right_cosets

std.algebra.right_cosets · Level L3

The right cosets Hg of a subgroup H of a finite group, labelled by their smallest element, and their number, which equals the index [G : H].

label(g) = min Hg

Signature

right_cosets(T: i64[n, n], H: f64[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 h·g over h in H, for each g in exact rational arithmetic, on all 40 test cases.
All 202 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

—

Called by

is_normal_subgroup

sha256:228d2ebc061c8a99754fa0b2d609ce74e8aa9db7a9b9777c00d452c1be630d8b

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.right_cosets · Ω:right_cosets
Pins: sha256:d6f8ba175deb0cc2b8552d982c127d3c6be269e2e05b67f4511bc8152e1024d8this graph alone
Evidence: sha256:eb18e71a0b7b69137f52d3f6cd117366358ed0d457da10e6a2263bde8a931240the 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.