poly_identity

std.seq.poly_identity · Level L3

Whether p = f·g as polynomials, as 1 or 0: the product's coefficients, every list highest degree first, compared with p's one by one, not at sample points; and the product itself. Factors and product are compared as given, so leading zeros must be removed first, and a rescaled or reordered factor is the caller's to normalize. Exact for integer coefficients; for rational ones, multiply p by the product of the factors' denominators, and each factor by its own, first.

p = f·g ⇔ pₖ = Σᵢ fᵢ·gₖ₋ᵢ for every k

Signature

poly_identity(p: f64[a+c], f: f64[a], g: f64[c+1]) → f64[], f64[a+c]

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 the double loop, then every coefficient compared in exact rational arithmetic, on all 40 test cases.
All 363 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
largest error, in units in the last place: 0

Identity

Calls

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Called by

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sha256:c29301fcaf540770c88f171104da1e4117273c44eb58b04cde4786f43bf38e93

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.poly_identity · Ω:poly_identity
Pins: sha256:97e3b4bc22daa35adf54ac19e5b287408ce039623d6f194c12f9675e3db72c87this graph alone
Evidence: sha256:864d44d0996274f64b277cc01024bf5301293fdd7e3c76174c167a78b09940edthe 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.