[Merged by Bors] - feat: Generalize corollaries of rank-nullity theorem.#9626
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[Merged by Bors] - feat: Generalize corollaries of rank-nullity theorem.#9626
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…eanprover-community/mathlib4 into erd1/rankNullityGeneralization
erdOne
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Jan 10, 2024
…eanprover-community/mathlib4 into erd1/rankNullityGeneralization
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@erdOne are you still interested in working on this PR? Or is it obsolete now? |
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I'm busy until mid-March. I think I'll come back to this after that. Feel free to adopt if this is needed elsewhere. |
…://github.com/leanprover-community/mathlib4 into erd1/rankNullityGeneralization
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Can you add a description of the PR? Also, is it possible to split it? Correct me if I am wrong, but I have the impression you both generalize/move current results and add a new class. Maybe these two things are intertwined and difficult to separate, so don't worry if it is too much work to do it. |
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bors merge |
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Apr 5, 2024
Added a class `HasRankNullity` consisting of the rings that satisfy the rank-nullity theorem. Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class, and moved them into a new file `LinearAlgebra.Dimension.RankNullity`. Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>
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Added a class `HasRankNullity` consisting of the rings that satisfy the rank-nullity theorem. Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class, and moved them into a new file `LinearAlgebra.Dimension.RankNullity`. Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>
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Build failed (retrying...):
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bors r- |
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✌️ erdOne can now approve this pull request. To approve and merge a pull request, simply reply with |
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Canceled. |
…lib4 into erd1/rankNullityGeneralization
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acmepjz
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Apr 12, 2024
Comment on lines
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| lemma exists_set_linearIndependent_of_lt_rank {n : Cardinal} (hn : n < Module.rank R M) : | ||
| ∃ s : Set M, #s = n ∧ LinearIndependent R ((↑) : s → M) := by | ||
| obtain ⟨⟨s, hs⟩, hs'⟩ := exists_lt_of_lt_ciSup' (hn.trans_eq (Module.rank_def R M)) | ||
| obtain ⟨t, ht, ht'⟩ := le_mk_iff_exists_subset.mp hs'.le | ||
| exact ⟨t, ht', .mono ht hs⟩ |
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Could you change the condition of this result to [Semiring R] [AddCommMonoid M] [Module R M]? Same as the following exists_finset_linearIndependent_of_le_rank.
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It's OK if you do it in later PR; I only need to use the ring version.
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bors merge |
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Added a class `HasRankNullity` consisting of the rings that satisfy the rank-nullity theorem. Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class, and moved them into a new file `LinearAlgebra.Dimension.RankNullity`. Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>
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Pull request successfully merged into master. Build succeeded: |
xgenereux
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Apr 15, 2024
Added a class `HasRankNullity` consisting of the rings that satisfy the rank-nullity theorem. Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class, and moved them into a new file `LinearAlgebra.Dimension.RankNullity`. Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>
atarnoam
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Apr 16, 2024
Added a class `HasRankNullity` consisting of the rings that satisfy the rank-nullity theorem. Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class, and moved them into a new file `LinearAlgebra.Dimension.RankNullity`. Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>
uniwuni
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Apr 19, 2024
Added a class `HasRankNullity` consisting of the rings that satisfy the rank-nullity theorem. Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class, and moved them into a new file `LinearAlgebra.Dimension.RankNullity`. Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>
callesonne
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Apr 22, 2024
Added a class `HasRankNullity` consisting of the rings that satisfy the rank-nullity theorem. Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class, and moved them into a new file `LinearAlgebra.Dimension.RankNullity`. Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>
Jun2M
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Apr 24, 2024
Added a class `HasRankNullity` consisting of the rings that satisfy the rank-nullity theorem. Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class, and moved them into a new file `LinearAlgebra.Dimension.RankNullity`. Co-authored-by: Andrew Yang <36414270+erdOne@users.noreply.github.com>
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Added a class
HasRankNullityconsisting of the rings that satisfy the rank-nullity theorem.Generalized the corollaries of the rank-nullity theorem from division rings to rings satisfying the class,
and moved them into a new file
LinearAlgebra.Dimension.RankNullity.