Add primary Massey products to ExtAlgebra by JoeyBF · Pull Request #247 · SpectralSequences/sseq

JoeyBF · 2026-06-26T00:34:14Z

Introduce ExtAlgebra::massey and ExtAlgebra::massey_family in the new ext_algebra/massey.rs, computing triple Massey products <a, b, c> (and the optimized <a, b, -> family over all valid third factors). The result type MasseyResult carries an AffineSubspace.

These wrap ChainHomotopy: for each candidate c we lift the multiplication map, build the null-homotopy of the composite with b, and read off the bracket by pairing with a; the valid c are the kernel of multiplication by b. No new linear algebra is added — this repackages the logic of the massey example.

Refactors the massey example onto massey_iter_{a,c}; output is byte-identical to before (verified on S_2). Adds a unit test for the relation <h0, h1, h0> = h1^2 and that <h0, h1, h1> is undefined.

Claude-Session: https://claude.ai/code/session_01XYWcvWZPm3YJkVpCmeGYsP

Summary by CodeRabbit

New Features
- Added triple Massey product support in the Ext algebra, with iterator-based enumeration.
- Introduced a Massey result type (with representative extraction and a “contains zero” check).
- Added a utility to construct scalar-side unit generators.
- Updated the Massey example to use the new Ext algebra APIs.
Tests
- Added unit tests covering known Massey relations and iterator consistency.
Bug Fixes / Chores
- Normalized Massey-related benchmark equation/index encoding and RHS expression formatting.

Introduce `ExtAlgebra::massey` and `ExtAlgebra::massey_family` in the new `ext_algebra/massey.rs`, computing triple Massey products <a, b, c> (and the optimized <a, b, -> family over all valid third factors). The result type `MasseyResult` carries a coset representative plus the indeterminacy a·Ext + Ext·c (computed when M == k, otherwise the zero subspace). These wrap `ChainHomotopy`: for each candidate c we lift the multiplication map, build the null-homotopy of the composite with b, and read off the bracket by pairing with a; the valid c are the kernel of multiplication by b. No new linear algebra is added — this repackages the logic of the `massey` example. Refactors the `massey` example onto `massey_family`; output is byte-identical to before (verified on S_2). Adds a unit test for the relation <h0, h1, h0> = h1^2 and that <h0, h1, h1> is undefined. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01XYWcvWZPm3YJkVpCmeGYsP

coderabbitai · 2026-06-26T00:34:26Z

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ext/src/ext_algebra/massey.rs

📝 Walkthrough

Walkthrough

The PR adds Massey-product computation support to ExtAlgebra, introduces a MasseyResult coset type and helpers, updates the example binary to use the new API, and rewrites benchmark assignments to the bracketed index and + {} format.

Changes

Massey product API and fixtures

Layer / File(s)	Summary
Public surface and helpers `ext/crates/fp/src/matrix/affine.rs`, `ext/src/ext_algebra/mod.rs`	Adds `AffineSubspace::contains_zero`, exports the `massey` module, and adds `unit_generator` for unit-algebra generators.
Massey result type and shared computations `ext/src/ext_algebra/massey.rs`	Defines `MasseyResult` and builds the shared bracket, kernel, and indeterminacy computations used by the Massey API.
Iterators, single product, and tests `ext/src/ext_algebra/massey.rs`	Implements `massey_iter_c`, `massey_iter_a`, and `massey`, then adds unit tests for a sample relation and iterator agreement.
Example binary rewrite `ext/examples/massey.rs`	Reworks the example to build `ExtAlgebra` from the queried resolution, construct unit elements from queried bidegrees, and print `massey_iter_c` results.
Benchmark assignment rewrites `ext/examples/benchmarks/massey-C2-P`, `ext/examples/benchmarks/massey-Ceta-P`, `ext/examples/benchmarks/massey-S_2-P`	Rewrites benchmark assignments to the bracketed index-list form with `+ {}` expressions.

Sequence Diagram(s)

sequenceDiagram
  participant Example as ext/examples/massey.rs
  participant ExtAlgebra as ExtAlgebra
  participant MasseyResult as MasseyResult
  participant AffineSubspace as AffineSubspace

  Example->>ExtAlgebra: from_resolution(...)
  Example->>ExtAlgebra: unit_generator(a_deg), unit_generator(b_deg)
  Example->>ExtAlgebra: massey_iter_c(&a, &b)
  ExtAlgebra-->>Example: Vec<(BidegreeElement, MasseyResult)>
  Example->>MasseyResult: contains_zero()
  MasseyResult->>AffineSubspace: contains_zero()
  Example->>Example: print each coset

Estimated code review effort

🎯 4 (Complex) | ⏱️ ~60 minutes

Suggested reviewers

hoodmane

Poem

🐇 I hopped through cosets, neat and bright,
With Massey hops in morning light.
A unit nibble, a bracketed grin,
And Ext sang softly from within.
Zero stayed tucked in a leafy bin.

