> IIUC Sturm sequence is essentially
> consists of two parts: purely algebraic computation and
> determination of signs.  So it make sense to expose
> computational part also for unordered rings.

Yes, that's what I'm trying to do.

> However,
> machinations with sign of leading coefficient look strange.

Why is that? Doesn't the leading coefficient determine sign
at infinity?

> ToolsForSign realy is rather weak and I would
> avoid it if possible.

> Also, in analogy with other domains we could pass sign
> determining function as a parameter.

Why not put sign determining function into ToolsForSign to
make it not weak?

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