F5 algorithm
E838597
The F5 algorithm is an efficient method in computational algebra for computing Gröbner bases by using signature-based criteria to avoid redundant polynomial reductions.
Statements (46)
| Predicate | Object |
|---|---|
| instanceOf |
Gröbner basis algorithm
ⓘ
algorithm ⓘ |
| aimsTo | avoid redundant polynomial reductions ⓘ |
| application |
algebraic geometry computations
ⓘ
cryptanalysis of multivariate schemes ⓘ solving systems of polynomial equations ⓘ symbolic computation ⓘ |
| assumes | a fixed monomial order ⓘ |
| avoids | unnecessary S-polynomial reductions ⓘ |
| basedOn | polynomial reduction ⓘ |
| category | signature-based Gröbner basis algorithm ⓘ |
| comparesTo | Buchberger algorithm NERFINISHED ⓘ |
| field |
commutative algebra
ⓘ
computational algebra ⓘ computer algebra ⓘ |
| hasFeature |
criteria to detect useless reductions
ⓘ
criterion to discard syzygy-related reductions ⓘ incremental construction of Gröbner bases ⓘ |
| hasVariant |
F5C algorithm
NERFINISHED
ⓘ
F5R algorithm NERFINISHED ⓘ improved F5 variants ⓘ |
| implementedIn |
Magma (computer algebra system)
NERFINISHED
ⓘ
Maple (via packages) NERFINISHED ⓘ Mathematica (via packages) NERFINISHED ⓘ Singular (computer algebra system) NERFINISHED ⓘ |
| improvesOn | Buchberger algorithm NERFINISHED ⓘ |
| input | polynomial ideals ⓘ |
| knownFor |
high practical efficiency on many benchmarks
ⓘ
reducing number of polynomial reductions ⓘ |
| optimizationGoal |
minimize intermediate expression swell
ⓘ
minimize number of reductions to zero ⓘ |
| output | Gröbner basis of an ideal ⓘ |
| property | efficient for Gröbner basis computation ⓘ |
| purpose | computing Gröbner bases ⓘ |
| relatedConcept |
leading terms of polynomials
ⓘ
module of syzygies ⓘ syzygies ⓘ term orders ⓘ |
| relatedTo | F4 algorithm NERFINISHED ⓘ |
| typicalImplementationLanguage | computer algebra systems ⓘ |
| uses |
criteria to reject critical pairs
ⓘ
signature-based criteria ⓘ signatures to track polynomial origin ⓘ |
| worksOver | polynomial rings ⓘ |
| worksWith |
S-polynomials
ⓘ
critical pairs ⓘ |
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.