Talk:Generator preimage

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can anyone explain why the algorithm works?

I'm the person who added the "example" section as well as the "Wolfram Language implementation" there, so I understand how to do it, but I have no real idea why it works.

It's clear enough to me that the pseudoinverse step is how we convert the input mapping into generators. But then how do we "massage" those generators by combining them one at a time with the comma basis, defactoring, dot-producting with the original row to get a thing we prepend before HNF'ing so that it has some effect on what remains when we grab that row back out...? It's quite tricksy.

--Cmloegcmluin (talk) 18:04, 6 October 2021 (UTC)