antiderivative_check
std.seq.antiderivative_check · Level L2Whether a candidate polynomial F is an antiderivative of the polynomial f, F′ = f, checked coefficient by coefficient (coefficients highest degree first, F one longer than f), as 1 or 0. A candidate that fails does not show that f has no antiderivative; agreement at sampled points would not show F′ = f.
Signature
antiderivative_check(F: f64[m+1], f: f64[m]) → 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's coefficients times their degrees, against fin 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.
- 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:d5f9ebd40f195a9ace0d6ae7dc7e4410cc09be441cad0427eab0adb37645d208The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.
Control handle
- Symbol
- Ω:std.seq.antiderivative_check · Ω:antiderivative_check
- Pins
sha256:2cc2a0e6ce8f263b75b1bbcc0b3936ba2cb598fb381d951e27712aa71a2b2184this graph alone- Evidence
sha256:0e83bcc38b3c8a37c0060c31957ac49f6fab956645aab1ccc2a56021258268f0the 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.