conjugacy_classes

std.algebra.conjugacy_classes · Level L3

The conjugacy classes of a finite group: each x is labelled by the smallest element of its class {g·x·g⁻¹ : g ∈ G}, every g enumerated; and the number of classes. Two classes are equal or disjoint, and together they cover G. A class is not a coset.

cl(x) = {gxg⁻¹ : g ∈ G}

Signature

conjugacy_classes(T: i64[n, n]) → 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 the smallest g·x·g⁻¹ over every g in exact rational arithmetic, on all 40 test cases.
All 205 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_inverses

Called by

—

sha256:7d9c363bf583a315144cfaf1fcf43f9e216693854b8f0f9c55723b052010eb7a

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.conjugacy_classes · Ω:conjugacy_classes
Pins: sha256:1b89c89fa471c813eba124fe8e8dd935c7cc6ca817d54925e99a40eb34cce731this graph and the 2 it reaches through calls
Evidence: sha256:e7c86318dea795462b5f9e7be6e5d93f01662824584b061467b8397eddb2ccd9the 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.