[Merged by Bors] - feat(analysis/normed_space/exponential): exponentials of negations, scalar actions, and sums #13036
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These live in their respective namespaces for now to match `list.prod_commute` and `multiset.prod_commute`. This also renames the existing additive versions to `sum_add_commute`, to avoid confusion.
These live in their respective namespaces for now to match `list.prod_commute` and `multiset.prod_commute`. This also renames the existing additive versions to `sum_add_commute`, to avoid confusion.
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| noncomputable def invertible_exp [char_zero 𝕂] (x : 𝔸) : invertible (exp 𝕂 𝔸 x) := | ||
| invertible_exp_of_mem_ball $ (exp_series_radius_eq_top 𝕂 𝔸).symm ▸ edist_lt_top _ _ |
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| noncomputable def invertible_exp [char_zero 𝕂] (x : 𝔸) : invertible (exp 𝕂 𝔸 x) := | |
| invertible_exp_of_mem_ball $ (exp_series_radius_eq_top 𝕂 𝔸).symm ▸ edist_lt_top _ _ | |
| noncomputable def invertible_exp (x : 𝔸) : invertible (exp 𝕂 𝔸 x) := | |
| invertible_exp_of_mem_ball $ (exp_series_radius_eq_top 𝕂 𝔸).symm ▸ edist_lt_top _ _ |
Same with the rest of this section, we have this instance for is_R_or_C 𝕂. Also, how about making this an instance and removing this awkward requirement from inv_of_exp?
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It seems we don't tend to make invertible declarations actually instances, as this easily leads to diamonds. The awkward requirement in inv_of_exp is deliberate, as it makes this lemma immune to diamond problems.
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Fair enough. Let's just remove the [char_zero 𝕂] assumptions and merge this.
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Yep, I agree I should do that.
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…calar actions, and sums (#13036) The new lemmas are: * `exp_invertible_of_mem_ball` * `exp_invertible` * `is_unit_exp_of_mem_ball` * `is_unit_exp` * `ring.inverse_exp` * `exp_neg_of_mem_ball` * `exp_neg` * `exp_sum_of_commute` * `exp_sum` * `exp_nsmul` * `exp_zsmul` I don't know enough about the radius of convergence of `exp` to know if `exp_nsmul` holds more generally under extra conditions.
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The new lemmas are:
exp_invertible_of_mem_ballexp_invertibleis_unit_exp_of_mem_ballis_unit_expring.inverse_expexp_neg_of_mem_ballexp_negexp_sum_of_commuteexp_sumexp_nsmulexp_zsmulI don't know enough about the radius of convergence of
expto know ifexp_nsmulholds more generally under extra conditions.commute.*_sum_{left,right}lemmas #13035