Comment #19 on issue 2225 by mrock...@gmail.com: Enhancing Matrix Norm http://code.google.com/p/sympy/issues/detail?id=2225
I think it can be useful. Remember that CASs like SymPy can handle easily very large symbolic expressions that you could never feasibly handle by hand. Also, just because something *can* be large doesn't necessarily mean that it *will*. If someone gives it a large symbolic non-diagonal matrix, then it might be large. But there are cases where it won't (like if the matrix is small, or if it is diagonal).
There are other functions that can also blow up. For example, if you try computing integrate((a*x**2 + b*x + c)/(d*x**2 + e*x + f), x), it will take about an hour to finish, and the result will be several full-screens of output (I think you might have to do this in my integration3 branch due to a bug in master). But that doesn't mean that we should ban integrate(). In fact, it is one of the most important functions in SymPy. It is not to difficult to come up with other examples where even the input is small, but the output will be large (like expand((x + y + z)**10000)).
Also, don't assume that you know what will and will not be useful to people. It may surprise you what various things are applied in more advanced mathematics (or physics or whatever) that you don't even know about. An example I can think of off the top of my head where symbolic eigenvalues would be useful is in classifying systems of second order PDEs with symbolic or with non-constant coefficients. Based on the signs and other properties of eigenvalues, it will have a different classification, elliptic, parabolic, or hyperbolic. If the coefficients are non-constant, different regions of the domain will have different types. I think there are other methods that you can use other than eigenvalues to determine this for second order PDEs, but perhaps not so for higher order ones (this is something that I just learned recently in my PDEs class, so I hope what I just said is all correct).
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