9g (part 2): drop Riem, ‖·‖²_g, II, (∇R)— last typeclass-dispatch notations#40
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This was referenced May 19, 2026
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Summary
9g (part 2) — completes the
_gnotation drop started in #39.Notations dropped
Riem(X, Y) ZriemannCurvature HasMetric.metric X Y Z‖V‖²_gfun y => HasMetric.metric.metricInner y (V y) (V y); Bilin:frobeniusSq BII(X, Y)(∇R)[X](Y, Z) WcovDerivRiemann X Y Z Wbianchi_secondsorry)Also removed
MetricNormSqtypeclass + 3 instances (Tangent,Section,Bilin).After this PR, the only scoped notation left in OpenGALib's Riemannian namespace is
⟦X, Y⟧forVectorField.mlieBracket _ X Y— which is metric-independent and stays.Why
All
_gnotations dispatched via typeclass toHasMetric.metric, hardcoding a single metric per manifold. Dropping them is the precursor to 9h, which will replaceHasMetric.metricwith explicit(g : RiemannianMetric I M)parameters file-by-file (enabling Ricci flow / conformal change / comparison geometry where multiple metrics naturally appear).Vol_g
vol_g(28 grep hits) is only docstring/comment usage — no Lean notation exists. No action needed; left as math prose.Test plan
lake buildclean per commit