is_normal_subgroup

std.algebra.is_normal_subgroup · Level L3

Whether a subset H of a finite group is a normal subgroup, as 1 or 0: a subgroup with gH = Hg for every g, which is equivalent to gHg⁻¹ = H. The trivial subgroup and the whole group are always normal.

gH = Hg ∀g

Signature

is_normal_subgroup(T: i64[n, n], H: 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 a subgroup whose left and right coset labels agree in exact rational arithmetic, on all 40 test cases.
All 40 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

is_subgroup left_cosets right_cosets

Called by

quotient_group

sha256:684fbf1f384f11891e83e9fc5baddf068df62320527e2567d9688d2ae27fd821

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.is_normal_subgroup · Ω:is_normal_subgroup
Pins: sha256:ee8348a0055ef9139a83395126bb26e6f02911b09c41a343ba46827309260c53this graph and the 5 it reaches through calls
Evidence: sha256:b75de6a90bfabd0fd1db8e2d9b8a2858ff8e47b8afbd765741db1bef5279bbc0the 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.