[Merged by Bors] - refactor(LinearAlgebra) : Remove unused commutativity hypothesis #9475
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Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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Remove unused commutativity hypothesis: * Removes the requirement for the Semirings to be commutative in `LinearMap.ext_basis` and `LinearMap.sum_repr_mul_repr_mulₛₗ` in `LinearAlgebra/Basis/Bilinear` * Remove the requirement for some Semirings to be commutative in `AuxToLinearMap`, `CommSemiring` and `CommRing` in `LinearAlgebra/Matrix/SesquilinearForm` * In addition, the rings in `CommRing` can just be `Semiring` No changes to the proofs are required. It would also be possible to weaken commutativity from `Rₗ` in `LinearMap.sum_repr_mul_repr_mul` to `[SMulCommClass Rₗ Rₗ Pₗ]` in order to make `sum_repr_mul_repr_mulₛₗ` and `sum_repr_mul_repr_mul` consistent, but I have not done that in this PR because there might be a performance impact (see #7538 (review)). Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>
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…lts from SesquilinearForm (#9485) Give definitions in `LinearAlgebra/Matrix/BilinearForm` in terms of the equivalent definitions in `LinearAlgebra/Matrix/SesquilinearForm` and derive the `BilinearForm` results as effectively special cases of the equivalent results in `SesquilinearForm`. This reduces the length of `LinearAlgebra/Matrix/BilinearForm` by over 100 lines. The aim is to: * Clarify how results in `BilinearForm` relate to results in `SesquilinearForm` * Reduce duplication of argument between the two files * Validate that the results in `SesquilinearForm` are sufficiently general to provide the results in `BilinearForm` in their existing form - in fact, some loosening of the hypothesis in `SesquilinearForm` is required. Further loosening was already applied in #9475 Co-authored-by: Christopher Hoskin <mans0954@users.noreply.github.com> Co-authored-by: Christopher Hoskin <christopher.hoskin@overleaf.com>
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Remove unused commutativity hypothesis:
LinearMap.ext_basisandLinearMap.sum_repr_mul_repr_mulₛₗinLinearAlgebra/Basis/BilinearAuxToLinearMap,CommSemiringandCommRinginLinearAlgebra/Matrix/SesquilinearFormCommRingcan just beSemiringNo changes to the proofs are required.
It would also be possible to weaken commutativity from
RₗinLinearMap.sum_repr_mul_repr_multo[SMulCommClass Rₗ Rₗ Pₗ]in order to makesum_repr_mul_repr_mulₛₗandsum_repr_mul_repr_mulconsistent, but I have not done that in this PR because there might be a performance impact (see #7538 (review)).Used in #9334