add divrem for EuclideanRingResidueRing

[fieker]

would resolve oscar-system/Oscar.jl#4340

[codecov]

Codecov Report

❌ Patch coverage is 87.17949% with 5 lines in your changes missing coverage. Please review.
✅ Project coverage is 88.19%. Comparing base (7a473f4) to head (cad3977).
⚠️ Report is 354 commits behind head on master.

Files with missing lines	Patch %	Lines
src/generic/Residue.jl	87.17%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #1921      +/-   ##
==========================================
+ Coverage   88.17%   88.19%   +0.01%     
==========================================
  Files         120      120              
  Lines       30303    30342      +39     
==========================================
+ Hits        26719    26759      +40     
+ Misses       3584     3583       -1     

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[fingolfin]

Add some tests?

[thofma]

I am a bit confused. The code is for residue rings of euclidean rings, but then does something with leading coefficients?

[fieker]

On Thu, Dec 05, 2024 at 05:29:11AM -0800, Tommy Hofmann wrote: I am a bit confused. The code is for residue rings of euclidean rings, but then does something with leading coefficients?

We can try to do it with canonical_unit? The probelm is that coprime base and gcd loose the units

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[fieker]

possibly we need a more sane algorithm?

[thofma]

How about just doing the Euclidean division in the "base ring" and then project down?

[fieker]

On Thu, Dec 05, 2024 at 07:37:57AM -0800, Tommy Hofmann wrote: How about just doing the Euclidean division in the "base ring" and then project down?

I guess it comes down to what euc. function we want on the quotient? For Z/nZ we choose phi(a) = gcd(a, n) you're suggesting to use on R/mR - choose the euc-minimal rep of a + mR - euc(a)? but keep the canonical unit? and not try to do eps a to find a minimal rep?

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