Refactor/remove BilinForm #10553
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I don't think this is meaningfully true; the axiomatization is basically nonsense for non-commutative semirings, so while we may support |
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This is one of the steps in #10553. Once we eliminate `_root_.BilinForm`, we can drop the `LinearMap.` prefix. Requested on Zulip [by me](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Bounded.20bilinear.20forms/near/261981962) (2021), [by @kmill](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/.60bilinear_form.60/near/310675731) (2022), and perhaps one or two other places. Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com>
riccardobrasca
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This is one of the steps in #10553. Once we eliminate `_root_.BilinForm`, we can drop the `LinearMap.` prefix. Requested on Zulip [by me](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Bounded.20bilinear.20forms/near/261981962) (2021), [by @kmill](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/.60bilinear_form.60/near/310675731) (2022), and perhaps one or two other places. Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com>
thorimur
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Feb 24, 2024
This is one of the steps in #10553. Once we eliminate `_root_.BilinForm`, we can drop the `LinearMap.` prefix. Requested on Zulip [by me](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Bounded.20bilinear.20forms/near/261981962) (2021), [by @kmill](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/.60bilinear_form.60/near/310675731) (2022), and perhaps one or two other places. Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com>
thorimur
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Feb 26, 2024
This is one of the steps in #10553. Once we eliminate `_root_.BilinForm`, we can drop the `LinearMap.` prefix. Requested on Zulip [by me](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Bounded.20bilinear.20forms/near/261981962) (2021), [by @kmill](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/.60bilinear_form.60/near/310675731) (2022), and perhaps one or two other places. Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com>
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Replaces `BilinForm` with `LinearMap.BilinForm` in support of #10553 Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com>
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Replaces `BilinForm` with `LinearMap.BilinForm` in support of #10553 Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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kbuzzard
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Replaces `BilinForm` with `LinearMap.BilinForm` in support of #10553 Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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…dules over commutative semirings (#11280) Require the module in the definition of the `BilinForm` structure to be over a commutative semiring. This PR is a per-requisite for #11278. It supersedes #10422. It's been pointed out elsewhere that the current definition over a non-commutative semiring doesn't make mathematical sense: #10553 (comment) Eventually the non-commutative situation may be considered in a mathematically meaningful way in the context of sesquilinear maps (e.g. something like #9334 (review)). Co-authored-by: @Vierkantor Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
dagurtomas
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Mar 22, 2024
This is one of the steps in #10553. Once we eliminate `_root_.BilinForm`, we can drop the `LinearMap.` prefix. Requested on Zulip [by me](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Bounded.20bilinear.20forms/near/261981962) (2021), [by @kmill](https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/.60bilinear_form.60/near/310675731) (2022), and perhaps one or two other places. Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com>
dagurtomas
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Replaces `BilinForm` with `LinearMap.BilinForm` in support of #10553 Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
dagurtomas
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…dules over commutative semirings (#11280) Require the module in the definition of the `BilinForm` structure to be over a commutative semiring. This PR is a per-requisite for #11278. It supersedes #10422. It's been pointed out elsewhere that the current definition over a non-commutative semiring doesn't make mathematical sense: #10553 (comment) Eventually the non-commutative situation may be considered in a mathematically meaningful way in the context of sesquilinear maps (e.g. something like #9334 (review)). Co-authored-by: @Vierkantor Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
utensil
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Replaces `BilinForm` with `LinearMap.BilinForm` in support of #10553 Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
utensil
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…dules over commutative semirings (#11280) Require the module in the definition of the `BilinForm` structure to be over a commutative semiring. This PR is a per-requisite for #11278. It supersedes #10422. It's been pointed out elsewhere that the current definition over a non-commutative semiring doesn't make mathematical sense: #10553 (comment) Eventually the non-commutative situation may be considered in a mathematically meaningful way in the context of sesquilinear maps (e.g. something like #9334 (review)). Co-authored-by: @Vierkantor Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Replaces `BilinForm` with `LinearMap.BilinForm` in support of #10553 Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Louddy
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…dules over commutative semirings (#11280) Require the module in the definition of the `BilinForm` structure to be over a commutative semiring. This PR is a per-requisite for #11278. It supersedes #10422. It's been pointed out elsewhere that the current definition over a non-commutative semiring doesn't make mathematical sense: #10553 (comment) Eventually the non-commutative situation may be considered in a mathematically meaningful way in the context of sesquilinear maps (e.g. something like #9334 (review)). Co-authored-by: @Vierkantor Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
Louddy
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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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…dules over commutative semirings (#11280) Require the module in the definition of the `BilinForm` structure to be over a commutative semiring. This PR is a per-requisite for #11278. It supersedes #10422. It's been pointed out elsewhere that the current definition over a non-commutative semiring doesn't make mathematical sense: #10553 (comment) Eventually the non-commutative situation may be considered in a mathematically meaningful way in the context of sesquilinear maps (e.g. something like #9334 (review)). Co-authored-by: @Vierkantor Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
atarnoam
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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>
uniwuni
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Apr 19, 2024
…dules over commutative semirings (#11280) Require the module in the definition of the `BilinForm` structure to be over a commutative semiring. This PR is a per-requisite for #11278. It supersedes #10422. It's been pointed out elsewhere that the current definition over a non-commutative semiring doesn't make mathematical sense: #10553 (comment) Eventually the non-commutative situation may be considered in a mathematically meaningful way in the context of sesquilinear maps (e.g. something like #9334 (review)). Co-authored-by: @Vierkantor Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
uniwuni
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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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…dules over commutative semirings (#11280) Require the module in the definition of the `BilinForm` structure to be over a commutative semiring. This PR is a per-requisite for #11278. It supersedes #10422. It's been pointed out elsewhere that the current definition over a non-commutative semiring doesn't make mathematical sense: #10553 (comment) Eventually the non-commutative situation may be considered in a mathematically meaningful way in the context of sesquilinear maps (e.g. something like #9334 (review)). Co-authored-by: @Vierkantor Co-authored-by: Christopher Hoskin <christopher.hoskin@gmail.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
callesonne
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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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There seems to be broad agreement that in the long term
structure BilinFormshould not exist - instead we should useM →ₗ[R] M →ₗ[R] R.Many
BilinFormresults already have equivalents e.g. following #9485, many of the results inLinearAlgebra/Matrix/BilinearFormare just wrappers around results inLinearAlgebra/Matrix/SesquilinearForm.One possible objection to removing
BilinFormaltogether at this stage is that it supports non-commutative semirings, whichM →ₗ[R] M →ₗ[R] Rdoes not support without further assumptions.Zulip discussion:
Related issues/PRs:
BilinFormwith a scalar valued biLinearMap#10238BilinearMapabbreviation #10424TraceFormwithLinearMap.BilinForm#11057The text was updated successfully, but these errors were encountered: