Giter Club home page Giter Club logo

Comments (3)

Vierkantor avatar Vierkantor commented on June 26, 2024

I have the following result on my ideal-span-norm branch:

noncomputable def basis.localization_localization {R S : Type*} [comm_ring R] [comm_ring S]
  [algebra R S] {ι : Type*} [fintype ι] (b : basis ι R S)
  (M : submonoid R) (Rₘ Sₘ : Type*)
  [comm_ring Rₘ] [algebra R Rₘ] [comm_ring Sₘ] [algebra S Sₘ]
  [algebra Rₘ Sₘ] [algebra R Sₘ] [is_scalar_tower R Rₘ Sₘ] [is_scalar_tower R S Sₘ]
  [is_localization M Rₘ] [is_localization (M.map (algebra_map R S)) Sₘ]
  (hM : submonoid.map (algebra_map R S) M ≤ S ⁰) :
  basis ι Rₘ Sₘ :=

That is what we're looking for, right?

from mathlib.

riccardobrasca avatar riccardobrasca commented on June 26, 2024

I have the following result on my ideal-span-norm branch:

noncomputable def basis.localization_localization {R S : Type*} [comm_ring R] [comm_ring S]
  [algebra R S] {ι : Type*} [fintype ι] (b : basis ι R S)
  (M : submonoid R) (Rₘ Sₘ : Type*)
  [comm_ring Rₘ] [algebra R Rₘ] [comm_ring Sₘ] [algebra S Sₘ]
  [algebra Rₘ Sₘ] [algebra R Sₘ] [is_scalar_tower R Rₘ Sₘ] [is_scalar_tower R S Sₘ]
  [is_localization M Rₘ] [is_localization (M.map (algebra_map R S)) Sₘ]
  (hM : submonoid.map (algebra_map R S) M ≤ S ⁰) :
  basis ι Rₘ Sₘ :=

That is what we're looking for, right?

Yes! This should replace basis.localization, whose assumptions essentially never apply (we take a -basis of a -vector space).

from mathlib.

Vierkantor avatar Vierkantor commented on June 26, 2024

I PR'd the result above in #18261.

from mathlib.

Related Issues (20)

Recommend Projects

  • React photo React

    A declarative, efficient, and flexible JavaScript library for building user interfaces.

  • Vue.js photo Vue.js

    🖖 Vue.js is a progressive, incrementally-adoptable JavaScript framework for building UI on the web.

  • Typescript photo Typescript

    TypeScript is a superset of JavaScript that compiles to clean JavaScript output.

  • TensorFlow photo TensorFlow

    An Open Source Machine Learning Framework for Everyone

  • Django photo Django

    The Web framework for perfectionists with deadlines.

  • D3 photo D3

    Bring data to life with SVG, Canvas and HTML. 📊📈🎉

Recommend Topics

  • javascript

    JavaScript (JS) is a lightweight interpreted programming language with first-class functions.

  • web

    Some thing interesting about web. New door for the world.

  • server

    A server is a program made to process requests and deliver data to clients.

  • Machine learning

    Machine learning is a way of modeling and interpreting data that allows a piece of software to respond intelligently.

  • Game

    Some thing interesting about game, make everyone happy.

Recommend Org

  • Facebook photo Facebook

    We are working to build community through open source technology. NB: members must have two-factor auth.

  • Microsoft photo Microsoft

    Open source projects and samples from Microsoft.

  • Google photo Google

    Google ❤️ Open Source for everyone.

  • D3 photo D3

    Data-Driven Documents codes.