is_basis_for
std.topology.is_basis_for · Level L3Whether a finite family B is a basis of the given topology τ, as 1 or 0: B is a basis, its members are open, and every open set of τ is a union of members.
B ⊆ τ, U = ∪{B ∈ B : B ⊆ U} ∀U ∈ τ
Signature
is_basis_for(tau: f64[m, n], B: f64[c, 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 basis, inside τ, whose unions give every open setin 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
sha256:54582aa8cbd3a338ab25dd6756be7d0842b0a32972d3b53f25ff02974f5aaa8cThe semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.topology.is_basis_for · Ω:is_basis_for
- Pins
sha256:d1aa120e56367829b5e97d32538d16fd37979399f35283c546716c06e6377d88this graph and the 3 it reaches through calls- Evidence
sha256:46b68c19c22059b9cb3057b7cb2931a9ecdfa469b523ba35437e6da2c12fa42bthe 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.