orbits

std.algebra.orbits · Level L3

The orbits G·x = {g·x : g ∈ G} of a finite group action, every g enumerated: each point is labelled by the smallest point of its orbit, so two points share a label exactly when some g sends one to the other; and the number of orbits. The orbits partition the points. One generator's powers, or a single g·x, are not an orbit.

G·x = {g·x : g ∈ G}

Signature

orbits(T: i64[n, n], A: i64[n, k]) → f64[k], 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 over every g in exact rational arithmetic, on all 40 test cases.
All 172 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:aee240639783901e21d6183c56cb93bf870feca0b20a65c4cd995c4372aaf6da

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.orbits · Ω:orbits
Pins: sha256:71536b95f8318035b164449d2f0d4e7a9a90562bcf6cc727dd1158ddebc8a66fthis graph alone
Evidence: sha256:1f58218938391f8c34be1cde81532639104bdf9a29565d8b74cd7c408ef87b0bthe 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.