group_center

std.algebra.group_center · Level L3

The center Z(G) of a finite group as a 0/1 mask: the elements that commute with every element, each checked against the whole group. It is a normal subgroup; it is all of G exactly when G is abelian, and z ∈ Z(G) exactly when z's conjugacy class is {z}.

Z(G) = {z : zg = gz ∀g}

Signature

group_center(T: i64[n, n]) → f64[n]

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 rows of T that equal the matching columns in exact rational arithmetic, on all 40 test cases.
All 160 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

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Called by

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sha256:159abae8cac3ad9672c5ed1221288c3169d048db66d7fdfb1b5909278eae2528

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.group_center · Ω:group_center
Pins: sha256:854cddc3d3d81481397cb91cb86c5e5f6d59848bab420a0fd40f4fe96840afd9this graph alone
Evidence: sha256:377b201cc1eff5f8c40f4925d17b3b81bce0c21362320c352a87aec7269a9767the 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.