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Let $L = F(S)$ for $S \subseteq L$. Does there exists a transcendental basis $T \subseteq S$ with $F(S) = F(T)$?

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#extension-field #transcendence-theory #transcendence-degree #algebraic-independence
65
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Which general methods are there for determining if $t$ and $e^t$, where $t$ is any given transcendental number, are algebraically independent?

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#abstract-algebra #number-theory #algebraic-independence
121
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Proof check: Existence of algebraically independent real numbers (over the rationals).

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#polynomials #solution-verification #algebraic-independence
148
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Is algebraic dependence a transitive relation?

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#irrational-numbers #algebraic-independence
96
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A question on algebraic independence

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#solution-verification #field-theory #algebraic-independence
198
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interpretation of independent linear inequalities

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#linear-algebra #optimization #convex-optimization #linear-programming #algebraic-independence
86
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Find the minimum subset of linear equations that derives a given linear equation.

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#linear-algebra #numerical-linear-algebra #discrete-optimization #algebraic-independence
131
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Linear independence vs probabilistic independence

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#linear-algebra #probability-theory #random-variables #independence #algebraic-independence
175
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Are $\pi$ and $\tan^{-1}\left(2\right)$ rational multiples of each other?

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#trigonometry #irrational-numbers #pi #quantum-computation #algebraic-independence
83
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Vector space spanned by incidence vectors of maximal cliques in a graph

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#graph-theory #vector-spaces #algebraic-independence
53
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Checking subspaces for independence

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#linear-algebra #vector-spaces #algebraic-independence
86
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How to quickly spot linearly dependent vectors in matrices without calculations?

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#linear-algebra #numerical-linear-algebra #matrix-rank #algebraic-independence
61
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Bilinear map and linearly independent set

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#linear-algebra #vector-spaces #linear-transformations #bilinear-form #algebraic-independence
239
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Over any field, if some polynomials are algebraically dependent, are their derivatives linearly dependent?

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#polynomials #field-theory #jacobian #positive-characteristic #algebraic-independence
92
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Probability Algebra With a Wordle Example

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#probability #probability-theory #random-variables #conditional-probability #algebraic-independence

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