is_subgroup

std.algebra.is_subgroup · Level L3

Whether a subset H of a finite group (a 0/1 mask) is a subgroup, as 1 or 0: it contains the identity, and it is closed under products and inverses, each checked over all its elements. Closed under products alone suffices in a finite group, but all three are checked.

e ∈ H, HH ⊆ H, H⁻¹ ⊆ H

Signature

is_subgroup(T: i64[n, n], H: f64[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 identity, products and inverses over every element of H 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 group_inverses

Called by

is_normal_subgroup

sha256:e12fa7957e8ed3ddb0241d8b5aa6a1557c32f9e714dd0e426ab9f876f1c3b238

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_subgroup · Ω:is_subgroup
Pins: sha256:2430ee7a4659f697329b22939fce28d4012c1685a4c85c944bf08a45f4c8fa76this graph and the 2 it reaches through calls
Evidence: sha256:881de70bdddd577b6bce2f1589c9ec42ef0405a170ca413645c73c265f25e658the 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.