is_tree

std.linalg.is_tree · Level L2

Whether a finite undirected simple graph is a tree, as 1 or 0: connected, with exactly n − 1 edges. Connected with n − 1 edges is a complete certificate; n − 1 edges alone is not.

[connected and |E| = n − 1]

Signature

is_tree(A: f64[n, 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 one breadth-first-search component and n − 1 edges 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

component_count

Called by

—

sha256:5c2c2fb3c8c44d813038d6f9b7a2be39239bc187c77deeaead6250898c7b516a

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.is_tree · Ω:is_tree
Pins: sha256:79578c7900643c28861e38825aab8de8720ab430db4d568be3a7c122bc599bccthis graph and the 4 it reaches through calls
Evidence: sha256:ed11295f2756da66b6708cc94adeff479989761655e71ee8be6e2a1a0cbd6e5athe 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.