quadratic_laplacian

std.seq.quadratic_laplacian · Level L2

The Laplacian of the quadratic u(x, y) = c₀ + c₁x + c₂y + c₃x² + c₄xy + c₅y², a constant: 2c₃ + 2c₅. Poisson's equation Δu = f holds inside a domain for a quadratic candidate exactly when f is that constant.

Δu = 2c₃ + 2c₅

Signature

quadratic_laplacian(c: f64[6]) → f64[]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference 2*c[3] + 2*c[5] in exact rational arithmetic, on all 40 test cases.
All 40 float64 results inside the running error bound; the closest uses 43% of it.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them inside the running error bound at u = 2⁻²⁴; the closest uses 37% of it.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0.50

Identity

Calls

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Called by

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sha256:f07075738d179fe3857e69c0dd28ec82ab5a65a0309762b4344b2506e8c329bc

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.seq.quadratic_laplacian · Ω:quadratic_laplacian
Pins: sha256:c6bb127615c9bd594de3d571808fdd877fb543aea6e2a9adfd2d482e39e890b3this graph alone
Evidence: sha256:b23ae534660793d4cf0b6afde8f81e9cc7827ad46db478e65f4bc9d754612458the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.