Split ExtAlgebra into a ring ExtAlgebra and a module ExtModule by JoeyBF · Pull Request #277 · SpectralSequences/sseq

JoeyBF · 2026-08-01T05:58:42Z

Closes#259.

What

ExtAlgebra today conflates two different objects: the ring$\mathrm{Ext}(k,k)$ and a module$\mathrm{Ext}(M,k)$ over it, glued together by an is_unit flag and a without_unit constructor. This PR splits them into two types that implement the actualalgebra::Algebra / algebra::Module traits:

ExtAlgebra — the ring $\mathrm{Ext}(k,k)$. Owns the resolution of $k$ and the per-generator ring-product cache (class_product_map). impl Algebra<2> for ExtAlgebra.
ExtModule — the module $\mathrm{Ext}(M,k)$ over it. Owns the resolution of $M$ and a shared Arc<ExtAlgebra>, plus its own module-action cache. impl Module<2> for ExtModule with type Algebra = ExtAlgebra.

"An algebra is a module over itself" makes the $M = k$ case structural: it's an ExtModule sharing the ring's Arc, and is_unit is just Arc::ptr_eq. without_unit becomes ExtModule::intrinsic.

The bigrading is why this is possible now: Ext is bigraded $(s,t)$, so it needs Algebra<2> / Module<2>. That capability is the previous PR in the stack (#268), which makes the Algebra/Module trait family multigrading-capable with zero behavior change for the singly-graded engine.

Also in this PR

ResolutionHomomorphism::linear_combination — a cheap primitive that assembles a multiply-by-a-class chain map by adding the cached per-generator maps (no quasi-inverse solves). It backs the trait product methods and is cross-validated against multiply_into by a new test.

Notes for review

Trait products are total, Option helpers stay inherent.Algebra::multiply_basis_elements / Module::act_on_basis panic if the bidegree isn't resolved (the trait contract — call compute_basis first). The existing Option-returning multiply_into / try_multiply remain as inherent helpers for the "maybe out of computed range" ergonomics the examples rely on.
Odd-prime sign. The product/action impls realise the ring product / right action up to the Koszul sign, exact only at $p = 2$. This is documented loudly at the impl sites so nobody wires it into odd-prime machinery generically — it matches the pre-existing up-to-sign product API and is out of scope for Split ExtAlgebra into a ring ExtAlgebra (over k) and an ExtModule (over M) #259.
Axis reinterpretation.min_degree / max_computed_degree report the filtration s axis (bounded-below direction) rather than t; documented at each site, consistent with the "degree-returns stay i32 = filtration" convention from Make the Algebra and Module traits multigrading-capable #268.

Stacking

This is built on #268 (the multigrade trait work). Until #268 merges, this PR's diff includes those commits too; it will collapse to just the ext-split commits once #268 lands and I rebase.

Testing

cargo test -p ext ext_algebra (10 tests incl. the #116 Massey regressions, class_product_map vs multiply_into, a trait-surface smoke test, an $M \neq k$ product test, and an odd-prime product test), plus the full just lint / just test CI-parity matrix, all green.

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https://claude.ai/code/session_01Nk9J57zb6GpvZxrduhGSdY

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Summary by CodeRabbit

New Features
- Added support for multigraded algebra and module computations while preserving convenient single-degree usage.
- Introduced separate Ext algebra and Ext module workflows, including intrinsic and non-unit module constructions.
- Added linear combinations of resolution homomorphisms.
Bug Fixes
- Improved Massey product calculations, including kernel handling, zero targets, indeterminacy, and homotopy validation.
- Improved product-map reuse and support for products across distinct resolutions.
Compatibility
- Updated Steenrod and module operations to work consistently with the expanded grading API.

coderabbitai · 2026-08-01T05:58:59Z

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📥 Commits

Reviewing files that changed from the base of the PR and between 5adc5f1 and 0c37296.

📒 Files selected for processing (6)

ext/crates/algebra/Cargo.toml
ext/crates/algebra/src/algebra/algebra_trait.rs
ext/crates/algebra/src/algebra/steenrod_algebra.rs
ext/examples/product.rs
ext/src/ext_algebra/massey.rs
ext/src/resolution_homomorphism.rs

📝 Walkthrough

Walkthrough

This PR generalizes algebra and module APIs to MultiDegree, adds ModuleExt compatibility wrappers, and separates ExtAlgebra from ExtModule. It also updates Massey products, secondary computations, resolution maps, examples, and feature forwarding.

