[Merged by Bors] - refactor(linear_algebra/quadratic_form/basic): generalize to semiring #14303
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…gebra/quadratic_form/basic` 150 lines seems worthy of its own file, especially if this grows `fun_like` boilerplate in future. No lemmas have been renamed or proofs changed.
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adamtopaz
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LGTM! I just had one small question/comment for you to consider.
Also, it seems that the file quadratic_form/basic is starting to get large, and trying to do too much. We should consider splitting it up (in a later PR). I think the basic defs should go in basic while the anisotropic stuff could go in a separate file called anisotropic for example.
I completely agree! |
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…#14303) This uses a slightly nicer strategy than the one suggested by @adamtopaz [on Zulip](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Exterior.20algebras.20over.20semiring/near/282808284). The main motivation here is to be able to talk about `0 : quadratic_form R M` even when there is no negation available, as that will let us merge `clifford_algebra` (which currently requires negation) and `exterior_algebra` (which does not). It's likely this generalization is broadly not very useful, so this adds a `quadratic_form.of_polar` constructor to preserve the old more convenient API. Note the `.bib` file changed slightly as I ran the autoformatting tool.
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This uses a slightly nicer strategy than the one suggested by @adamtopaz on Zulip.
The main motivation here is to be able to talk about
0 : quadratic_form R Meven when there is no negation available, as that will let us mergeclifford_algebra(which currently requires negation) andexterior_algebra(which does not).It's likely this generalization is broadly not very useful, so this adds a
quadratic_form.of_polarconstructor to preserve the old more convenient API.Note the
.bibfile changed slightly as I ran the autoformatting tool.linear_algebra/quadratic_form/basic#14305