Macaulay2
E852921
Macaulay2 is a specialized computer algebra system designed for research in algebraic geometry and commutative algebra, particularly focused on computations involving polynomial rings and modules.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Macaulay2 canonical | 1 |
| Macaulay2 language | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T10236312 — 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: Macaulay2 Context triple: [Buchberger algorithm, implementedIn, Macaulay2]
-
A.
Gröbner basis
A Gröbner basis is a particular generating set of an ideal in a polynomial ring that allows algorithmic solutions to many problems in computational algebra, such as ideal membership and solving systems of polynomial equations.
-
B.
Cohen–Macaulay ring
A Cohen–Macaulay ring is a commutative Noetherian ring whose depth equals its Krull dimension, giving it especially well-behaved homological and geometric properties.
-
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.
Eisenbud’s Commutative Algebra
Eisenbud’s *Commutative Algebra* is a widely used graduate-level textbook that develops modern commutative algebra with strong connections to algebraic geometry, featuring topics such as free resolutions, syzygies, and Castelnuovo–Mumford regularity.
-
E.
Castelnuovo–Mumford regularity
Castelnuovo–Mumford regularity is an invariant in commutative algebra and algebraic geometry that measures the complexity of the minimal graded free resolution of a module or sheaf, often used to control vanishing of cohomology and bounds on generators.
- 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: Macaulay2 Target entity description: Macaulay2 is a specialized computer algebra system designed for research in algebraic geometry and commutative algebra, particularly focused on computations involving polynomial rings and modules.
-
A.
Gröbner basis
A Gröbner basis is a particular generating set of an ideal in a polynomial ring that allows algorithmic solutions to many problems in computational algebra, such as ideal membership and solving systems of polynomial equations.
-
B.
Cohen–Macaulay ring
A Cohen–Macaulay ring is a commutative Noetherian ring whose depth equals its Krull dimension, giving it especially well-behaved homological and geometric properties.
-
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.
Eisenbud’s Commutative Algebra
Eisenbud’s *Commutative Algebra* is a widely used graduate-level textbook that develops modern commutative algebra with strong connections to algebraic geometry, featuring topics such as free resolutions, syzygies, and Castelnuovo–Mumford regularity.
-
E.
Castelnuovo–Mumford regularity
Castelnuovo–Mumford regularity is an invariant in commutative algebra and algebraic geometry that measures the complexity of the minimal graded free resolution of a module or sheaf, often used to control vanishing of cohomology and bounds on generators.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
computer algebra system
ⓘ
mathematical software ⓘ research software ⓘ |
| hasDocumentationURL | https://faculty.math.illinois.edu/Macaulay2/Documentation/ ⓘ |
| hasDownloadURL | https://faculty.math.illinois.edu/Macaulay2/Downloads/ ⓘ |
| hasFeature |
Betti table computation
ⓘ
Groebner basis computation ⓘ Hilbert function computation ⓘ Hilbert polynomial computation ⓘ arbitrary precision arithmetic ⓘ cohomology computation ⓘ documentation system ⓘ free resolution computation ⓘ homology computation ⓘ interactive interpreter ⓘ interface to external programs ⓘ package system ⓘ primary decomposition ⓘ scripting language ⓘ symbolic computation ⓘ |
| hasInterfaceLanguage | English ⓘ |
| hasProgrammingLanguage |
Macaulay2 language
ⓘ
linked to:
Macaulay2
|
| hasWebsite | https://faculty.math.illinois.edu/Macaulay2/ ⓘ |
| isFreeOfCharge | true ⓘ |
| isOpenSource | true ⓘ |
| license | GNU General Public License ⓘ |
| primaryDomain |
algebraic geometry
ⓘ
commutative algebra ⓘ |
| supportsComputationOn |
graded modules
ⓘ
homological invariants ⓘ ideals ⓘ modules ⓘ polynomial rings ⓘ sheaves ⓘ |
| supportsInterface |
Emacs interface
ⓘ
command-line interface ⓘ text-based interface ⓘ |
| supportsOperatingSystem |
Linux
ⓘ
Windows ⓘ macOS ⓘ |
| typicalUse |
computational experiments
ⓘ
prototyping mathematical algorithms ⓘ research in algebraic geometry ⓘ research in commutative algebra ⓘ teaching advanced algebra ⓘ |
| writtenInLanguage |
C
ⓘ
C++ ⓘ Macaulay2 language ⓘ |
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: Macaulay2 Description of subject: Macaulay2 is a specialized computer algebra system designed for research in algebraic geometry and commutative algebra, particularly focused on computations involving polynomial rings and modules.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: Macaulay2