refactor(RingTheory/Trace): Define TraceForm with LinearMap.BilinForm
#11057
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This was referenced Feb 28, 2024
mans0954
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LinearMap.BilinFormTraceForm with LinearMap.BilinForm
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…Mathlib, migrate all of `_root_.BilinForm` to `LinearMap.BilinForm` (#11278) Remove `structure BilinForm` from `LinearAlgebra/BilinearForm/Basic` and migrate all of `_root_.BilinForm` to `LinearMap.BilinForm` Closes: #10553 This isn't the end of the story, as there's still a lot of overlap between `LinearAlgebra/BilinearForm` and `LinearAlgebra/SesquilinearForm` but that can be sorted out in subsequent PRs. Supersedes: - #11057 - #11032 - #10432 - #10422 Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Vierkantor <vierkantor@vierkantor.com>
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…Mathlib, migrate all of `_root_.BilinForm` to `LinearMap.BilinForm` (#11278) Remove `structure BilinForm` from `LinearAlgebra/BilinearForm/Basic` and migrate all of `_root_.BilinForm` to `LinearMap.BilinForm` Closes: #10553 This isn't the end of the story, as there's still a lot of overlap between `LinearAlgebra/BilinearForm` and `LinearAlgebra/SesquilinearForm` but that can be sorted out in subsequent PRs. Supersedes: - #11057 - #11032 - #10432 - #10422 Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Vierkantor <vierkantor@vierkantor.com>
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…Mathlib, migrate all of `_root_.BilinForm` to `LinearMap.BilinForm` (#11278) Remove `structure BilinForm` from `LinearAlgebra/BilinearForm/Basic` and migrate all of `_root_.BilinForm` to `LinearMap.BilinForm` Closes: #10553 This isn't the end of the story, as there's still a lot of overlap between `LinearAlgebra/BilinearForm` and `LinearAlgebra/SesquilinearForm` but that can be sorted out in subsequent PRs. Supersedes: - #11057 - #11032 - #10432 - #10422 Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Vierkantor <vierkantor@vierkantor.com>
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…Mathlib, migrate all of `_root_.BilinForm` to `LinearMap.BilinForm` (#11278) Remove `structure BilinForm` from `LinearAlgebra/BilinearForm/Basic` and migrate all of `_root_.BilinForm` to `LinearMap.BilinForm` Closes: #10553 This isn't the end of the story, as there's still a lot of overlap between `LinearAlgebra/BilinearForm` and `LinearAlgebra/SesquilinearForm` but that can be sorted out in subsequent PRs. Supersedes: - #11057 - #11032 - #10432 - #10422 Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Vierkantor <vierkantor@vierkantor.com>
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…Mathlib, migrate all of `_root_.BilinForm` to `LinearMap.BilinForm` (#11278) Remove `structure BilinForm` from `LinearAlgebra/BilinearForm/Basic` and migrate all of `_root_.BilinForm` to `LinearMap.BilinForm` Closes: #10553 This isn't the end of the story, as there's still a lot of overlap between `LinearAlgebra/BilinearForm` and `LinearAlgebra/SesquilinearForm` but that can be sorted out in subsequent PRs. Supersedes: - #11057 - #11032 - #10432 - #10422 Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Vierkantor <vierkantor@vierkantor.com>
Mathlib/RingTheory/Trace.lean
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| @@ -190,8 +193,8 @@ variable (R S) | |||
| /-- The `traceForm` maps `x y : S` to the trace of `x * y`. | |||
| It is a symmetric bilinear form and is nondegenerate if the extension is separable. -/ | |||
| noncomputable def traceForm : BilinForm R S := | |||
| -- Porting note: dot notation `().toBilin` does not work anymore. | |||
| LinearMap.toBilin (LinearMap.compr₂ (lmul R S).toLinearMap (trace R S)) | |||
| -- Porting note: dot notation `().toBilin` does not work anymore. | |||
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| -- Porting note: dot notation `().toBilin` does not work anymore. |
This does not make sense anymore.
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traceForm got redefined in #12078, but the porting note remains.
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Well, I guess it's time to remove it.
| BilinForm.nondegenerate_of_det_ne_zero (traceForm K L) _ | ||
| (det_traceForm_ne_zero (FiniteDimensional.finBasis K L)) | ||
| #align trace_form_nondegenerate traceForm_nondegenerate | ||
| theorem traceForm_separatingLeft [FiniteDimensional K L] [IsSeparable K L] : |
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Why erasing traceForm_nondegenerate? Even if traceForm_separatingLeft is stronger we can have both (as a lot of people will look for nondegeneracy).
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The description of the PR is wrong, right? You use |
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@eric-wieser do you think I should close this PR without merging? I'm not sure that it's useful now #11278 has been merged. |
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Closing this, for now at least, as I don't think it helps us move things forwards. |
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Redefine
traceForm : BilinForm R SusingLinearMap.BilinForminstead ofBilinForm.Contributes to #10553