F4 algorithm
E838596
The F4 algorithm is an efficient method for computing Gröbner bases using structured linear algebra techniques to speed up polynomial ideal calculations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| F4 algorithm canonical | 2 |
How this entity was disambiguated
This entity first appeared as the object of triple T10055760 — 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: F4 algorithm Context triple: [Gröbner basis, relatedAlgorithm, F4 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.
-
B.
Forney algorithm
The Forney algorithm is a key error-location and error-value computation method used in decoding Reed–Solomon and other BCH error-correcting codes in digital communication systems.
-
C.
Berlekamp–Massey algorithm
The Berlekamp–Massey algorithm is a key algorithm in coding theory and cryptography used to efficiently determine the shortest linear feedback shift register that generates a given binary sequence.
-
D.
Cantor–Zassenhaus algorithm
The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
-
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: F4 algorithm Target entity description: The F4 algorithm is an efficient method for computing Gröbner bases using structured linear algebra techniques to speed up polynomial ideal calculations.
-
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.
Forney algorithm
The Forney algorithm is a key error-location and error-value computation method used in decoding Reed–Solomon and other BCH error-correcting codes in digital communication systems.
-
C.
Berlekamp–Massey algorithm
The Berlekamp–Massey algorithm is a key algorithm in coding theory and cryptography used to efficiently determine the shortest linear feedback shift register that generates a given binary sequence.
-
D.
Cantor–Zassenhaus algorithm
The Cantor–Zassenhaus algorithm is a probabilistic method used to factor polynomials over finite fields efficiently, widely employed in computational algebra and cryptography.
-
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 (49)
| Predicate | Object |
|---|---|
| instanceOf |
Gröbner basis algorithm
ⓘ
algorithm ⓘ |
| advantage |
better use of cache and memory hierarchy via dense linear algebra
ⓘ
efficient handling of large polynomial systems ⓘ significant speedup over classical Buchberger algorithm ⓘ |
| application |
algebraic cryptanalysis
ⓘ
computing algebraic varieties ⓘ computing elimination ideals ⓘ solving systems of polynomial equations ⓘ |
| author | Jean-Charles Faugère NERFINISHED ⓘ |
| basedOn | Buchberger algorithm NERFINISHED ⓘ |
| category | symbolic computation algorithm ⓘ |
| complexityDependsOn |
degrees of input polynomials
ⓘ
number of variables ⓘ sparsity of polynomials ⓘ term ordering ⓘ |
| computes | Gröbner basis of a polynomial ideal ⓘ |
| coreIdea |
batch S-polynomial computations into linear algebra problems
ⓘ
replace repeated polynomial reductions by simultaneous reductions via matrix operations ⓘ |
| field |
computational algebraic geometry
ⓘ
computational commutative algebra ⓘ computer algebra ⓘ |
| implementedIn |
Magma computer algebra system
NERFINISHED
ⓘ
Maple computer algebra system NERFINISHED ⓘ SageMath computer algebra system NERFINISHED ⓘ Singular computer algebra system ⓘ |
| improvesOn | Buchberger algorithm NERFINISHED ⓘ |
| influenced |
F5 algorithm
NERFINISHED
ⓘ
later Gröbner basis algorithms ⓘ |
| input | finite set of multivariate polynomials ⓘ |
| namedAfter | Jean-Charles Faugère NERFINISHED ⓘ |
| optimization |
selection strategies for critical pairs
ⓘ
sparse matrix techniques ⓘ symbolic preprocessing before matrix construction ⓘ |
| output | Gröbner basis NERFINISHED ⓘ |
| publishedIn | Journal of Pure and Applied Algebra NERFINISHED ⓘ |
| purpose | computing Gröbner bases ⓘ |
| relatedTo |
Buchberger algorithm
NERFINISHED
ⓘ
F5 algorithm NERFINISHED ⓘ Macaulay matrix method NERFINISHED ⓘ |
| requires |
field arithmetic
ⓘ
monomial ordering ⓘ |
| technique |
construction of Macaulay matrices
ⓘ
row-reduction of coefficient matrices ⓘ |
| titleOfOriginalPaper | A new efficient algorithm for computing Gröbner bases (F4) NERFINISHED ⓘ |
| uses |
Gaussian elimination
NERFINISHED
ⓘ
structured linear algebra ⓘ |
| worksOver | polynomial rings over fields ⓘ |
| yearProposed | 1999 ⓘ |
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: F4 algorithm Description of subject: The F4 algorithm is an efficient method for computing Gröbner bases using structured linear algebra techniques to speed up polynomial ideal calculations.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.