List questions from symmetric-polynomials

Published on 25 Mar 2026 - 16:03

863

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(From Artin)Prove the general formula of discriminant of $x^n + px + q$ for $n ≥ 2$

Published on 25 Mar 2026 - 12:29

125

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Solve the system of equations

Published on 27 Feb 2017 - 19:29

466

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Details about plethysm

Published on 27 Feb 2017 - 23:22

90

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Prove that the two definitions of the discriminant are equivalent

Published on 25 Mar 2026 - 12:26

144

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An inequality of symmetric polynomials using AGM inequality?

Published on 10 Mar 2017 - 15:48

204

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For $2x+2y-3z\geq0$ and similar prove that $\sum\limits_{cyc}(7z-3x-3y)(x-y)^2\geq0$

Published on 26 Mar 2026 - 3:08

283

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Are all the solutions of the system $\begin{cases} f(x,y)=0 \\ f(y,x)=0 \end{cases}$ (if there are any) pairs of equal numbers?

Published on 28 Mar 2026 - 1:08

149

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Checking if a poly. is sym.

Published on 24 Mar 2017 - 21:50

304

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Polynomials invariant under specific permutations or subgroups of $S_n$.

Published on 25 Mar 2026 - 13:54

76

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A system of polynomial equations with odd degree

Published on 25 Mar 2017 - 6:23

329

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What is the most efficient way to compute elementary symmetric functions?

Published on 07 Apr 2017 - 5:36

26

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Finitely many $\alpha$ s.t. all conjugates $\leq N$ ($N \geq 1$)

Published on 30 Jan 2023 - 13:41

92

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$k[x_1,.\dots,x_n]$ is a free module over the ring of symmetric polyomials

Published on 26 Mar 2026 - 1:11

83

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Does $\sum_{j=1,j\neq k}^n\frac{z_k}{z_k-z_j}=\sum_{j=1,j\neq m}^n\frac{z_m}{z_m-z_j}$ implies the $(z_j)_{j=1,...,n}$ are the nth roots of $z_1^n$?

Published on 28 Mar 2026 - 6:59

List Question

Inequality for positive real numbers less than $1$: $8(abcd+1)>(a+1)(b+1)(c+1)(d+1)$

(From Artin)Prove the general formula of discriminant of $x^n + px + q$ for $n ≥ 2$

Solve the system of equations

Details about plethysm

Prove that the two definitions of the discriminant are equivalent

An inequality of symmetric polynomials using AGM inequality?

For $2x+2y-3z\geq0$ and similar prove that $\sum\limits_{cyc}(7z-3x-3y)(x-y)^2\geq0$

Are all the solutions of the system $\begin{cases} f(x,y)=0 \\ f(y,x)=0 \end{cases}$ (if there are any) pairs of equal numbers?

Checking if a poly. is sym.

Polynomials invariant under specific permutations or subgroups of $S_n$.

A system of polynomial equations with odd degree

What is the most efficient way to compute elementary symmetric functions?

Finitely many $\alpha$ s.t. all conjugates $\leq N$ ($N \geq 1$)

$k[x_1,.\dots,x_n]$ is a free module over the ring of symmetric polyomials

Does $\sum_{j=1,j\neq k}^n\frac{z_k}{z_k-z_j}=\sum_{j=1,j\neq m}^n\frac{z_m}{z_m-z_j}$ implies the $(z_j)_{j=1,...,n}$ are the nth roots of $z_1^n$?

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