Comment #7 on issue 1850 by [email protected]: solve_linear_system contains duplicate rref algorithm
http://code.google.com/p/sympy/issues/detail?id=1850

Thanks for writing this little manifesto. You clearly care about the problem!

I for the most part agree with what you're saying here. This is a problem. I actually don't understand why we even need all these separate solve functions at the user level. Shouldn't solve() be able to figure out what is meant from the input? Matching an equation or system of equations to linear or polynomial or whatever is fast and easy. And if the user wants something different, we could employ a hints system. Actually, according to my original comment, solve_linear_system didn't use to be part of the user namespace. But for some reason, it was added.

Regarding changing the API, we will have to deprecate the old behavior, if possible. This will make things easiest on our users.

Regarding uses in SymPy, I personally just use Matrix directly. One very important (perhaps the most important) use of solve_linear_system in SymPy is the one in heurisch. See issue 1441, in particular comment 5. So that can provide a useful benchmark for the linear system stuff. That's the old Risch. The new Risch (which I wrote) also has to solve some linear systems, but as I said, it just uses Matrix and rref directly. Even so, the ability to exit early when we know the system is inconsistant would be nice.

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