Loading measurements…
- Measured on: the CPU the programs ran on, pinned to a fixed clock. The CPU is pinned to that clock. The builds are generic, not tuned for this CPU.
- Time: the whole call, from the instance as text to the reduced basis as text, parsing and formatting included. Geometric mean of the runs, minus the cost of a trivial call. Hover for runs, fastest, slowest.
- Timeout: counts as 2× the longest time limit (PAR-2).
- Factor: against the reference, below 1 is faster. Leaves out an instance where either program returned a wrong result or failed, where both timed out, or where one finished only after the other's time limit.
- Memory: geometric mean of the finished runs' peaks.
- mathicgb: computes over GF(p) alone. Its F4 returns a Gröbner basis whose tails are not reduced, and no option of its command line reduces them. Its answers are therefore not checked, and its time is a lower bound on what the reduced basis costs.
- Min time: an instance that a shown program other than grobx finished in less than is left out. Where none of them has a time or a timeout, grobx's time decides; where grobx has none either, the instance is left out.
- Over ℚ, by how sure the basis is:
- Certain:
- Singular std: computes in ℚ.
- Singular slimgb: computes in ℚ.
- Macaulay2: computes in ℚ.
- CoCoA: computes in ℚ.
- Checked independently of the lift; right with high probability, not proven:
- grobx: checks the result at one more prime.
- msolve: checks the result at one more prime.
- msolve -l 44: checks the result at one more prime.
- Singular modStd: checks the result at one more prime. Its optional check over ℚ is turned off.
- Groebner.jl: checks the result at one more prime, less strictly than grobx.
- Giac: checks at further primes until the chance of an error is below 10−15.
- groebner.rs: checks the result at one more prime, but its primes are fixed, not random.
- sylvester.rs: accepts the result once two more primes leave it unchanged, but its primes are fixed, not random.
- Not checked independently of the lift; right with high probability, not proven:
- Maple: with method=fgb, accepts the result once enough primes agree. Its documentation puts the chance of an error below 10−18.
- Certain: