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[Merged by Bors] - refactor(algebra/{dual_number,triv_sq_zero_ext}): support non-commutative rings #18384
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eric-wieser
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Feb 22, 2023
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This looks fine to me. The maintainer merge |
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🚀 Pull request has been placed on the maintainer queue by j-loreaux. |
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Two superficial comments but otherwise LGTM. bors d+ |
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Feb 22, 2023
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bors merge |
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Feb 23, 2023
…tive rings (#18384) This changes the definition of multiplication on `triv_sq_zero_ext R M` as follows ```diff -x * y = (x.1 * y.1, x.1 • y.2 + y.1 • x.2) +x * y = (x.1 * y.1, x.1 • y.2 + op y.1 • x.2) ``` which for `R=M` gives the more natural `x.1 * y.2 + x.2 * y.1` in the second term instead of `x.1 * y.2 + y.1 * x.2`. This adds some slightly annoying typeclass arguments that could eventually be cleaned up by #10716; but that PR has rotted under the mathlib4 tide. Either way, the weird typeclass arguments needed with `triv_sq_zero_ext R M` are all invisible when working with `dual_number R`. This is motivated by wanting to talk about `dual_number (quaternion R)` or `dual_number (matrix n n R)`. Unfortunately this breaks the `topological_semiring` instance (making it need an `@` and trigger the `fails_quickly` linter), but this instance isn't really interesting anyway.
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Mar 15, 2023
Some more results following on from #18384. For now this just has the list lemmas. The multiset and finset lemmas are hard to state cleanly.
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This changes the definition of multiplication on
triv_sq_zero_ext R Mas followswhich for
R=Mgives the more naturalx.1 * y.2 + x.2 * y.1in the second term instead ofx.1 * y.2 + y.1 * x.2.This adds some slightly annoying typeclass arguments that could eventually be cleaned up by #10716; but that PR has rotted under the mathlib4 tide. Either way, the weird typeclass arguments needed with
triv_sq_zero_ext R Mare all invisible when working withdual_number R.This is motivated by wanting to talk about
dual_number (quaternion R)ordual_number (matrix n n R).Unfortunately this breaks the
topological_semiringinstance (making it need an@and trigger thefails_quicklylinter), but this instance isn't really interesting anyway.