Changes

Multidegree API

Layer / File(s)	Summary
Generalized algebra degree contracts `ext/crates/algebra/src/algebra/*`, `ext/crates/sseq/src/coordinates/degree.rs`, `ext/crates/algebra/Cargo.toml`	Algebra methods accept multidegrees, scalar conversions are added, and Steenrod dispatch becomes manual.
Multigraded module contract and implementations `ext/crates/algebra/src/module/*`	`Module<N>` uses `MultiDegree<N>`, while `ModuleExt` provides compatible scalar-style methods. Concrete modules implement the new API.
ModuleExt consumer migration `ext/src/chain_complex/`, `ext/src/resolution.rs`, `ext/src/secondary.rs`, `web_ext/sseq_gui/src/actions.rs`, `ext/tests/*`	Consumers import `ModuleExt` and use its dimension and action wrappers.

Ext algebra and module abstractions

Layer / File(s)	Summary
Separate ExtAlgebra and ExtModule `ext/src/ext_algebra/mod.rs`	`ExtAlgebra` owns ring data and caches. `ExtModule` owns module data and shares the ring algebra.
Massey and secondary Ext integration `ext/src/ext_algebra/massey.rs`, `ext/src/ext_algebra/secondary.rs`	Massey and secondary computations use `ExtModule`, intrinsic algebra access, and shared product maps.
Resolution homomorphism combination `ext/src/resolution_homomorphism.rs`	`linear_combination` validates compatible summands and combines their generator images within a bounded bidegree.

Examples

Layer / File(s)	Summary
ExtModule example migration `ext/examples/massey.rs`, `ext/examples/product.rs`, `ext/examples/secondary*.rs`	Examples use `ExtModule` constructors and updated algebra, resolution, and secondary accessors.
Example module implementations `ext/examples/bruner.rs`, `ext/examples/ext_m_n.rs`, `ext/examples/lift_hom.rs`, `ext/examples/resolution_size.rs`, `ext/examples/sq0.rs`, `ext/examples/steenrod.rs`	Examples use `ModuleExt` and implement multidegree module methods where required.

Estimated code review effort: 5 (Critical) | ~120 minutes

Possibly related PRs

SpectralSequences/sseq#240: Introduced the ExtAlgebra APIs that this PR separates into ring and module abstractions.
SpectralSequences/sseq#247: Added the Massey-product implementation that this PR migrates to ExtModule.
SpectralSequences/sseq#258: Updated the Massey computation paths that this PR incorporates while changing the owning abstraction.

Suggested reviewers:hoodmane

Poem

A rabbit sorts degrees in rows,
While ExtAlgebra’s ring cache glows.
ExtModule hops into place,
Massey maps run with shared grace.
Multidegrees guide each trail.
“Hop!” says the rabbit. “Build and prevail!”

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Description Check	✅ Passed	Check skipped - CodeRabbit’s high-level summary is enabled.
Title check	✅ Passed	The title clearly and concisely describes the primary change: splitting ExtAlgebra into ring and module types.
Linked Issues check	✅ Passed	The changes implement issue `#259` by separating ring and module responsibilities, updating Massey computations, caches, consumers, and supporting APIs.
Out of Scope Changes check	✅ Passed	The multigrading, linear-combination, API, example, and consumer changes directly support the ExtAlgebra and ExtModule split.
Docstring Coverage	✅ Passed	Docstring coverage is 100.00% which is sufficient. The required threshold is 80.00%.

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Actionable comments posted: 4

🤖 Prompt for all review comments with AI agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.
Inline comments:
In `@ext/examples/sq0.rs`:
- Around line 287-288: Update element_to_string_multi to pass the halved degree
to the inner module, matching basis_element_to_string_multi and DoubleModule’s
2n representation; use the converted degree value when calling the inner
formatter so it receives n rather than 2n.
In `@ext/src/ext_algebra/massey.rs`:
- Around line 63-72: The documentation for massey_b_hom in
ext/src/ext_algebra/massey.rs lines 63-72 must qualify the caching behavior:
generator product maps are cached and shared, while multi-generator classes
assemble a fresh combined map per call. Update the related documentation at
ext/src/ext_algebra/massey.rs lines 294-296 with the same qualification; no code
changes are required.
In `@ext/src/ext_algebra/secondary.rs`:
- Around line 43-49: Rename the public type SecondaryExtAlgebra to
SecondaryExtModule throughout the implementation, including both impl blocks,
its module documentation, all constructors, and every construction site such as
examples and SecondaryExtAlgebra::new. Preserve the existing behavior and ensure
references use the renamed type consistently.
In `@ext/src/resolution_homomorphism.rs`:
- Around line 174-177: Enforce the documented empty-name precondition at the
start of linear_combination by asserting that name is empty, so invalid callers
fail immediately before maps or save state are populated.

