vector_space_instance

std.linalg.vector_space_instance · Level L1

The eight vector-space axioms on given coordinate vectors u, v, w in Rⁿ and scalars a, b, as 1 or 0 when all hold: associativity and commutativity of addition, the zero vector, additive inverses, both distributive laws, compatibility of scalar multiplication, and 1u = u. With integer data they are checked exactly. Instances that pass do not prove that a candidate structure is a vector space; one that fails disproves it.

(u + v) + w = u + (v + w), …, 1u = u

Signature

vector_space_instance(u: f64[n], v: f64[n], w: f64[n], a: f64[], b: 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 the axioms hold in exact arithmetic on Rⁿ 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

—

Called by

—

sha256:5f489b8f78c860b4c07750b26a31e206287438ac8a377f27c0497153ca9991d6

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.vector_space_instance · Ω:vector_space_instance
Pins: sha256:d3f0ce5e733fdda6f081ee226335857c4011a211dfc20ecd9970f5b53ff9b920this graph alone
Evidence: sha256:26b8c09fbf04b14f5087f14a4d63d3e99dcdd4ab1f818284c19915360ee38713the 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.