Comment #8 on issue 1850 by [email protected]: solve_linear_system contains
duplicate rref algorithm
http://code.google.com/p/sympy/issues/detail?id=1850
Sorry for the length -- it grew over a few days.
We could go with just having solve() do everything. But solve() has to
introduce overhead to classify systems, and as we see in dsolve(), this
overhead can be significant. Often, we already know the system we're
solving is linear, so it seems natural to have such a function.
A second reason would be that there is a very natural way to return
solutions for under-determined linear systems, but not in general. Having
a linear system solver can avoid the need for post-processing. (I'm
particularly thinking of the calculation of series solutions of linear
ODE's) Your need to exit early for over-determined systems is a similar
benefit.
But these are not strong arguments, and I agree that dropping the current
functions in favor of solve + hints would be a good improvement.
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