sin(4*pi*j/N)*sin(2*pi*j/N)*sin(6*pi/N)*sin(2*pi/N)*sin(2*(pi
+ pi*j)/N)*sin(-2*(pi - pi*j)/N) + sin(12*pi/N)*sin(4*pi/N)^2*sin(2*pi/N)*sin(-2*(pi
- pi*j)/N) - sin(2*pi*j/N)*sin(12*pi/N)*sin(4*pi/N))*sin(2*pi*k/N))/(sin(2*pi*j/N)*sin(2*pi*k/N)*sin(6*pi/N)*sin(2*pi/N)*sin(2*(pi
+ pi*k)/N)*sin(-2*(pi - pi*k)/N))]

However, it is my hope that this equation has no solutions. Indeed, if I add to the assumption that AA(N,j,k)>0, I obtain a contradiction (inconsistent assumptions), but if I add AA(N,j,k)==0, I don't get inconsistent assumptions.

Is there a way to check if this is a floating point error, or if there really is a solution with my assumptions?