space: Jordan spectral primitives (trace / determinant / unit)#56
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Add trace/determinant/unit to the Jordan-algebra hierarchy (0.4.2 W2), derived from each space's spectrum: - Base JordanAlgebraSpace: trace = sum(spectrum), determinant = prod(spectrum), unit as @AbstractMethod. - HermitianSpace: trace via the diagonal (real(einsum '...ii->...'), no eigh), unit = eye(n); inherits the base determinant. - ElementwiseJordanSpace: trace/determinant reduce the element's own axes, unit = ones(shape). - Tree and stacked mixins (direct sums): trace additive, determinant multiplicative, unit assembled from the leaf/copy units -- inherited by every Jordan composite with no per-class edits. All primitives preserve leading batch axes. The oracle trace(x) == inner(unit(), x) holds on every Euclidean Jordan algebra across all five space families. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
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Summary
Adds the Jordan spectral primitives (0.4.2 W2) to every Jordan-algebra space, derived from each space's
spectrum:trace(x)=Σ λᵢ,determinant(x)=Π λᵢ,unit()= the algebra identitye.All three preserve leading batch axes, and the tree/stacked composites get them for free through the leafwise mixins (no per-class edits).
Changes
JordanAlgebraSpace: derivedtrace/determinant;unitas@abstractmethod.HermitianSpace:tracevia the diagonal (real(einsum "...ii->..."), no eigendecomposition);unit = eye(n); inherits the basedeterminant.ElementwiseJordanSpace:trace/determinantreduce the element's own axes;unit = ones(shape).traceadditive,determinantmultiplicative,unitassembled from the leaf/copy units.test_stacked_space.pyupdated for the new abstractunit.Testing
tests/spaces/test_jordan_invariants.py: parametrized over all five families (elementwise, Hermitian, Euclidean-elementwise, stacked, tree; real+complex) —trace == Σspectrum,determinant == Πspectrum,unitis the Jordan identity (e∘x==x), and the oracletrace(x) == ⟨unit(), x⟩on every EJA — plus direct batch-axis, multi-dim-elementwise, and stacked direct-sum tests.Notes
An adversarial review pass caught two real bugs pre-merge: the stacked
trace/determinantusedops.sum/ops.prodwithout an axis, collapsing leading batch axes (unlike every other family). Fixed toaxis=-1and covered by a regression test.🤖 Generated with Claude Code