is_isomorphism
std.linalg.is_isomorphism · Level L3Whether a map f, given as the image of each vertex, is an isomorphism from graph A to graph B, as 1 or 0: f is a bijection, and A(u, v) = B(f(u), f(v)) for every pair, edges and non-edges alike.
f bijective and A = B∘(f × f)
Signature
is_isomorphism(A: f64[n, n], B: f64[n, n], perm: i64[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
a permutation, and A[u, v] == B[f(u), f(v)] everywherein 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
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sha256:b62c8e1e9fb76afc754340073bd4aeac63db42a9e19115bad35494934b47be94The 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_isomorphism · Ω:is_isomorphism
- Pins
sha256:7aa6bc83d2e6fec5262de6024dc7791a60534e9554156e507b7b70ae0402cf38this graph alone- Evidence
sha256:a6bee8a70a6b1f6358485b0df299f3810641f17050c9012933f5466f63905aa5the 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.