is_ring

std.algebra.is_ring · Level L3

Whether two finite tables form a ring with 1 ≠ 0, as 1 or 0: every axiom of ring_axioms holds.

[all ring axioms]

Signature

is_ring(Ad: i64[n, n], Mu: i64[n, n]) → 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 every ring axiom in exact rational arithmetic, on all 40 test cases.
All 40 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%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

ring_axioms

Called by

is_ideal

sha256:602c50880d64d01aa5226aa93ba0a25be03358072f4d3c1f8f55408577ab7d59

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.is_ring · Ω:is_ring
Pins: sha256:969a8540d5e376b4995466f747057a411b146afb559debcbbfe2b042a5906020this graph and the 4 it reaches through calls
Evidence: sha256:8fecf929746063c4af9f044391b7ad3970bc7f8f94e002036eeefaadf7e8d51cthe 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.