ring_poly_add

std.algebra.ring_poly_add · Level L3

The sum of two polynomials over a finite ring, coefficient by coefficient with the ring's addition table: (p + q)ᵢ = pᵢ + qᵢ. The coefficients are elements of the ring, as int64 labels, both lists the same length (pad the shorter with the ring's zero).

(p + q)ᵢ = pᵢ + qᵢ

Signature

ring_poly_add(Ad: i64[n, n], p: i64[a], q: i64[a]) → i64[a]

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 Ad[p_i, q_i] in exact rational arithmetic, on all 40 test cases.
All 137 int64 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 int64 nearest the exact value): 100%
bit-equal to the NumPy formula in int64: 100%
largest error, in units in the last place: 0

Identity

Calls

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Called by

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sha256:517f15860c86c89c985caead77234756872fce51d0a14fac8b7325a25c40405f

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

Control handle

Symbol: Ω:std.algebra.ring_poly_add · Ω:ring_poly_add
Pins: sha256:b26b9cc65e503af19e7bebfad420be97c3c8df05e1eed383fc5af8aed7b43c5fthis graph alone
Evidence: sha256:4cff84fd71252359bcce756015213305f22d0abd4f073e5f1d537e8f12ced95athe 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.