leading_minors

std.linalg.leading_minors · Level L4

The leading principal minors Δ₁, …, Δₙ of an integer matrix (the determinants of its top-left k × k blocks), exactly, by fraction-free elimination without row exchanges: a Scan of minor_step. Each Δ_k is right as long as the earlier ones are nonzero; valid marks those, and after the first zero minor the later values are not minors.

Δ_k = det A[1..k, 1..k]

Signature

leading_minors(A: f64[n, n]) → f64[n], 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 same elimination on Python integers in exact rational arithmetic, on all 40 test cases.
All 300 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 inside the running error bound at u = 2⁻²⁴; the closest uses 1% of it.

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

minor_step

Called by

is_positive_definite

sha256:e4a8cc1dcae9fcfe6975e12dabd123748fd369aa8fe7504d11698da5cdfe384d

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.leading_minors · Ω:leading_minors
Pins: sha256:df8c8fa628126061cc75cd3e9389ca26e701e17b448f6242ead597da956824f3this graph and the 1 it reaches through calls
Evidence: sha256:c0024bb3d5f7b5f17ae4a01eae426b3c86955a07746eff984e18eeda2142ba11the 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.