MrLee
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 May30 comment Solutions to the diophantine equation: $2a^2 + 2b^2- c^2- d^2 = 0$ Also you have set the parameter q=1 to obtain your formulas. I assume this is because there are 4 unknowns in the equation with 1 constraint $2*a^{2}+2*b^{2}-c^{2}-d^{2}=0$ so the solutions should be parametrized by 3 variables. Is this correct? (In particular one could have chosen any value for q) May29 comment Solutions to the diophantine equation: $2a^2 + 2b^2- c^2- d^2 = 0$ Also it seems to me that this technique should apply fo more generic equations of the form $x^{T}Ax$ = 0 with A being some symmetric matrix and x an integer vector. Is this correct? May29 comment Solutions to the diophantine equation: $2a^2 + 2b^2- c^2- d^2 = 0$ This is a very nice and detailed answer! As I pointed out in my last comment in response to WillO it puzzles me that the t that I obtain is rational. (Since I am looking for integer solutions) May29 comment Solutions to the diophantine equation: $2a^2 + 2b^2- c^2- d^2 = 0$ The other solution is $t=-\frac{2(2p+q-r-s)}{2p^{2}-r^{2}-s^{2}}$. This looks very close to the formula that you have written down, except that this expression for t is rational in general. So do you use now s to enforce that t is integer? If yes, can you ellaborate on that? May29 comment Solutions to the diophantine equation: $2a^2 + 2b^2- c^2- d^2 = 0$ Ok. So how did you derive these equations? Is there some reference? May29 comment Solutions to the diophantine equation: $2a^2 + 2b^2- c^2- d^2 = 0$ On Mathoverflow it was pointed out that the equations (together with the a+b+c+d=0 condition) define a "conic in P^2". Can someone explain to me in simple terms what this means? Jan13 comment Manifold of Density Matrices Can you please explain in more detail why this is the case and how I can modify the proof to take positive semi-definite matrices into account? Nov18 comment Generalization of Gaussian Curvature? I'm not saying that this is going to be some kind of curvature. I'm just speculating at the moment because I cannot give a meaningful interpretation of the quantity described above. Oct10 comment Atlas of Complex Projective Space Well my question is rather concrete and to be honest the wikipedia article or the reference doesn't help me with my specific question. I'd be happy if you could adress my actual question.