Question

Proof of rational + algebraic is algebraic and rational + transcendental is transcendental?

score 58 · Answer 1 · 2026-03-25 09:28:50

58

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Proof of rational + algebraic is algebraic and rational + transcendental is transcendental?

Published on 25 Mar 2026 - 9:28

score 363 · Answer 2 · 2026-03-25 02:59:03

363

Views

Positive definiteness of a multivariate polynomial function

Published on 25 Mar 2026 - 2:59

score 45 · Answer 3 · 2026-03-25 09:27:32

45

Views

How to evaluate $f(x)$ at the point $(x^2 + ax + b) \in \text{Spec} \, \mathbb{R}[x] $?

Published on 25 Mar 2026 - 9:27

score 227 · Answer 4 · 2018-08-11 19:52:06

227

Views

Solve for $x$ given $4x^2 + 12x + \frac{12}{x} + \frac{4}{x^2} = 47$

Published on 11 Aug 2018 - 19:52

score 78 · Answer 5 · 2026-03-25 19:03:29

78

Views

For which $f \in \mathbb{C}[x,y]$, $fy-\lambda$ is irreducible in $\mathbb{C}[x,y]$ for infinitely many $\mathbb{C} \ni \lambda$'s

Published on 25 Mar 2026 - 19:03

score 70 · Answer 6 · 2026-03-25 17:52:49

70

Views

For which $f \in \mathbb{C}[x,y]$, $\mathbb{C}(x)[y]/(fy-\lambda)$ is isomorphic to $\mathbb{C}(t)$?

Published on 25 Mar 2026 - 17:52

score 98 · Answer 7 · 2026-03-26 10:56:30

98

Views

Find Polynomials with Integer Coefficients with Particular Roots

Published on 26 Mar 2026 - 10:56

score 110 · Answer 8 · 2026-03-25 04:42:32

110

Views

How to prove that $\Bbb C[X,Y]/(XY) \ncong \Bbb C[X,Y]/(X) \times \Bbb C[X,Y]/(Y)$

Published on 25 Mar 2026 - 4:42

score 208 · Answer 9 · 2018-08-12 22:22:26

208

Views

How does one create a polynomial equation based on graphic features?

Published on 12 Aug 2018 - 22:22

score 2.4k · Answer 10 · 2026-03-30 22:56:09

2.4k

Views

Which $f,g \in \mathbb{C}[x,y]$ satisfy $\mathbb{C}(fy,gy)=\mathbb{C}(x,y)$?

Published on 30 Mar 2026 - 22:56

score 416 · Answer 11 · 2026-03-25 06:24:52

416

Views

Factoring quartic into 2 quadratic polynomials: $x^{4}+ax^{3}+bx^{2}+cx+d =(x^{2}+g_{1}x+h_{1})(x^{2}+g_{2}x+h_{2})$

Published on 25 Mar 2026 - 6:24

score 31 · Answer 12 · 2026-03-25 20:08:00

31

Views

What is the relation between polynomial factorisation and field size?

Published on 25 Mar 2026 - 20:08

score 50 · Answer 13 · 2026-03-27 21:37:23

50

Views

Is there accepted notation for the various "duals" of a polynomial? Does any interesting theory surround them?

Published on 27 Mar 2026 - 21:37

score 25 · Answer 14 · 2026-03-25 20:08:37

25

Views

Relation between Polynomial factorisation and field size in theory and practice.

Published on 25 Mar 2026 - 20:08

score 276 · Answer 15 · 2026-03-25 15:47:25

276

Views

Rational Roots of a Quadratic Equation

Published on 25 Mar 2026 - 15:47

List Question

Proof of rational + algebraic is algebraic and rational + transcendental is transcendental?

Positive definiteness of a multivariate polynomial function

How to evaluate $f(x)$ at the point $(x^2 + ax + b) \in \text{Spec} \, \mathbb{R}[x] $?

Solve for $x$ given $4x^2 + 12x + \frac{12}{x} + \frac{4}{x^2} = 47$

For which $f \in \mathbb{C}[x,y]$, $fy-\lambda$ is irreducible in $\mathbb{C}[x,y]$ for infinitely many $\mathbb{C} \ni \lambda$'s

For which $f \in \mathbb{C}[x,y]$, $\mathbb{C}(x)[y]/(fy-\lambda)$ is isomorphic to $\mathbb{C}(t)$?

Find Polynomials with Integer Coefficients with Particular Roots

How to prove that $\Bbb C[X,Y]/(XY) \ncong \Bbb C[X,Y]/(X) \times \Bbb C[X,Y]/(Y)$

How does one create a polynomial equation based on graphic features?

Which $f,g \in \mathbb{C}[x,y]$ satisfy $\mathbb{C}(fy,gy)=\mathbb{C}(x,y)$?

Factoring quartic into 2 quadratic polynomials: $x^{4}+ax^{3}+bx^{2}+cx+d =(x^{2}+g_{1}x+h_{1})(x^{2}+g_{2}x+h_{2})$

What is the relation between polynomial factorisation and field size?

Is there accepted notation for the various "duals" of a polynomial? Does any interesting theory surround them?

Relation between Polynomial factorisation and field size in theory and practice.

Rational Roots of a Quadratic Equation

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