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[Merged by Bors] - feat(RingTheory/PowerSeries): Construction of Q such that P(Q(X)) = X#26645

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[Merged by Bors] - feat(RingTheory/PowerSeries): Construction of Q such that P(Q(X)) = X#26645
erdOne wants to merge 6 commits intoleanprover-community:masterfrom
erdOne:erd1/substInv

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@erdOne erdOne commented Jul 2, 2025

Co-authored-by: Junnosuke Koizumi
Co-authored-by: Hyeon, Seung-Hyeon
Co-authored-by: Yuichiro Taguchi

This contribution was created as part of the ZMC conference 2025 "Anabelian Geometry and its Computer Formalization".


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@github-actions github-actions bot added the t-algebra Algebra (groups, rings, fields, etc) label Jul 2, 2025
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github-actions bot commented Jul 3, 2025

PR summary 18a09f9093

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ coeff_one_substInv
+ coeff_subst_sum_C_substInvFun_mul_X_pow_sub_X
+ constantCoeff_substInv
+ hasSubst_substInv
+ substInv
+ substInvFun
+ subst_substInv_left
+ subst_substInv_right

You can run this locally as follows
## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.


No changes to technical debt.

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh pr_summary
  • The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@kckennylau
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I understand that this is a very neat direct proof. But would it be better to first construct the inverse for p = 0+x+O(x^2)? Then presumably you can use "universal polynomials" like they did when defining WittVector.wittAdd? (both of these might be not desirable)

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erdOne commented Jul 3, 2025

Do you mean constructing the inverse to the power series $$\sum a_k X^k \in R[[X, a_1, a_2,\dots]]$$ and then specialize?

@kckennylau
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Yes but I think I still want a1=1 here.

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erdOne commented Jul 3, 2025

It is easy to get what you are describing from what I already have by plugging in R = MvPolynomial Nat R; but I'm not sure what benefits you will get from this?

Comment thread Mathlib/RingTheory/PowerSeries/Substitution.lean Outdated
Comment thread Mathlib/RingTheory/PowerSeries/Substitution.lean Outdated
Comment thread Mathlib/RingTheory/PowerSeries/Substitution.lean Outdated
@kckennylau
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ah I should have been more clear. I think from doing 0+x+O(x^2) first you get the benefit of not having to use 1/, so the proofs should be "easier"?

@grunweg grunweg added t-ring-theory Ring theory and removed t-algebra Algebra (groups, rings, fields, etc) labels Aug 5, 2025
@kbuzzard kbuzzard added the awaiting-author A reviewer has asked the author a question or requested changes. label Aug 20, 2025
@erdOne erdOne removed the awaiting-author A reviewer has asked the author a question or requested changes. label Apr 1, 2026
@riccardobrasca
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Can you add a variant assuming IsUnit? Thanks!

@WenrongZou
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Can you add a variant assuming IsUnit? Thanks!

I am happy to add a variant assuming IsUnit in later PRs. I talked Andrew to pick up this PR (which he did not plan to do it recently) since I will need it. If Andrew @erdOne don't mind, I was wondering whether I can take over this PR. Thanks!

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kbuzzard commented Apr 8, 2026

There's nothing wrong with this PR, let's just merge it and others can add variants later.

bors merge

@mathlib-triage mathlib-triage bot added the ready-to-merge This PR has been sent to bors. label Apr 8, 2026
mathlib-bors bot pushed a commit that referenced this pull request Apr 8, 2026
…= X` (#26645)

This contribution was created as part of the ZMC conference 2025 "Anabelian Geometry and its Computer Formalization".

Co-authored-by: Junnosuke Koizumi
Co-authored-by: Hyeon, Seung-Hyeon
Co-authored-by: Yuichiro Taguchi
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mathlib-bors bot commented Apr 8, 2026

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(RingTheory/PowerSeries): Construction of Q such that P(Q(X)) = X [Merged by Bors] - feat(RingTheory/PowerSeries): Construction of Q such that P(Q(X)) = X Apr 8, 2026
@mathlib-bors mathlib-bors bot closed this Apr 8, 2026
xroblot pushed a commit to xroblot/mathlib4 that referenced this pull request Apr 10, 2026
…= X` (leanprover-community#26645)

This contribution was created as part of the ZMC conference 2025 "Anabelian Geometry and its Computer Formalization".

Co-authored-by: Junnosuke Koizumi
Co-authored-by: Hyeon, Seung-Hyeon
Co-authored-by: Yuichiro Taguchi
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8 participants