is_homomorphism
std.algebra.is_homomorphism · Level L3Whether a map f from a finite group G to a finite group K (f[a] the image of a) is a homomorphism, as 1 or 0: f(a·b) = f(a)·f(b) for every pair. A homomorphism need not be injective.
f(ab) = f(a)f(b) ∀a, b
Signature
is_homomorphism(TG: i64[n, n], TK: i64[m, m], f: 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
f(a·b) against f(a)·f(b) for every pairin 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
—
sha256:005ab0fcfb35c98cd626e043f9278beed8be057ebc11bc79b592e8b20dcd8dd2The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.algebra.is_homomorphism · Ω:is_homomorphism
- Pins
sha256:b93a46deb5674bf6396bd551db8e600d67926f537428365c2683530cda8aa926this graph alone- Evidence
sha256:7a229bcc296b1ecb81f92b1e50935a322ca0c80d7f2f42577a6b3b2b02fb31e1the 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.