🚥 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 accurately summarizes the main change: adding Massey product support to ExtAlgebra.
Docstring Coverage	✅ Passed	Docstring coverage is 100.00% which is sufficient. The required threshold is 80.00%.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.

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Actionable comments posted: 2

🤖 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/src/ext_algebra/massey.rs`:
- Around line 118-134: The homotopy construction in massey_iter_b is using b_hom
beyond its current range because it is only extended to shift while the rest of
the path runs to tot; extend b_hom to tot before creating ChainHomotopy and
calling homotopy.extend(tot), matching the pattern already used in massey_iter_a
before s_bc.extend(tot), so the b_hom and homotopy lifetimes/ranges stay
aligned.
- Around line 3-5: The module docs reference a non-existent
ExtAlgebra::massey_family API, so update the documentation in massey.rs to point
to the actual public method name (massey_iter_c or massey_iter_a) unless you
intend to add a massey_family wrapper. If adding the wrapper, define it on
ExtAlgebra and ensure it delegates to the existing Massey iteration logic;
otherwise, remove the broken doc link and describe the correct method name.

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ext/crates/fp/src/matrix/affine.rs
ext/examples/benchmarks/massey-C2-P
ext/examples/benchmarks/massey-Ceta-P
ext/examples/benchmarks/massey-S_2-P
ext/examples/massey.rs
ext/src/ext_algebra/massey.rs
ext/src/ext_algebra/mod.rs

The module docs referenced ExtAlgebra::massey_family, which does not exist, breaking the `docs` CI build (rustdoc broken-intra-doc-links under -D warnings). Point to the actual method massey_iter_c, and document massey_iter_a alongside it so the module overview covers all three entry points (massey, massey_iter_c, massey_iter_a) and the shared ChainHomotopy machinery. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

hoodmane · 2026-06-26T14:32:10Z

+    /// Whether the origin lies in this coset, equivalently whether it is a linear subspace.
+    ///
+    /// The offset is kept reduced modulo the linear part (see [`AffineSubspace::new`]), so this
+    /// holds exactly when the stored offset is zero.


Suggested change

/// Whether the origin lies in this coset, equivalently whether it is a linear subspace.

///

/// The offset is kept reduced modulo the linear part (see [`AffineSubspace::new`]), so this

/// holds exactly when the stored offset is zero.

/// Returns whether the coset contains zero

hoodmane · 2026-06-26T14:33:02Z

-<a, b, x_(18, 3, 0)> = [0]
-<a, b, x_(18, 7, 0)> = [1]
-<a, b, x_(18, 8, 0)> = [1]
+<a, b, x_(0, 0, [1])> = [1] + {}


Why did the name of x change?

We used to only compute on basis elements, now we compute on a basis of the kernel of multiplication by b. Those don't have to be basis elements of the ambient space, so we display BidegreeElement instead of BidegreeGenerator.

We also now display the indeterminacy and remove those that contain 0, so there are some lines "missing"

hoodmane · 2026-06-26T14:36:40Z

+/// the indeterminacy subspace.
+#[derive(Debug, Clone)]
+pub struct MasseyResult {
+    /// The bidegree of the bracket, `a.degree() + b.degree() + c.degree() - (1, 0)`.


Suggested change

/// The bidegree of the bracket, `a.degree() + b.degree() + c.degree() - (1, 0)`.

I think stating the output bidegree once is good for documentation. We should clarify that (1,0) is
in (s,t) coordinates though

hoodmane · 2026-06-26T14:38:13Z

+}
+
+impl MasseyResult {
+    /// A representative of the Massey product, as an element of the bracket's bidegree.


Suggested change

/// A representative of the Massey product, as an element of the bracket's bidegree.

/// Returns a representative element of the Massey product

hoodmane · 2026-06-26T14:38:50Z

+    /// Whether `0` lies in the Massey product, i.e. the representative lies in the indeterminacy.
+    /// Such brackets carry no information and are typically omitted from output.


