api: unify det() error behavior across all dimensions

[acgetchell]

Dependencies

• chore: bump MSRV to Rust 1.95 and adopt new stable features #67
• perf: integer-only forward elimination for gauss_solve (BigInt hybrid) #72
• perf: improve exact arithmetic benchmark coverage with diverse inputs #80
• docs: strengthen LDLT symmetry precondition documentation #84
• bug: inf_norm silently returns 0.0 for matrices containing NaN #85
• feat: const-ify Lu::det, Ldlt::det, inf_norm, det_errbound, and solve methods #86

Summary

det() has inconsistent error semantics depending on dimension: D≤4 returns Ok(~0.0) for singular matrices while D≥5 returns Err(LaError::Singular). A user switching from D=4 to D=5 gets a different error model for the same logical operation.

Current State

• D=0–4: det() dispatches to det_direct(), which is a closed-form cofactor expansion. A singular matrix produces Ok(0.0) (or a near-zero value). No Singular error is possible.
• D≥5: det() falls through to self.lu(tol).map(|lu| lu.det()). If no pivot exceeds tol, it returns Err(LaError::Singular).

This means:

// D=4: returns Ok(0.0)
Matrix::<4>::zero().det(DEFAULT_PIVOT_TOL) // Ok(0.0)

// D=5: returns Err(Singular)
Matrix::<5>::zero().det(DEFAULT_PIVOT_TOL) // Err(Singular { pivot_col: 0 })

Proposed Changes

Options (need to pick one):

Option A: Always succeed (return Ok(f64))

For D≥5, catch Singular from LU and return Ok(0.0). This makes det() infallible for finite inputs. Pro: simple, consistent. Con: loses the singularity signal for large D.

Option B: Always error on singular

For D≤4, check if the det_direct() result is below some tolerance and return Err(Singular). Pro: consistent error semantics. Con: introduces a tolerance dependency for the closed-form path, and near-zero determinants aren't necessarily singular (could be a well-conditioned matrix with a small determinant).

Option C: Split the API

Rename det_direct() to emphasize it never fails, and document that det() may return Singular only for D≥5. Pro: no behavior change. Con: the inconsistency remains.

Option D: Return Result<f64, LaError> with separate det_direct for D≤4

Keep det() as-is but strengthen documentation to explicitly call out the dimensional behavior. Add a prominent note in the det() rustdoc.

Benefits

• Consistent, predictable API regardless of dimension
• Fewer surprises for generic code parameterized over D

Implementation Notes

• This is a breaking change depending on the chosen option (milestone: v0.5.0)
• Related: det_direct() is const fn and cannot return Result ergonomically, so it should remain separate regardless
• Also gated on generic_const_exprs stabilization for the full v0.5.0 API revision

[acgetchell]

Blocked by v0.4.1 release (all v0.4.1 issues should ship first). Also gated on generic_const_exprs stabilization for the full API revision.