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Algebraic independence

In abstract algebra, a subset S {\displaystyle S} of a field L {\displaystyle L} is algebraically independent over a subfield K {\displaystyle K} if the elements of S {\displaystyle S} do not satisfy any non-trivial polynomial equation with coefficients in K {\displaystyle K} .

Algebraic matroids, Results and open problems & Example

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Algebraic matroids

Zorn's lemmaCardinalityFinite setMatroidVámos matroid
9 related topics

Results and open problems

Lindemann–Weierstrass theoremAlgebraic numbersLinearly independentSchanuel conjectureComplex numbers
6 related topics

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Real numbersTranscendental numbersRational numbers
3 related topics

Algebraic independence of known constants

NesterenkoGamma function
2 related topics

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Algebraic independence of known constants

Results and open problems

Algebraic matroids

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Algebraic independence

Nodes34
Edges33
Triples4
Avg. degree1.94
Density0.058824
Components1

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Algebraic independence

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related to Results and open problems · 4
Algebraic independence → It, The Lindemann, The Schanuel, Weierstrass

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displaystyle independent algebraically matroid numbers pi set algebraic field transcendental elements mathbb known sqrt element polynomial coefficients generated independence matroids

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SubjectPredicateObjectConfidenceSrc
Algebraic independencerelated to Results and open problemsThe Lindemann0.60section
Algebraic independencerelated to Results and open problemsWeierstrass0.60section
Algebraic independencerelated to Results and open problemsIt0.60section
Algebraic independencerelated to Results and open problemsThe Schanuel0.60section

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