Over inexact rings, it is generally impossible to determine the rank or to check whether a square matrix is singular, so such a check should not be done at all, IMO. This implies that the `check` keyword should be ignored. This is also what https://trac.sagemath.org/ticket/13932 is about. For inexact rings like RDF/CDF, the Matlab behavior is consistent and predictable. In particular, the answer does not depend on numerical noise. In other words, for near-singular square matrices, the method should _not_ attempt to find a least-squares solution, but continue the computation as if the matrix was regular (which may lead to a warning or error). Otherwise, the output of the method would just be very unpredictable, so one would always have to check which type of solution it decided to return.
For inexact rings other than RDF/CDF, other notions of "approximate solution" may be more appropriate, but that does not seem to be a problem as long as it clearly documented. For exact rings, it is possible to determine the rank and whether an exact solution exists. Therefore, I would expect the method to always return an exact solution if it exists and raise an error otherwise, regardless of whether the matrix is square or not. The `check` keyword is, in my understanding, a detail that helps speed up a computation if one already knows a priori that what it would check is unnecessary. Otherwise, the output may just be wrong. I will try to reply to your changes on the ticket soon. -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sage-devel/54c30868-5900-40fb-bac6-d131cfd78112%40googlegroups.com.
