is_group

std.algebra.is_group · Level L3

Whether a finite Cayley table is a group, as 1 or 0: all four axioms of group_axioms hold.

[closure ∧ associativity ∧ identity ∧ inverses]

Signature

is_group(T: 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 all four axioms 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

group_axioms

Called by

is_abelian

sha256:4670a6319e0ad3b0813648e85af9be6df9bfbbdaa683116a6507b604ed41289f

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_group · Ω:is_group
Pins: sha256:e5cd0c78da2c8b866e33ca6f5abf6db6ef769c9a03da4d5a08b732166c8b8be9this graph and the 1 it reaches through calls
Evidence: sha256:83390173c16290a3153bef4b56c08c9e4c385e0e604c61d6ff715bc7707ee0d5the 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.