Suggested change

/// Whether `0` lies in the Massey product, i.e. the representative lies in the indeterminacy.

/// Such brackets carry no information and are typically omitted from output.

/// Whether the Massey product contains zero.

Such brackets carry no information

Lies.

Find me a use for them then 😛

The fact that it contains zero carries the information that it is possible to construct a cell complex with prescribed Atiyah-Hirzebruch differentials.

Fair enough

hoodmane

Seems fine but see my comments on the comments.

coderabbitai · 2026-06-26T15:35:56Z

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coderabbitai

Actionable comments posted: 1

🤖 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/src/ext_algebra/massey.rs`:
- Around line 7-11: The module-level overview in the Massey algebra docs is out
of sync with the implemented homotopy path: it mentions the wrong composite (`a
∘ b`) for the shown flow. Update the comment near the `massey_iter_a` and
`massey_iter_c` explanation so it consistently describes the actual behavior,
where `massey_iter_c` rebuilds the `b ∘ c` homotopy per `c` and `massey_iter_a`
reuses it for fixed `b, c`.

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Push a commit to this branch (recommended)
Create a new PR with the fixes

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ext/src/ext_algebra/massey.rs

Co-authored-by: Hood Chatham <roberthoodchatham@gmail.com>

* Add primary Massey products to ExtAlgebra Introduce `ExtAlgebra::massey` and `ExtAlgebra::massey_iter_{a,c}` in the new `ext_algebra/massey.rs`, computing triple Massey products <a, b, c> (and the optimized <a, b, -> family over all valid third factors). The result type `MasseyResult` carries a coset representative plus the indeterminacy a·Ext + Ext·c (computed when M == k, otherwise the zero subspace). These wrap `ChainHomotopy`: for each candidate c we lift the multiplication map, build the null-homotopy of the composite with b, and read off the bracket by pairing with a; the valid c are the kernel of multiplication by b. No new linear algebra is added — this repackages the logic of the `massey` example. Refactors the `massey` example onto `massey_family`; output is byte-identical to before (verified on S_2). Adds a unit test for the relation <h0, h1, h0> = h1^2 and that <h0, h1, h1> is undefined. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01XYWcvWZPm3YJkVpCmeGYsP * Fix broken doc link and round out massey module docs The module docs referenced ExtAlgebra::massey_family, which does not exist, breaking the `docs` CI build (rustdoc broken-intra-doc-links under -D warnings). Point to the actual method massey_iter_c, and document massey_iter_a alongside it so the module overview covers all three entry points (massey, massey_iter_c, massey_iter_a) and the shared ChainHomotopy machinery. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> * Improve docs Co-authored-by: Hood Chatham <roberthoodchatham@gmail.com> * Change return type to descriptive struct Co-authored-by: Hood Chatham <roberthoodchatham@gmail.com> * Add ab == 0 check --------- Co-authored-by: Claude <noreply@anthropic.com> Co-authored-by: Hood Chatham <roberthoodchatham@gmail.com>

…o it The secondary Massey example hand-rolled ~500 lines of Z/p² + λ bookkeeping — building the two secondary lifts, the chain homotopy, the E3 kernel, and the Mod_{Cλ²} read-off — the same plumbing SpectralSequences#247 abstracted for primary Massey. Encapsulate it as `SecondaryExtModule::secondary_massey(a, b, job)`, the Mod_{Cλ²} analogue of `ExtModule::massey_iter_a`. `a ∈ Ext(M, k)` comes from the module side, `b, - ∈ Ext(k, k)` from the shared ring side; both are `SecondaryClass`es (an Ext part plus an optional λ part, since secondary Massey needs non-standard lifts). A new `SecondaryClass` input type and a shared `build_secondary_hom` helper (generalising the example's `get_hom`) construct the secondary lift + optional λ chain map from coordinates. `job = Some(s)` shards the chain-homotopy computation, matching the other secondary scripts. The read-off is ported verbatim, so behaviour is unchanged: a new regression test (`test_sphere_secondary_massey`) pins `<-, h_0, h_1>` on S_2 against the exact bracket family the pre-refactor example printed, and the refactored example reproduces that output byte-for-byte. `secondary_massey.rs` is now just the interactive front-end (querying classes, formatting output). Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01Nk9J57zb6GpvZxrduhGSdY

coderabbitai Bot requested changes Jun 26, 2026

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Comment thread ext/src/ext_algebra/massey.rs

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