group_inverses
std.algebra.group_inverses · Level L3The inverse of every element of a finite group, a⁻¹ with a·a⁻¹ = a⁻¹·a = e, read from the table (0 where none exists).
a⁻¹: a·a⁻¹ = a⁻¹·a = e
Signature
group_inverses(T: i64[n, 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 first b with T[a, b] = T[b, a] = ein exact rational arithmetic, on all 40 test cases. - All 157 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:d3568febb945861c1fdcc5a262bc6290fb8526488a820ca9c79da5544160ed5bThe semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.algebra.group_inverses · Ω:group_inverses
- Pins
sha256:0df13ec4c24b2cd33c6c5d99e48f1f7aaaaca36335ca80b5661e4e3fb39298cbthis graph and the 1 it reaches through calls- Evidence
sha256:0a6263615e3cea95782c912fd960610176a2bdd9c62f4d23e9ec9632082181c6the 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.