Triple

T9867909
Position Surface form Disambiguated ID Type / Status
Subject Hans Zassenhaus E239880 entity
Predicate notableWork P4 FINISHED
Object Zassenhaus algorithm for factoring polynomials over the rationals
The Zassenhaus algorithm for factoring polynomials over the rationals is a classical computational method that reduces rational polynomial factorization to modular factorization and then recombines the results using lifting techniques.
E827382 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Zassenhaus algorithm for factoring polynomials over the rationals | Statement: [Hans Zassenhaus, notableWork, Zassenhaus algorithm for factoring polynomials over the rationals]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Zassenhaus algorithm for factoring polynomials over the rationals
Context triple: [Hans Zassenhaus, notableWork, Zassenhaus algorithm for factoring polynomials over the rationals]
  • A. Berlekamp’s algorithm for factoring polynomials over finite fields
    Berlekamp’s algorithm for factoring polynomials over finite fields is a foundational deterministic method in computational algebra that efficiently decomposes polynomials into irreducible factors over finite fields and underpins many modern algorithms in coding theory and cryptography.
  • B. 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.
  • C. Buchberger algorithm
    The Buchberger algorithm is a fundamental procedure in computational algebra for computing Gröbner bases of polynomial ideals, enabling systematic solutions to systems of polynomial equations.
  • D. Lenstra elliptic-curve factorization method
    The Lenstra elliptic-curve factorization method is an integer factorization algorithm that uses properties of elliptic curves over finite fields to efficiently find nontrivial factors of large numbers, especially those with relatively small prime divisors.
  • E. Euclidean algorithm for polynomials
    The Euclidean algorithm for polynomials is a procedure that repeatedly applies polynomial division to compute the greatest common divisor of two polynomials over a given field or ring.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Zassenhaus algorithm for factoring polynomials over the rationals
Triple: [Hans Zassenhaus, notableWork, Zassenhaus algorithm for factoring polynomials over the rationals]
Generated description
The Zassenhaus algorithm for factoring polynomials over the rationals is a classical computational method that reduces rational polynomial factorization to modular factorization and then recombines the results using lifting techniques.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Zassenhaus algorithm for factoring polynomials over the rationals
Target entity description: The Zassenhaus algorithm for factoring polynomials over the rationals is a classical computational method that reduces rational polynomial factorization to modular factorization and then recombines the results using lifting techniques.
  • A. Berlekamp’s algorithm for factoring polynomials over finite fields
    Berlekamp’s algorithm for factoring polynomials over finite fields is a foundational deterministic method in computational algebra that efficiently decomposes polynomials into irreducible factors over finite fields and underpins many modern algorithms in coding theory and cryptography.
  • B. 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.
  • C. Buchberger algorithm
    The Buchberger algorithm is a fundamental procedure in computational algebra for computing Gröbner bases of polynomial ideals, enabling systematic solutions to systems of polynomial equations.
  • D. Lenstra elliptic-curve factorization method
    The Lenstra elliptic-curve factorization method is an integer factorization algorithm that uses properties of elliptic curves over finite fields to efficiently find nontrivial factors of large numbers, especially those with relatively small prime divisors.
  • E. Euclidean algorithm for polynomials
    The Euclidean algorithm for polynomials is a procedure that repeatedly applies polynomial division to compute the greatest common divisor of two polynomials over a given field or ring.
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69ca84e7506c819095cbde4ff16512bb completed March 30, 2026, 2:12 p.m.
NER Named-entity recognition batch_69cdb3d34e4c81908c0fc14dd6d015cc completed April 2, 2026, 12:09 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1eae2189c81909629e4bd46097051 completed April 5, 2026, 4:53 a.m.
NEDg Description generation batch_69d1ebec25508190ac4c0adb629f79b0 completed April 5, 2026, 4:58 a.m.
NED2 Entity disambiguation (via description) batch_69d1ec65d5e881909e4caa180b0f8867 completed April 5, 2026, 5 a.m.
Created at: March 30, 2026, 8:36 p.m.