Triple
T13255892
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Paolo Ruffini |
E315656
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Ruffini's rule for polynomial division
Ruffini's rule for polynomial division is a simplified algorithm for dividing polynomials by linear factors, often used as a shortcut form of synthetic division.
|
E1030529
|
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: Ruffini's rule for polynomial division | Statement: [Paolo Ruffini, knownFor, Ruffini's rule for polynomial division]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Ruffini's rule for polynomial division Context triple: [Paolo Ruffini, knownFor, Ruffini's rule for polynomial division]
-
A.
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.
-
B.
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.
-
C.
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.
-
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.
Polynomial Root Finder
Polynomial Root Finder is a TI-84 Plus calculator application that computes the roots of polynomial equations quickly and accurately.
- 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: Ruffini's rule for polynomial division Triple: [Paolo Ruffini, knownFor, Ruffini's rule for polynomial division]
Generated description
Ruffini's rule for polynomial division is a simplified algorithm for dividing polynomials by linear factors, often used as a shortcut form of synthetic division.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Ruffini's rule for polynomial division Target entity description: Ruffini's rule for polynomial division is a simplified algorithm for dividing polynomials by linear factors, often used as a shortcut form of synthetic division.
-
A.
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.
-
B.
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.
-
C.
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.
-
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.
Polynomial Root Finder
Polynomial Root Finder is a TI-84 Plus calculator application that computes the roots of polynomial equations quickly and accurately.
- 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_69d806b1d9ac8190852c5571d5bd5f0f |
completed | April 9, 2026, 8:06 p.m. |
| NER | Named-entity recognition | batch_69d98f7614fc8190a1cac076d706e9aa |
completed | April 11, 2026, 12:01 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f70a4240d881909f0ee898fd272826 |
completed | May 3, 2026, 8:41 a.m. |
| NEDg | Description generation | batch_69f70c9718d08190b09fc6723712ef55 |
completed | May 3, 2026, 8:51 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69f70d32b38881909d500b81a0164bda |
completed | May 3, 2026, 8:54 a.m. |
Created at: April 9, 2026, 9:24 p.m.