[Ether]

R uses the rq() function in the quantreg package which does quantile regression. It converts the problem to SDP and solves it. If you set the tau parameter of rq() to 50%, it will do L1 regression.

Python has a convex optimization package that contains a function for L1 regression. You don't have to know how to setup the problem, just pass it your A & b data.

AMPL is a modeling language which allows you to state the problem as a constrained minimization, and then AMPL expands it into a linear program format that can be passed to your linear solver of choice.

Octave has glpk, the GNU Linear Programming kit. You have to manually code the problem as a linear program and then pass it to glpk() for solution.

Matlab has the linprog() function which does the same thing as Octave's glpk(). It also has the CVX package, which allows you to use Matlab as a modeling language, but it is not intended for large problems.