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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| F5 algorithm canonical | 4 |
| F5C algorithm | 1 |
| F5R algorithm | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10055761 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: F5 algorithm Context triple: [Gröbner basis, relatedAlgorithm, F5 algorithm]
-
A.
Benettin algorithm
The Benettin algorithm is a numerical method used in dynamical systems theory to estimate Lyapunov exponents, which quantify the rate of separation of nearby trajectories and indicate chaos.
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B.
Cristian's algorithm
Cristian's algorithm is a clock synchronization method in distributed systems that estimates accurate time on client machines by querying a time server and adjusting for message delays.
-
C.
Thompson's algorithm
Thompson's algorithm is a classic computer science method for converting regular expressions into nondeterministic finite automata (NFAs), widely used in pattern matching and lexical analysis.
-
D.
Marzullo's algorithm
Marzullo's algorithm is a method for selecting the most likely correct time interval from multiple, possibly conflicting time sources, commonly used in clock synchronization systems.
-
E.
LLL algorithm
The LLL algorithm is a polynomial-time lattice basis reduction algorithm widely used in computational number theory and cryptography to find relatively short, nearly orthogonal lattice vectors.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: F5 algorithm Target entity description: The F5 algorithm is an efficient method in computational algebra for computing Gröbner bases by using signature-based criteria to avoid redundant polynomial reductions.
-
A.
Benettin algorithm
The Benettin algorithm is a numerical method used in dynamical systems theory to estimate Lyapunov exponents, which quantify the rate of separation of nearby trajectories and indicate chaos.
-
B.
Cristian's algorithm
Cristian's algorithm is a clock synchronization method in distributed systems that estimates accurate time on client machines by querying a time server and adjusting for message delays.
-
C.
Thompson's algorithm
Thompson's algorithm is a classic computer science method for converting regular expressions into nondeterministic finite automata (NFAs), widely used in pattern matching and lexical analysis.
-
D.
Marzullo's algorithm
Marzullo's algorithm is a method for selecting the most likely correct time interval from multiple, possibly conflicting time sources, commonly used in clock synchronization systems.
-
E.
LLL algorithm
The LLL algorithm is a polynomial-time lattice basis reduction algorithm widely used in computational number theory and cryptography to find relatively short, nearly orthogonal lattice vectors.
- F. None of above. chosen
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 ⓘ |
| 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
ⓘ
linked to:
F5 algorithm
F5R algorithm ⓘ
linked to:
F5 algorithm
improved F5 variants ⓘ |
| implementedIn |
Magma (computer algebra system)
ⓘ
linked to:
Magma (algebra system)
Maple (via packages) ⓘ
linked to:
Maple
Mathematica (via packages) ⓘ
linked to:
Mathematica
Singular (computer algebra system) ⓘ |
| improvesOn | Buchberger algorithm ⓘ |
| 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 ⓘ |
| 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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: F5 algorithm Description of subject: The F5 algorithm is an efficient method in computational algebra for computing Gröbner bases by using signature-based criteria to avoid redundant polynomial reductions.
Referenced by (6)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: F5 algorithm
linked to: F5 algorithm