[Merged by Bors] - feat(MvPolynomial): multiplicativity of totalDegree over domains

[erdOne]

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[github-actions]

PR summary b814af2026

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff

+ degree_mem_support
+ totalDegree_mul_of_isDomain

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for script/declarations_diff.sh contains some details about this script.

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No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[chrisflav]

Thanks!
maintainer merge

[github-actions]

🚀 Pull request has been placed on the maintainer queue by chrisflav.

[adomani]

This looks good to me, thanks!

I wonder whether this could be generalized further using machinery similar to UniqueSums: I remember that there arbitrary linear orders in the univariate case were later replaced by UniqueSums. This can wait for a later PR, though.

I'll ping @alreadydone as well, in case this piques his interest as well!

bors d+

[mathlib-bors]

✌️ erdOne can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

[alreadydone]

LGTM! I'm not sure how you'd define a degree without a total order ...

[adomani]

I meant more that, in the presence of a linear order, there is a UniqueSums on the grading monoid and you can probably prove multiplicativity with a UniqueSums assumption on the grading monoid.

Anyway, this discussion is not really for the current PR!

@erdOne, feel free to make the suggested change and merge!

[erdOne]

bors merge

[mathlib-bors]

Pull request successfully merged into master.

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