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Configuration used: Organization UI

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📥 Commits

Reviewing files that changed from the base of the PR and between 99ddfb6 and 5adc5f1.

📒 Files selected for processing (46)

ext/crates/algebra/Cargo.toml
ext/crates/algebra/src/algebra/adem_algebra.rs
ext/crates/algebra/src/algebra/algebra_trait.rs
ext/crates/algebra/src/algebra/field.rs
ext/crates/algebra/src/algebra/milnor_algebra.rs
ext/crates/algebra/src/algebra/steenrod_algebra.rs
ext/crates/algebra/src/module/finite_dimensional_module.rs
ext/crates/algebra/src/module/finitely_presented_module.rs
ext/crates/algebra/src/module/free_module.rs
ext/crates/algebra/src/module/hom_module.rs
ext/crates/algebra/src/module/homomorphism/free_module_homomorphism.rs
ext/crates/algebra/src/module/homomorphism/full_module_homomorphism.rs
ext/crates/algebra/src/module/homomorphism/hom_pullback.rs
ext/crates/algebra/src/module/homomorphism/mod.rs
ext/crates/algebra/src/module/homomorphism/quotient_homomorphism.rs
ext/crates/algebra/src/module/mod.rs
ext/crates/algebra/src/module/module_trait.rs
ext/crates/algebra/src/module/quotient_module.rs
ext/crates/algebra/src/module/rpn.rs
ext/crates/algebra/src/module/suspension_module.rs
ext/crates/algebra/src/module/tensor_module.rs
ext/crates/sseq/src/coordinates/degree.rs
ext/examples/bruner.rs
ext/examples/ext_m_n.rs
ext/examples/lift_hom.rs
ext/examples/massey.rs
ext/examples/product.rs
ext/examples/resolution_size.rs
ext/examples/secondary.rs
ext/examples/secondary_product.rs
ext/examples/sq0.rs
ext/examples/steenrod.rs
ext/src/chain_complex/chain_homotopy.rs
ext/src/chain_complex/finite_chain_complex.rs
ext/src/chain_complex/mod.rs
ext/src/ext_algebra/massey.rs
ext/src/ext_algebra/mod.rs
ext/src/ext_algebra/secondary.rs
ext/src/nassau.rs
ext/src/resolution.rs
ext/src/resolution_homomorphism.rs
ext/src/secondary.rs
ext/src/yoneda.rs
ext/tests/extend_identity.rs
ext/tests/non_zero_min_degree.rs
web_ext/sseq_gui/src/actions.rs

Generalize the `Algebra` trait family to be multigrading-capable, as the foundation for treating Ext(k,k) as a genuine bigraded algebra (issue SpectralSequences#259). - `Algebra<const N: usize = 1>`: degree *inputs* now take `impl Into<MultiDegree<N>>`, so singly-graded callers keep passing bare `i32`s (via new `From<i32> for MultiDegree<1>`). The default `N = 1` keeps every existing `A: Algebra` bound and `dyn` usage working unchanged. - `enum_dispatch` cannot handle a generic trait, so `Algebra` is removed from `SteenrodAlgebra`'s dispatch list and hand-rolled via `dispatch_steenrod!` (the pattern already used for `PairAlgebra`). `UnstableAlgebra`, `GeneratedAlgebra`, and `MuAlgebra` stay singly-graded and keep enum_dispatch. - Milnor, Adem, and Field implement `Algebra` (default `N = 1`), converting the incoming degree to `i32` at each method boundary. - Degree-returning methods stay `i32` (the distinguished filtration direction), so the resolution engine's degree arithmetic is untouched. - `algebra` now depends on `sseq` for `MultiDegree` (no dependency cycle). Behavior is unchanged for the singly-graded path; all 51 algebra tests pass. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Nk9J57zb6GpvZxrduhGSdY

