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Secant root step rational · case 02

The interpolation correction omits the x span.

Member previewVariant 2 · 3 implementations · 4 checks per implementation

Case contract

Integer sample values and compatible sample-array lengths. Rational results are reduced Fraction strings; spacing is positive unless explicitly stated otherwise. The two function observations are integers; return None for equal residuals, otherwise one exact secant step. Exact operational definition: str(Fraction(x1)-Fraction(f1*(x1-x0),f1-f0)) if f1!=f0 else None

Why this case matters

Small exact fixtures expose this error without platform timing, external services, or probabilistic observations. Discrete calculus results depend on the stated convention.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
fixture 1: (0, -2, 4, 2)	`"7/2"`	`"2"`	Failed

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