Fix QuadraticSpline edge-case crashes: n=2 BoundsError, Rational t starting at 0, duplicate knots

[ChrisRackauckas-Claude]

Note

This PR should be ignored until reviewed by @ChrisRackauckas.

Fixes #542.

Changes

1. n = 2 no longer throws BoundsError. For two data points the knot vector [t1, t1, t2, t2, t2] has boundary multiplicity 2 < degree + 1, so the deficient B-spline basis cannot be evaluated at the interval midpoint in quadratic_spline_parameters (it under-indexed into N[0]). Since a quadratic spline through two points is underdetermined and the natural choice is the linear interpolant, the parameter computation now special-cases length(t) == 2 with uᵢ₊ = (u[1] + u[2]) / 2, which yields α = 0, β = u₂ - u₁ — i.e. exactly the linear interpolant. All downstream code paths (evaluation, derivative, integral, cached parameters, vector-valued u) share these parameters, so they are all fixed by this one change.

2. Rational knots with t[1] == 0 no longer throw DivideError. The coefficient eltype was computed as typeof(t[1] / t[1]), which evaluates 0 // 0. Replaced with typeof(one(eltype(t)) / one(eltype(t))) in all three occurrences (interpolation_utils.jl and both QuadraticSpline constructors).

3. Duplicate time points now throw an informative ArgumentError instead of a raw SingularException from the tridiagonal collocation solve. Both interior duplicates (t = [0, 1, 1, 2, 3]) and boundary duplicates (t[2] == t[1]) are caught at construction in quadratic_spline_params.

Verification

All three failures were reproduced on unmodified master before the fix (BoundsError, DivideError, SingularException respectively). After the fix, ran locally:

• n = 2: evaluation gives A(0.25) == 1.5 for u = [1, 3], derivative 2.0, integral over the domain 2.0 — exact linear interpolant; cached-parameters and Vector{Vector} constructors verified too.
• Rational: QuadraticSpline([1//1, 4//1, 9//1], [0//1, 1//1, 2//1]) (i.e. u = (t+1)^2) reproduces the quadratic exactly: A(1//2) == 9//4, A(3//2) == 25//4.
• Duplicates: both reproducers from the issue now throw ArgumentError with a clear message.
• Full local test suite passes: Core 2550 pass (5 pre-existing broken), Methods 41385 pass, Extensions 13178 pass, Misc 10 pass.
• Runic formatting check is clean on all changed files.

Tests for all three cases added to the QuadraticSpline testset in test/interpolation_tests.jl.

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