- Remove 'Grading' section header and condense explanation - Simplify steenrod_algebra.rs enum comment - Preserve essential information about genericity and dispatch strategy Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Nk9J57zb6GpvZxrduhGSdY

…equences#259) Split the conflated `ExtAlgebra` into two objects that match the two things a resolution computes: - `ExtAlgebra` is the ring `Ext(k, k)`, backed by a resolution of `k`. It owns the ring-product cache (`res(k) -> res(k)`) and is the single home for the multiply-by-a-class maps Massey products need (`ExtAlgebra::class_product_map`), fixing the awkwardness noted in SpectralSequences#258 where `massey_b_hom` rebuilt that map from scratch each call. - `ExtModule` is a module `Ext(M, k)` over that ring, backed by a resolution of `M`. It holds a shared `Arc<ExtAlgebra>` (so all modules over the same `k` reuse one ring cache) and its own module-action cache (`res(M) -> res(k)`). `M == k` collapses to "a module over itself": `ExtModule` shares its resolution `Arc` with the ring, so `is_unit` is now a structural `ptr_eq` (`ExtModule::is_unit`) rather than a stored flag. `without_unit` is replaced by `ExtModule::intrinsic` for the resolution-intrinsic `d2` path. `ExtAlgebra` implements `algebra::Algebra<2>` and `ExtModule` implements `algebra::module::Module<2>` (with `Algebra = ExtAlgebra`), realising the "resolving an algebra yields an Algebra, resolving a module yields a Module" correspondence on the real trait family. The trait product/action methods are total; the inherent `multiply_into`/`try_multiply` keep their `Option`-returning out-of-range ergonomics. The shared product core lives in module-level helpers (`cached_generator_product_map`, `products_into`, `combine_product`) so ring and module products do not duplicate logic. Massey products move to `ExtModule` (a, b in the ring; c in the module), with `massey_b_hom` now sourced from the shared ring cache via `class_product_map`. `SecondaryExtAlgebra` wraps an `ExtModule`; the four examples and in-module tests are updated. Behaviour is unchanged: the three Massey regression tests (SpectralSequences#116), the product test, and the d2 test all pass. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Nk9J57zb6GpvZxrduhGSdY

Add `ResolutionHomomorphism::linear_combination`, which builds the chain map `∑ cᵢ·fᵢ` from maps sharing a source, target, and shift by summing their generator images directly — no quasi-inverse lift. `ExtAlgebra::class_product_map` now uses it for multi-generator classes: a single generator returns the cached per-generator map, and a general class *adds* the cached generator maps instead of re-solving the class from scratch via `from_class`. This realises the "storing lifts per generator, adding maps is cheap" design and gives the shared ring cache a real payoff for the multiply-by-a-class maps Massey products consume. A new regression test cross-checks the two independent linear-combination strategies at the first two-generator bidegree of Ext(F₂,F₂) — (n=15, s=5): `class_product_map` sums maps at the chain level, `multiply_into` sums them at the hom_k level, and the induced products must agree. They do. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Nk9J57zb6GpvZxrduhGSdY

JoeyBF mentioned this pull request Aug 1, 2026
Split the secondary layer + add SecondaryExtModule::secondary_massey #278
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coderabbitaiBot requested changes Aug 1, 2026
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Comment threadext/examples/sq0.rs Outdated
Comment threadext/src/ext_algebra/massey.rs
Comment threadext/src/ext_algebra/secondary.rs
Comment threadext/src/resolution_homomorphism.rs

JoeyBF force-pushed the claude/259-phase2-ext-split branch from 5adc5f1 to 8ef36daCompare August 1, 2026 06:28

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JoeyBF force-pushed the claude/259-phase2-ext-split branch 2 times, most recently from 4c96f46 to 285e8bcCompare August 1, 2026 07:31

claude added 3 commits August 26, 2026 19:02

JoeyBF force-pushed the claude/259-phase2-ext-split branch from 285e8bc to 0c37296Compare August 26, 2026 19:03

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Split ExtAlgebra into a ring ExtAlgebra and a module ExtModule - #277

Split ExtAlgebra into a ring ExtAlgebra and a module ExtModule#277
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