stabilizer

std.algebra.stabilizer · Level L3

The stabilizer Stab(x) = {g : g·x = x} of a point under a finite group action, every g checked, as a 0/1 mask over G. It is a subgroup of G. It is not the orbit, and not the kernel of the action (the elements that fix every point).

Stab(x) = {g : g·x = x}

Signature

stabilizer(T: i64[n, n], A: i64[n, k], x: f64[]) → 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 g with A[g, x] = x in exact rational arithmetic, on all 40 test cases.
All 152 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

orbit_stabilizer

sha256:78df5185e27e140b763e50d85c3be2c21ebb0fc9f9525ac6be2d744bdfdac7ce

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.stabilizer · Ω:stabilizer
Pins: sha256:98b0b39fb25913295c770eb3301604544c165d91eb9f663d2ea715c64eb6d15athis graph alone
Evidence: sha256:08ccd95c88220b55b9089afdd1cf3bc4bbd213ebef387b07b3a63ba0ab358e2dthe 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.