solution_set

std.elementwise.solution_set · Level L1

The solution set of an equation L(x) = R(x) over a finite domain, from the values of both sides on every candidate x and whether both sides are defined there: x is a solution exactly when both sides are defined and their values are equal.

{x : L(x), R(x) defined, L(x) = R(x)}

Signature

solution_set(lhs: f64[n], rhs: f64[n], defined: f64[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 defined and equal in exact rational arithmetic, on all 40 test cases.
All 146 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:ac3b1e2174ed8114db73b14c746ce33dca072c7aab42ed41dc3597ceecf06fe4

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.elementwise.solution_set · Ω:solution_set
Pins: sha256:308f68734f828021dff83cf8034265a62bc2257127845f943941a53335f4f891this graph alone
Evidence: sha256:92e62c930581488ec15413817e8c1654b160f3411670994e9b797bf6ef1456ddthe 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.