Throw for leading/trailing_coefficient of zero in multivariate setting

[lgoettgens]

This is the AA part of the discussion result of oscar-system/Oscar.jl#5231.

@wdecker @fingolfin could you please check that this aligns with what we discussed in triage yesterday? Thanks!

The test failures in Nemo are expected and need to be dealt with in the same manner as the changes to tests here.

[codecov]

Codecov Report

❌ Patch coverage is 92.85714% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 87.95%. Comparing base (2654e69) to head (47c2729).
⚠️ Report is 10 commits behind head on master.

Files with missing lines	Patch %	Lines
src/MPoly.jl	83.33%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2153      +/-   ##
==========================================
- Coverage   87.95%   87.95%   -0.01%     
==========================================
  Files         127      127              
  Lines       31735    31740       +5     
==========================================
+ Hits        27914    27918       +4     
- Misses       3821     3822       +1     

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[thofma]

Do you plan to make the adjustments also in other downstream packages (if they arise)? I don't have the bandwidth for this and I don't want us to be stuck with this next week or so.

[lgoettgens]

Do you plan to make the adjustments also in other downstream packages (if they arise)? I don't have the bandwidth for this and I don't want us to be stuck with this next week or so.

The downstream tests for Singular (https://github.com/Nemocas/AbstractAlgebra.jl/actions/runs/17447883134/job/49546580545?pr=2153), Oscar (https://github.com/Nemocas/AbstractAlgebra.jl/actions/runs/17447883135/job/49546584478?pr=2153), and Hecke (https://github.com/Nemocas/AbstractAlgebra.jl/actions/runs/17447883140/job/49546579898?pr=2153) did not show any issues. It's just the Nemo tests that have to be adapted. And that should be in scope for me.

But please, before merging this, someone should double-check that this PR here indeed aligns with the decision from triage. (I got really confused at some point and may have changed everything in the completely wrong direction.

[lgoettgens]

It's just the Nemo tests that have to be adapted. And that should be in scope for me.

Already done in Nemocas/Nemo.jl#2137. The downstream tests in https://github.com/Nemocas/AbstractAlgebra.jl/actions/runs/17447883154/job/49573635095 will verify that this will indeed do the job.

[thofma]

Thanks