Split ExtAlgebra into a ring ExtAlgebra and a module ExtModule - #277
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Split ExtAlgebra into a ring ExtAlgebra and a module ExtModule#277JoeyBF wants to merge 4 commits into
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📝 WalkthroughWalkthroughThis PR generalizes algebra and module APIs to ChangesMultidegree API
Ext algebra and module abstractions
Examples
Estimated code review effort: 5 (Critical) | ~120 minutes Possibly related PRs
Suggested reviewers: Poem
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Actionable comments posted: 4
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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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📒 Files selected for processing (46)
ext/crates/algebra/Cargo.tomlext/crates/algebra/src/algebra/adem_algebra.rsext/crates/algebra/src/algebra/algebra_trait.rsext/crates/algebra/src/algebra/field.rsext/crates/algebra/src/algebra/milnor_algebra.rsext/crates/algebra/src/algebra/steenrod_algebra.rsext/crates/algebra/src/module/finite_dimensional_module.rsext/crates/algebra/src/module/finitely_presented_module.rsext/crates/algebra/src/module/free_module.rsext/crates/algebra/src/module/hom_module.rsext/crates/algebra/src/module/homomorphism/free_module_homomorphism.rsext/crates/algebra/src/module/homomorphism/full_module_homomorphism.rsext/crates/algebra/src/module/homomorphism/hom_pullback.rsext/crates/algebra/src/module/homomorphism/mod.rsext/crates/algebra/src/module/homomorphism/quotient_homomorphism.rsext/crates/algebra/src/module/mod.rsext/crates/algebra/src/module/module_trait.rsext/crates/algebra/src/module/quotient_module.rsext/crates/algebra/src/module/rpn.rsext/crates/algebra/src/module/suspension_module.rsext/crates/algebra/src/module/tensor_module.rsext/crates/sseq/src/coordinates/degree.rsext/examples/bruner.rsext/examples/ext_m_n.rsext/examples/lift_hom.rsext/examples/massey.rsext/examples/product.rsext/examples/resolution_size.rsext/examples/secondary.rsext/examples/secondary_product.rsext/examples/sq0.rsext/examples/steenrod.rsext/src/chain_complex/chain_homotopy.rsext/src/chain_complex/finite_chain_complex.rsext/src/chain_complex/mod.rsext/src/ext_algebra/massey.rsext/src/ext_algebra/mod.rsext/src/ext_algebra/secondary.rsext/src/nassau.rsext/src/resolution.rsext/src/resolution_homomorphism.rsext/src/secondary.rsext/src/yoneda.rsext/tests/extend_identity.rsext/tests/non_zero_min_degree.rsweb_ext/sseq_gui/src/actions.rs
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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
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- 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
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Closes #259.
What
ExtAlgebratoday conflates two different objects: the ringis_unitflag and awithout_unitconstructor. This PR splits them into two types that implement the actualalgebra::Algebra/algebra::Moduletraits:ExtAlgebra— the ringclass_product_map).impl Algebra<2> for ExtAlgebra.ExtModule— the moduleArc<ExtAlgebra>, plus its own module-action cache.impl Module<2> for ExtModulewithtype Algebra = ExtAlgebra."An algebra is a module over itself" makes the$M = k$ case structural: it's an
ExtModulesharing the ring'sArc, andis_unitis justArc::ptr_eq.without_unitbecomesExtModule::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 theAlgebra/Moduletrait 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 againstmultiply_intoby a new test.Notes for review
Optionhelpers stay inherent.Algebra::multiply_basis_elements/Module::act_on_basispanic if the bidegree isn't resolved (the trait contract — callcompute_basisfirst). The existingOption-returningmultiply_into/try_multiplyremain as inherent helpers for the "maybe out of computed range" ergonomics the examples rely on.ExtAlgebrainto a ringExtAlgebra(over k) and anExtModule(over M) #259.min_degree/max_computed_degreereport the filtrationsaxis (bounded-below direction) rather thant; documented at each site, consistent with the "degree-returns stayi32= 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_mapvsmultiply_into, a trait-surface smoke test, anjust lint/just testCI-parity matrix, all green.🤖 Generated with Claude Code
https://claude.ai/code/session_01Nk9J57zb6GpvZxrduhGSdY
Generated by Claude Code
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