Discard rank deficient systems in Chinese remaindering

[ClementPernet]

As a follow up on #148: in the setting of a CRT solve, if the matrix mod p is not full rank, the system can be either

• inconsistent: then an exception will be raised and the CRT progress method should catch it and discard the current prime
• consistent: the CRT should also discard this prime as the solution is not unique and will likely cause the CRT to fail. This means the CRT should know about the consistency of the mod p system, which is not currently accessible.

[bdsaunders]

Nicely put. One way to communicate this is for solve() to put in the method object whether it found the matrix to be nonsingular or singular. The caller can check this side return info or not according to it's needs.

On Fri, Nov 30, 2018 at 11:46 AM Clément Pernet [email protected] wrote:

As a follow up on #148 https://github.com/linbox-team/linbox/issues/148: in the setting of a CRT solve, if the matrix mod p is not full rank, the system can be either

• inconsistent: then an exception will be raised and the CRT progress method should catch it and discard the current prime
• consistent: the CRT should also discard this prime as the solution is not unique and will likely cause the CRT to fail. This means the CRT should know about the consistency of the mod p system, which is not currently accessible.

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