isunit for univariate and multivariate polynomials is incorrect over Z/nZ

[wbhart]

It's not true that a polynomial is a unit in its polynomial ring iff its constant coefficient is a unit. This has been assumed in the current implementation. For example, it isn't true over Z/nZ.

As it is actually quite expensive in general to compute this, we should look carefully where isunit has been used in generic code and remove references to it where this is not precisely what is required.

[thofma]

This is just https://github.com/Nemocas/Nemo.jl/issues/323, right?

[wbhart]

Yes. We'll need to copy all the relevant ones over to here eventually. This one just stands out as being a major error that should be corrected sooner rather than later. So I'm listing it here so that it doesn't get forgotten.

[fieker]

Specifically for Z/nZ we have much more in Hecke.jl - it might have to move across the divide...

On Fri, Feb 02, 2018 at 03:39:32PM +0000, wbhart wrote:

Yes. We'll need to copy all the relevant ones over to here eventually. This one just stands out as being a major error that should be corrected sooner rather than later. So I'm listing it here so that it doesn't get forgotten.

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[wbhart]

We should implement an isunit_constant function to replace the existing isunit function that is used often in library code (where we only care if we have a constant polynomial that is a unit for example, instead of actually needing a unit).