Define is_homogeneous for MPolyRingElem

[fingolfin]

No description provided.

[thofma]

Tests not passing

[fieker]

Did you discuss this with the Geometry crowd? There might be a reason this function did not exist ... (other than oversight)

[fingolfin]

It didn't occur to me, given that it is already part of the AA documentation which promises it as being available for all MPolyRingElem subtypes. To quote docs/src/mpolynomial.md:

### Homogeneous polynomials

It is possible to test whether a polynomial is homogeneous with respect to the standard grading using the function

```@docs
is_homogeneous(x::MPolyRingElem{T}) where T <: RingElement
```

But sure, we can discuss it -- CC @ederc @wdecker @jankoboehm @simonbrandhorst @afkafkafk13 (I probably forgot someone, sorry)

[fingolfin]

To be clear, I think the question here is whether we should keep exporting AbstractAlgebra.Generic.is_homogeneous as AbstractAlgebra.is_homogeneous (which therefore also exists in Oscar).

I note that in Oscar, there is also a function _is_homogeneous which does more or less what the changes in this PR do for is_homogeneous.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 86.75%. Comparing base (bae82ed) to head (496bc96).
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  Coverage   86.75%   86.75%           
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[fingolfin]

I of course forgot to tag @HechtiDerLachs sorry!

[jankoboehm]

We discussed this a bit and would suggest that we have (to avoid confusion with the OSCAR function)

is_homogeneous with two required arguments, polynomial and weight vector

and a convenience function

is_standard_homogeneous for a polynomial to cover the typical use case.

That would also capture the setting we can realize here. Would that be fine?

[thofma]

Just a random comment: Maybe is_homogenous_standard? Grammar is worse, but easier to discover with tabcompletion.

Also, we could make is_homogeneous(f) for an element f of a non-graded polynomial ring spill out a useful error message.

[afkafkafk13]

Just a random comment: Maybe is_homogenous_standard? Grammar is worse, but easier to discover with tabcompletion.

This does not make it more understandable. You still need to know what the 'standard' refers to, if you want to make sense of suggested completion.

Also, we could make is_homogeneous(f) for an element f of a non-graded polynomial ring spill out a useful error message.

I am very much in favour of this suggestion. The error message should state that the user could either specify a grading or use 'is_standard_homogeneous' (or whatever name it bears at that moment).