same_coset

std.linalg.same_coset · Level L4

Whether integer vectors u and v represent the same element of the quotient space Rⁿ/W, as 1 or 0: v − u ∈ W, decided by exact rank; and dim(Rⁿ/W) = n − dim W. The elements of the quotient are cosets, not chosen representatives; the zero coset is W itself.

u + W = v + W ⇔ v − u ∈ W; dim Rⁿ/W = n − dim W

Signature

same_coset(W: f64[k, n], u: f64[n], v: f64[n]) → f64[], 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 exact ranks with and without v − u in exact rational arithmetic, on all 40 test cases.
All 80 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 37 of them exact, with zero error. Uncertified, too ill-conditioned at float32 for a finite bound: 3.

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

in_span rank_exact

Called by

—

sha256:c45a26810b37b8da161d8ea0e84fad972eb114e43afeece2eeed0deb132e372b

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.linalg.same_coset · Ω:same_coset
Pins: sha256:115c81b3bc2b2dc9b658fd117b72552b8c9e826aa8ecffef37f4dcb02238ba70this graph and the 3 it reaches through calls
Evidence: sha256:4f33222228e6434339e18c54cbb68ec984496824fdccf0743bf3a75781b31bf2the 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.