Register eigmax/eigmin as symbolic matrix atoms

eigmax(X)/eigmin(X) on a symbolic matrix crashed with
"MethodError: no method matching eigvals!(::Matrix{Num})": they have DCP
rules (symmetric_domain(), Convex/Concave) but, unlike logdet and
eigsummax, no @register_symbolic, so the call fell through to numeric
LinearAlgebra.eigmax and tried to compute eigenvalues of a Matrix{Num}.

Register both for Matrix{Num} so the call builds an unevaluated symbolic
atom and the existing rules fire. This also repairs the previously-broken
gDCP eigmax path (add_gdcprule with no backing registration). Collision-
safe: eigmax/eigmin return a scalar and a symbolic is not <: Number, so
no BasicSymbolic{SymReal} scalar method is overwritten (hasmethod goes
false->true, purely additive) — the same pattern as logdet/eigsummax.
Verified: clean from-disk precompile, eigmax(X)->Convex, eigmin(X)->
Concave, numeric eigmax/eigmin unchanged.

Part of #121.

Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com>
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

Author: ChrisRackauckas

src/atoms.jl

@@ -72,8 +72,17 @@ Symbolics.@register_symbolic invprod(x::AbstractVector)
 
 add_dcprule(invprod, array_domain(HalfLine{Real, :open}()), Positive, Convex, Decreasing)
 
+# eigmax/eigmin of a symbolic matrix must build an unevaluated symbolic atom so
+# the curvature pass can dispatch on it; without registration they fall through
+# to numeric `LinearAlgebra.eigmax`, which computes `eigvals!(::Matrix{Num})` and
+# throws. Unlike the matrix `log`/`inv`/`sqrt` atoms, these return a scalar and a
+# symbolic is not `<: Number`, so the emitted method is purely additive (no scalar
+# `BasicSymbolic{SymReal}` method is overwritten) — the same safe pattern as
+# `logdet` and `eigsummax`.
+Symbolics.@register_symbolic LinearAlgebra.eigmax(X::Matrix{Num})
 add_dcprule(eigmax, symmetric_domain(), AnySign, Convex, AnyMono)
 
+Symbolics.@register_symbolic LinearAlgebra.eigmin(X::Matrix{Num})
 add_dcprule(eigmin, symmetric_domain(), AnySign, Concave, AnyMono)
 
 """

test/qa/qa.jl

@@ -12,6 +12,7 @@ const SA = SymbolicAnalysis
 const SYMBOLIC_OWN = Any[
     Base.:*, Base.log, Base.sqrt,
     SA.LinearAlgebra.inv, SA.LinearAlgebra.logdet,
+    SA.LinearAlgebra.eigmax, SA.LinearAlgebra.eigmin,
     SA.Symbolics.arguments, SA.Symbolics.hasmetadata, SA.Symbolics.promote_symtype,
     SA.SymbolicUtils.promote_shape,
     SA.Manifolds.distance, SA.LogExpFunctions.xlogx,

test/test.jl

@@ -178,3 +178,15 @@ ex = propagate_curvature(propagate_sign(ex))
 ex = maximum(exp.(z)) |> unwrap
 ex = propagate_curvature(propagate_sign(ex))
 @test getcurvature(ex) == SymbolicAnalysis.Convex
+
+# eigmax/eigmin of a symbolic matrix must build symbolic atoms (Convex/Concave),
+# not fall through to numeric eigmax and crash on eigvals!(::Matrix{Num}).
+@variables X[1:3, 1:3]
+
+ex = eigmax(X) |> unwrap
+ex = propagate_curvature(propagate_sign(ex))
+@test getcurvature(ex) == SymbolicAnalysis.Convex
+
+ex = eigmin(X) |> unwrap
+ex = propagate_curvature(propagate_sign(ex))
+@test getcurvature(ex) == SymbolicAnalysis.Concave