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[Merged by Bors] - feat: local frame induced by a vector bundle trivialisation#31788

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[Merged by Bors] - feat: local frame induced by a vector bundle trivialisation#31788
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grunweg:localframes-construction1

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@grunweg grunweg commented Nov 18, 2025 •
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We construct local frames on a vector from local trivialisations. The former constructs, given a trivialisation e of the vector bundle and a basis of the model fibre, Basis.localFrame is a local frame on e.baseSet.

Future PRs will

  • define the coefficients of a section w.r.t. this local frame (and related smoothness of a section to the smoothness of its coefficients),
  • will use this to define the local extension of a tangent vector to a vector field near a point.

From the path towards geodesics and the Levi-Civita connection.

Co-authored-by: Patrick Massot patrickmassot@free.fr

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@grunweg grunweg changed the title feat: local frames induces by a vector bundle trivialisation feat: local frame induced by a vector bundle trivialisation Nov 18, 2025
@github-actions github-actions bot added the t-differential-geometry Manifolds etc label Nov 18, 2025
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github-actions bot commented Nov 18, 2025 •
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PR summary 6a54a80825

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference

Declarations diff

+ _root_.contMDiffAt_localFrame_of_mem
+ basisAt
+ contMDiffOn_localFrame_baseSet
+ fintype_of_finiteDimensional
+ isLocalFrameOn_localFrame_baseSet
+ localFrame
+ localFrame_apply_of_mem_baseSet
+ localFrame_apply_of_notMem

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

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

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

No changes to technical debt.

You can run this locally as

./scripts/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).

@grunweg grunweg mentioned this pull request Nov 18, 2025
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@grunweg grunweg requested a review from ocfnash November 18, 2025 22:48
@ocfnash ocfnash self-assigned this Nov 19, 2025
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ocfnash approved these changes Nov 19, 2025
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Thanks!

bors d+

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mathlib-bors bot commented Nov 19, 2025

✌️ grunweg can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

@ghost ghost added the delegated This pull request has been delegated to the PR author (or occasionally another non-maintainer). label Nov 19, 2025
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5a266f7 
Co-authored-by: Oliver Nash <7734364+ocfnash@users.noreply.github.com>
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grunweg commented Nov 19, 2025

Thanks for the review!
bors merge

@ghost ghost added the ready-to-merge This PR has been sent to bors. label Nov 19, 2025
mathlib-bors bot pushed a commit that referenced this pull request Nov 19, 2025
@grunweg
feat: local frame induced by a vector bundle trivialisation (#31788)
5db554c 
We construct local frames on a vector from local trivialisations. The former constructs, given a trivialisation e of the vector bundle and a basis of the model fibre, Basis.localFrame is a local frame on e.baseSet.

Future PRs will
- define the coefficients of a section w.r.t. this local frame (and related smoothness of a section to the smoothness of its coefficients),
- will use this to define the local extension of a tangent vector to a vector field near a point.

From the path towards geodesics and the Levi-Civita connection.

Co-authored-by: Patrick Massot [patrickmassot@free.fr](mailto:patrickmassot@free.fr)
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mathlib-bors bot commented Nov 19, 2025

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat: local frame induced by a vector bundle trivialisation [Merged by Bors] - feat: local frame induced by a vector bundle trivialisation Nov 19, 2025
@mathlib-bors mathlib-bors bot closed this Nov 19, 2025
@grunweg grunweg deleted the localframes-construction1 branch November 19, 2025 13:03
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