in_kernel
std.linalg.in_kernel · Level L1Whether an integer vector x is in the kernel of an integer matrix A, Ax = 0, as 1 or 0, exactly. The solution set of homogeneous equations is a subspace; a set such as a line not through the origin is not.
[Ax = 0]
Signature
in_kernel(A: f64[m, n], x: 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
every row dotted with x is 0in 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
sha256:71ef7b17cabd87e6fd432d757c3a73eb2e7386ad201743eca8b5ef57ab299fc6The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.linalg.in_kernel · Ω:in_kernel
- Pins
sha256:520ec43d720bf2855f5f7d99782f5784a6492121dbd51b4a0ae8ef0a91f3f6afthis graph and the 1 it reaches through calls- Evidence
sha256:5aeab8d9f3fa7e7bc5e8c4ef4961828fe9e7c5b2e51689af829fe59acc06ba16the 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.