>From the documentation at 
https://www.mathworks.com/help/matlab/ref/mldivide.html, it appears to me 
that MATLAB gives a warning: "Warning: Matrix is close to singular or badly 
scaled. Results may be inaccurate."  That seems to me to be a better 
default behavior than what sage is doing now, but I think it would make 
sense to let users choose to turn off the warning (and maybe also let them 
upgrade it to an error).

On Friday, May 22, 2020 at 9:20:00 PM UTC-6, Michael Orlitzky wrote:
>
> On 5/22/20 6:40 PM, AlexGhitza wrote: 
> > I would also argue that, despite the validity of the arguments regarding 
> > inexact rings, this is a change in behavior that would have benefited 
> > from a deprecation warning for a short while. 
>
> We were pretty careful not to break anything in the sage library. For 
> typical inexact rings, the risk of breakage was minimal, because not 
> much worked to begin with. What we overlooked was that not all inexact 
> rings are typical, and that in cases like RealBallField and exact-SR, 
> the change could turn a right answer to a wrong one *in a situation that 
> wasn't ridiculous to begin with.* None of those cases were doctested, so 
> they were easy to overlook. 
>
>
> > Another user-friendlier way of doing this (making the check argument 
> > irrelevant in the inexact case) would have been to display a warning 
> > when the user asks for check=True in the inexact case, rather than 
> > simply ignoring it. 
>
> The base class defaults to check=True, and that can't be changed, so you 
> would get a warning on every inexact solve in that case. Moreover for 
> the "usual" inexact rings, things were unilaterally improved and not 
> deserving of a warning. 
>
> It will probably take a bit of domain-specific knowledge to make RBF/CBF 
> work as Nils expects, but reverting SR back to the old behavior when all 
> of its elements are exact shouldn't be hard if it doesn't cause any new 
> unforeseen problems. Let's just fix it instead of throwing warnings. 
>

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