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I think Daniel Lichtblau gave a useful answer in his comment. This is to get it on record. They (the present example and the Solve one) are similar issues. At heart, as noted by @Rojo, it has to do with internal ordering having an impact on simplification, cylindrical decomposition, and other under-the-hood functionality that is called upon by the likes ...


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In Mathematica, the type of variable is interpreted based on the context, and if there are no values associated with the variable, then often nothing is done. When you write PauliMatrix[1].f, since there are no values/rules associated with f, this just returns {{0, 1}, {1, 0}}.f because the function Dot doesn't evaluate unless the arguments are vectors, ...


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My initial response would have been that a number that is not positive or zero, and that is only negative if certain conditions are met, may still be complex if those conditions are not met. In that case it is neither zero nor positive, nor negative. So, let's see whether we can find an example of a parameter set that makes the last condition false while ...


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If you already know the interval on which you want to find one of your solution, you may use the instruction FindRoot[f[x]==0,{x,xmin,xmax}] Here, Mathematica will use Brent's algorithm (a combination of the bisection and secant methods) restricted to the interval [xmin,xmax]. With the example FindRoot[Sin[x]==0, {x, .1, 10}] where one searches for a ...


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RegionPlot3D[-a + b + c > 0 && -a + b + c^2 > 0 && a > 1 && b > 0 && c > 0, {a, -10, 20}, {b, -10, 10}, {c, -10, 10}, AxesLabel -> {a, b, c}]


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Problems of this sort are posted from time to time in Mathematica SE. Multiple instances of Nintegrate are nested one inside another, and an inner integrand contains one of the outer variables of integration. And, from the point of view of the inner NInterate, the outer variable is undefined. (Chuy noted this in a comment above.) The solution is to have ...



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