elimination theory
E1563165
UNEXPLORED
Elimination theory is a branch of algebra that studies how to systematically remove variables from systems of polynomial equations to derive relations among the remaining ones.
All labels observed (1)
| Label | Occurrences |
|---|---|
| elimination theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T22964606 — 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: elimination theory Context triple: [Sylvester determinant, field, elimination theory]
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A.
Hilbert’s Nullstellensatz
Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
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B.
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.
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C.
Bézout’s theorem
Bézout’s theorem is a fundamental result in algebraic geometry stating that, over an algebraically closed field, the number of intersection points of two projective plane curves (counted with multiplicity) equals the product of their degrees.
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D.
Hilbert’s fourteenth problem
Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
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E.
Hilbert scheme theory
Hilbert scheme theory is a branch of algebraic geometry that studies parameter spaces representing families of subschemes of projective space, capturing how such geometric objects vary in moduli.
- 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: elimination theory Target entity description: Elimination theory is a branch of algebra that studies how to systematically remove variables from systems of polynomial equations to derive relations among the remaining ones.
-
A.
Hilbert’s Nullstellensatz
Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
-
B.
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.
-
C.
Bézout’s theorem
Bézout’s theorem is a fundamental result in algebraic geometry stating that, over an algebraically closed field, the number of intersection points of two projective plane curves (counted with multiplicity) equals the product of their degrees.
-
D.
Hilbert’s fourteenth problem
Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
-
E.
Hilbert scheme theory
Hilbert scheme theory is a branch of algebraic geometry that studies parameter spaces representing families of subschemes of projective space, capturing how such geometric objects vary in moduli.
- F. None of above. chosen
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.