FA-6378 / Discrete calculus / Member archive

Trapezoidal integral nonuniform grid · case 03

Interval widths are assumed to be one.

Member previewVariant 3 · 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. x has distinct ordered coordinates and matches y; descending x yields negative integral. Exact operational definition: str(sum((Fraction((b-a)*(v+u),2) for a,b,u,v in zip(x,x[1:],y,y[1:])),Fraction()))

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, 1, 3], [0, 2, 2])	`"3"`	`"5"`	Failed

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