poly_degree

std.seq.poly_degree · Level L2

The degree of a polynomial, coefficients highest degree first: whether it has one (1 or 0: the zero polynomial has no degree), the degree n − 1 − k for the first nonzero coefficient cₖ, and that leading coefficient; 0 for both when there is no degree. Leading zeros do not change the polynomial, and −0 counts as zero. Exact.

deg p = n − 1 − min{k : cₖ ≠ 0}

Signature

poly_degree(c: f64[n]) → f64[], f64[], 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 the first nonzero coefficient, found by a loop in exact rational arithmetic, on all 40 test cases.
All 120 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

—

Called by

—

sha256:1e09309c2506d39604f07da00ecbb42599447ff3d9bd0cfbf8b4e52a7570c77f

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_degree · Ω:poly_degree
Pins: sha256:283194899252d0b39326f1f9b526471b9cf529a0173fce8f84a638f288d1b8dathis graph alone
Evidence: sha256:9c4b907ec586874f8449f968a2df61cd3efd6b921faf0863c36c5bcea6e24306the 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.