List questions from differential-algebra

Published on 25 Mar 2026 - 6:03

444

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Prove that $\int \sin(x^2)dx$ is not elementary

Published on 29 Apr 2026 - 12:54

331

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Why is $e^g$ transcendental over $\mathbb{C}(z)$ for $g$ rational?

Published on 23 Feb 2026 - 3:47

132

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Do derivations over a commutative ring form a ring?

Published on 25 Mar 2026 - 5:59

901

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Possible Research Topics

Published on 10 May 2026 - 8:34

380

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Are all derivations of real-valued functions derivatives?

Published on 25 Mar 2026 - 6:03

499

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Existence of homotopy operator is equivalent to zero homology

Published on 25 Mar 2026 - 6:04

279

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Constants in localizations of a differential ring

Published on 25 Mar 2026 - 6:04

172

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Is the Antiderivative of an Elementary Function Being Nonelementary Generic?

Published on 25 Mar 2026 - 7:42

247

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Please solve the differential equation in its simplest form.

Published on 25 Mar 2026 - 6:00

131

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Constants in localized differential rings

Published on 25 Mar 2026 - 7:31

150

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Closed forms of $\int_A^B \sin(\sin(ax))dx$ and $\int_A^B \sin(\sin(ax)) \cdot \sin(\sin(bx))dx$

Published on 25 Mar 2026 - 6:06

2.3k

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Inconsistencies in the definition of derivative of a polynomial over a field

Published on 25 Mar 2026 - 6:06

213

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Solving Riccati differential equation in general case

Published on 25 Mar 2026 - 7:35

155

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Can every "not-too-big" differential field be thought of as actually consisting of functions?

Published on 25 Mar 2026 - 6:06

List Question

Can we find a simple basis for the cokernel of this derivation?

Prove that $\int \sin(x^2)dx$ is not elementary

Why is $e^g$ transcendental over $\mathbb{C}(z)$ for $g$ rational?

Do derivations over a commutative ring form a ring?

Possible Research Topics

Are all derivations of real-valued functions derivatives?

Existence of homotopy operator is equivalent to zero homology

Constants in localizations of a differential ring

Is the Antiderivative of an Elementary Function Being Nonelementary Generic?

Please solve the differential equation in its simplest form.

Constants in localized differential rings

Closed forms of $\int_A^B \sin(\sin(ax))dx$ and $\int_A^B \sin(\sin(ax)) \cdot \sin(\sin(bx))dx$

Inconsistencies in the definition of derivative of a polynomial over a field

Solving Riccati differential equation in general case

Can every "not-too-big" differential field be thought of as actually consisting of functions?

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