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[Merged by Bors] - feat(group_theory/group_action/units): group actions on and by units#7438
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eric-wieser wants to merge 30 commits intomasterfrom
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[Merged by Bors] - feat(group_theory/group_action/units): group actions on and by units#7438eric-wieser wants to merge 30 commits intomasterfrom
eric-wieser wants to merge 30 commits intomasterfrom
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eric-wieser
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May 2, 2021
This lemma did not need a full algebra structure; written this way, it permits usage on `has_scalar (units R) A` given `algebra R A` (in some future PR). For now, the old algebra lemmas are left behind, to minimize the scope of this patch.
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eric-wieser
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May 10, 2021
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🎉 Great news! Looks like all the dependencies have been resolved:
💡 To add or remove a dependency please update this issue/PR description. Brought to you by Dependent Issues (:robot: ). Happy coding! |
…ction # Conflicts: # src/group_theory/group_action/group.lean # src/linear_algebra/determinant.lean
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fpvandoorn
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LGTM.
I will merge this with master to see if there are any new merge conflicts, but otherwise this is good to go.
bors d+
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May 25, 2021
…7438) This removes all the lemmas about `(u : α) • x` and `(↑u⁻¹ : α) • x` in favor of granting `units α` its very own `has_scalar` structure, along with providing the stronger variants to make it usable elsewhere. This means that downstream code need only reason about `[group G] [mul_action G M]` instead of needing to handle groups and `units` separately. The (multiplicative versions of the) removed and moved lemmas are: * `units.inv_smul_smul` → `inv_smul_smul` * `units.smul_inv_smul` → `smul_inv_smul` * `units.smul_perm_hom`, `mul_action.to_perm` → `mul_action.to_perm_hom` * `units.smul_perm` → `mul_action.to_perm` * `units.smul_left_cancel` → `smul_left_cancel` * `units.smul_eq_iff_eq_inv_smul` → `smul_eq_iff_eq_inv_smul` * `units.smul_eq_zero` → `smul_eq_zero_iff_eq` (to avoid clashing with `smul_eq_zero`) * `units.smul_ne_zero` → `smul_ne_zero_iff_ne` * `homeomorph.smul_of_unit` → `homeomorph.smul` (the latter already existed, and the former was a special case) * `units.measurable_const_smul_iff` → `measurable_const_smul_iff` * `units.ae_measurable_const_smul_iff` → `ae_measurable_const_smul_iff` The new lemmas are: * `smul_eq_zero_iff_eq'`, a `group_with_zero` version of `smul_eq_zero_iff_eq` * `smul_ne_zero_iff_ne'`, a `group_with_zero` version of `smul_ne_zero_iff_ne` * `units.neg_smul`, a version of `neg_smul` for units. We don't currently have typeclasses about `neg` on objects without `+`. We also end up needing some new typeclass instances downstream * `units.measurable_space` * `units.has_measurable_smul` * `units.has_continuous_smul` This goes on to remove lots of coercions from `alternating_map`, `matrix.det`, and some lie algebra stuff. This makes the theorem statement cleaner, but occasionally requires rewriting through `units.smul_def` to add or remove the coercion. Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Floris van Doorn <fpv@andrew.cmu.edu>
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This removes all the lemmas about
(u : α) • xand(↑u⁻¹ : α) • xin favor of grantingunits αits very ownhas_scalarstructure, along with providing the stronger variants to make it usable elsewhere.This means that downstream code need only reason about
[group G] [mul_action G M]instead of needing to handle groups andunitsseparately.The (multiplicative versions of the) removed and moved lemmas are:
units.inv_smul_smul→inv_smul_smulunits.smul_inv_smul→smul_inv_smulunits.smul_perm_hom,mul_action.to_perm→mul_action.to_perm_homunits.smul_perm→mul_action.to_permunits.smul_left_cancel→smul_left_cancelunits.smul_eq_iff_eq_inv_smul→smul_eq_iff_eq_inv_smulunits.smul_eq_zero→smul_eq_zero_iff_eq(to avoid clashing withsmul_eq_zero)units.smul_ne_zero→smul_ne_zero_iff_nehomeomorph.smul_of_unit→homeomorph.smul(the latter already existed, and the former was a special case)units.measurable_const_smul_iff→measurable_const_smul_iffunits.ae_measurable_const_smul_iff→ae_measurable_const_smul_iffThe new lemmas are:
smul_eq_zero_iff_eq', agroup_with_zeroversion ofsmul_eq_zero_iff_eqsmul_ne_zero_iff_ne', agroup_with_zeroversion ofsmul_ne_zero_iff_neunits.neg_smul, a version ofneg_smulfor units. We don't currently have typeclasses aboutnegon objects without+.We also end up needing some new typeclass instances downstream
units.measurable_spaceunits.has_measurable_smulunits.has_continuous_smulThis goes on to remove lots of coercions from
alternating_map,matrix.det, and some lie algebra stuff.This makes the theorem statement cleaner, but occasionally requires rewriting through
units.smul_defto add or remove the coercion.smul_inv#7568 (smul_inv : (c • x)⁻¹ = c⁻¹ • x⁻¹)