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refactor(number_theory/modular_forms/slash_actions): slash actions are families of distrib_mul_actions #18932

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@eric-wieser eric-wieser commented May 3, 2023

This replaces the bespoke slash_action β G α γ typeclass with:

  • Π b : β, distrib_mul_action (slash_act G b) α for the action itself, where slash_act G b is a type alias of mul_opposite (to allow for right actions)
  • smul_comm_class (slash_act G k) γ α for compatibility with the γ action

This means compatibility with multiple types simultaneously is possible, and that f ∣[k;γ] A notation can be discarded.

This keeps around slash_action.map k A f to provide f ∣[k] A notation, but it's now reducibly equal to slash_act.of k A • f


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It's not immediately clear that the switch to using distrib_mul_action is worth it, but this does at least prove it can be done.

@eric-wieser eric-wieser added WIP Work in progress awaiting-CI The author would like to see what CI has to say before doing more work. labels May 3, 2023
@eric-wieser eric-wieser added the t-number-theory Number theory (also use t-algebra or t-analysis to specialize) label May 3, 2023
@eric-wieser eric-wieser force-pushed the eric-wieser/slash_action.redo branch from e769b8a to 25af56d Compare May 4, 2023 21:34
@eric-wieser eric-wieser added RFC Request for comment and removed WIP Work in progress labels May 4, 2023
@github-actions github-actions bot removed the awaiting-CI The author would like to see what CI has to say before doing more work. label May 10, 2023
@kim-em kim-em added the too-late This PR was ready too late for inclusion in mathlib3 label Jul 16, 2023
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