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feat(SpaceTime): add spacetime derivative algebra - #1754

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feat(SpaceTime): add spacetime derivative algebra#1754
jstoobysmith merged 3 commits into
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nateabr:codex/spacetime-derivative-pairing

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@nateabr nateabr commented Oct 7, 2026 •
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Adds SpaceTimeDerivAlgebraℂ, the algebra of derivative symbols ∂_μ, and its pairing with
SpaceTimeAlgebra

this is an extraction from #1415

opus 5.5 and astra 6 was used to make this PR

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jstoobysmith
jstoobysmith reviewed Oct 8, 2026
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Couple of pedantic comments.

Comment thread Physlib/SpaceAndTime/SpaceTime/SpaceTimeDerivAlgebra/Basic.lean Outdated
Comment on lines +15 to +16
The algebra of derivative symbols on spacetime, paired with the spacetime algebra by evaluating
derivatives at the base point.

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Suggested change
The algebra of derivative symbols on spacetime, paired with the spacetime algebra by evaluating
derivatives at the base point.
The algebra of derivative symbols on spacetime, can evaluate on the spacetime algebra.

Comment thread Physlib/SpaceAndTime/SpaceTime/SpaceTimeDerivAlgebra/Basic.lean Outdated
In field theory, local quantities are built from a field and finitely many of its derivatives at
a point. This file sets up the algebra `SpaceTimeDerivAlgebraℂ` of derivative symbols `∂_μ` that
label such constant-coefficient expressions, and pairs it with the spacetime algebra so that a
symbol `P` and the Taylor series `taylorSeries x₀ φ` of a smooth field `φ` give the number

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This could be better explained constant-coefficient expressions and symbol 'P' are not clear

Comment thread Physlib/SpaceAndTime/SpaceTime/SpaceTimeDerivAlgebra/Basic.lean Outdated

Throughout we use the notation of `SpaceTimeAlgebra`, whose elements we call series. For
monomials `x^s`, iterated derivatives `∂^s f`, their base-point values `(∂^s f)(0)` and the
factorials `s!`, indexed by multisets `s` of directions. The Taylor series `taylorSeries x₀ φ` of

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This sentence 'For monomials...' could be made a bit clearer

Comment thread Physlib/SpaceAndTime/SpaceTime/SpaceTimeDerivAlgebra/Basic.lean Outdated
## A. The derivative algebra

The partial derivatives of a smooth field commute, so a constant-coefficient differential
expression is a polynomial in commuting symbols `∂_μ`, and it involves finitely many derivatives

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it involves... it is not clear what it is here.

Comment thread Physlib/SpaceAndTime/SpaceTime/SpaceTimeDerivAlgebra/Basic.lean
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awaiting-author

@github-actions github-actions Bot added the awaiting-author A reviewer has asked the author a question or requested changes label Oct 8, 2026
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nateabr commented Oct 8, 2026

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have made the changes you have requested, let me know what you think

-awaiting-author

@github-actions github-actions Bot removed the awaiting-author A reviewer has asked the author a question or requested changes label Oct 8, 2026
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jstoobysmith approved these changes Oct 9, 2026
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The overview of this file is now very nice! Approved. Will merge now.

@jstoobysmith
jstoobysmith added this pull request to the merge queue Oct 12, 2026
@jstoobysmith jstoobysmith added the ready-to-merge This PR is approved and will be merged shortly label Oct 12, 2026
Merged via the queue into leanprover-community:master with commit 664403d Oct 12, 2026
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