I think this might need some work:

S=RealBallField(100) 
M=Matrix(S,2,1,[1,1]) 
M.solve_right(vector([1,2])) 

There's enough information here to conclude there is no solution; or in a 
rather deranged way, perhaps it should give a rather large ball back so 
that the multiplication results in a vector consisting of balls that 
actually contain the values 1 and 2. Currently, it just returns a wrong 
answer.

For systems that are even generically overdetermined, I don't think it 
makes sense to default to a least squares solution in a routine that is 
supposed to detect inconsistent systems. There the stable numerical 
behaviour actually IS being inconsistent.

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