[Merged by Bors] - feat(RingTheory/Polynomial/ContentIdeal): the content ideal of a polynomial.#25333
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[Merged by Bors] - feat(RingTheory/Polynomial/ContentIdeal): the content ideal of a polynomial.#25333
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PR summary 8024e6939aImport changes for modified filesNo significant changes to the import graph Import changes for all files
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Ideal.span (p.coeffs.toSet)
jcommelin
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Jun 12, 2025
| principal, `p` is primitive if and only if its content ideal is the whole ring. | ||
| - `Submodule.IsPrincipal.contentIdeal_eq_span_content_of_isPrincipal`: if the content ideal of `p` | ||
| is principal, then it is equal to the ideal generated by the content of `p`. | ||
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@_Antoine Chambert-Loir|130609 said:
@**Fabrizio Barroero** , can you add as a TODO the statement of the Dedekind-Mertens lemma with a link to Coquand's paper ? (Does Mathlib have Prüfer rings?)
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Thanks 🎉 bors merge |
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…nomial. (#25333) We define the content ideal of a polynomial as ``` def contentIdeal (p : R[X]) := span p.coeffs.toSet ``` and prove some basic results in connection with the concept of content and primitivitiy. Zulip discussion [here](https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/contentIdeal/with/522432790)
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Pull request successfully merged into master. Build succeeded: |
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* master: (447 commits) chore(Data/Set): move very basic lemmas earlier (leanprover-community#25707) feat: preserve draft status when migrating PRs to fork (leanprover-community#25777) chore(Data/Set/Basic): deprecate lemmas that abuse the `Set α := α → Prop` defeq (leanprover-community#25669) refactor: redefine `ProperCone` as an `abbrev` for `ClosedSubmodule` (leanprover-community#25204) feat: interaction between ContinuousLinearMap.coprod and ContinuousLinearEquiv.prodComm (leanprover-community#25564) fix: outdated docstring (leanprover-community#25717) feat(MeasureTheory): convolution of measures with densities (leanprover-community#25718) feat: make sure that the simp normal form of equiv-like classes pushes `symm` and `trans` to the right (leanprover-community#25604) feat(ModelTheory): Formula.iSup and iInf (leanprover-community#21948) feat(RingTheory/Polynomial/ContentIdeal): the content ideal of a polynomial. (leanprover-community#25333) fix: typo in labels_from_comment.yml (leanprover-community#25727) feat: is{Inducing,Embedding}_prodMkLeft (leanprover-community#25705) feat: check that the mathlib options exist (leanprover-community#25687) feat(Algebra/Group/Even): Add missing lemmas (leanprover-community#20818) refactor: make `Matrix.kroneckerTMulAlgEquiv` heterogeneous (leanprover-community#25693) feat: allow contributors to remove labels with comments (leanprover-community#25723) chore: disable build.yml and bors.yml on forks (leanprover-community#25722) feat: improvements to user_activity_report.py (leanprover-community#25721) chore: update the migration script to check for necessary permissions and prefer ssh if possible (leanprover-community#25701) chore: update the migration script to check for necessary permissions and prefer ssh if possible (leanprover-community#25701) ...
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…nomial. (leanprover-community#25333) We define the content ideal of a polynomial as ``` def contentIdeal (p : R[X]) := span p.coeffs.toSet ``` and prove some basic results in connection with the concept of content and primitivitiy. Zulip discussion [here](https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/contentIdeal/with/522432790)
pfaffelh
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Jun 15, 2025
…nomial. (leanprover-community#25333) We define the content ideal of a polynomial as ``` def contentIdeal (p : R[X]) := span p.coeffs.toSet ``` and prove some basic results in connection with the concept of content and primitivitiy. Zulip discussion [here](https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/contentIdeal/with/522432790)
callesonne
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Jul 24, 2025
…nomial. (leanprover-community#25333) We define the content ideal of a polynomial as ``` def contentIdeal (p : R[X]) := span p.coeffs.toSet ``` and prove some basic results in connection with the concept of content and primitivitiy. Zulip discussion [here](https://leanprover.zulipchat.com/#narrow/channel/287929-mathlib4/topic/contentIdeal/with/522432790)
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We define the content ideal of a polynomial as
and prove some basic results in connection with the concept of content and primitivitiy.
Zulip discussion here