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I've heard the term "representation singularity" in a few contexts about numerical instability of algorithms to find Gröbner bases, but I can't seem to find a precise definition for what it actually means to have one. Can someone clarify this for me?

So far I understand it to mean something like "The result of an algorithm varies wildly depending on the choice of a representation of the initial input," however, I've also heard this related to algorithms which are numerically unstable in the sense that slight perturbations of the inputs give drastically different outputs, when one might consider slight perturbations to be distinct representations.

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