Question

Polynomial transformation of the roots of another irreducible polynomial.

score 178 · Answer 1 · 2014-09-01 21:45:23

178

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Polynomial transformation of the roots of another irreducible polynomial.

Published on 01 Sep 2014 - 21:45

score 90 · Answer 2 · 2014-09-02 21:48:31

90

Views

Prove that $f=X^3-\sqrt{3}$ is irreducible in $\mathbb{Q}(3^{1/4})$

Published on 02 Sep 2014 - 21:48

score 54 · Answer 3 · 2014-09-03 23:12:56

54

Views

When are the coordinates of the intersection points of plane curves actually algebraic conjugates

Published on 03 Sep 2014 - 23:12

score 123 · Answer 4 · 2014-09-06 22:57:30

123

Views

Can the product of only some of the algebraic conjugates be an integer?

Published on 06 Sep 2014 - 22:57

score 76 · Answer 5 · 2014-09-10 20:37:30

76

Views

Polynomial factοrisation

Published on 10 Sep 2014 - 20:37

score 2.3k · Answer 6 · 2014-09-18 05:29:09

2.3k

Views

If $f(x+a)$ is irreducible over $F$ then $f(x)$ is irreducible over $F$

Published on 18 Sep 2014 - 5:29

score 1.3k · Answer 7 · 2026-03-25 18:59:11

1.3k

Views

SAGE: Is it possible to extract the irreducible factor of a polynomial for the purpose of constructing a Number Field?

Published on 25 Mar 2026 - 18:59

score 63 · Answer 8 · 2014-09-21 15:35:07

63

Views

$\mathbb{Q}[x,y]/(f(x,y))$ is not a field for any irreducible $f(x,y) \in \mathbb{Q}[x,y]$.

Published on 21 Sep 2014 - 15:35

score 885 · Answer 9 · 2014-09-22 01:46:39

885

Views

Field extension of degree 3 and polynomial roots

Published on 22 Sep 2014 - 1:46

score 486 · Answer 10 · 2014-09-22 18:42:12

486

Views

Prove that $f(x)=x^4+8x^3+x^2+2x+5$ is irreducible in $\mathbb Q[x]$

Published on 22 Sep 2014 - 18:42

score 882 · Answer 11 · 2014-09-22 20:32:49

882

Views

Factorization into irreducible factors

Published on 22 Sep 2014 - 20:32

score 447 · Answer 12 · 2014-09-23 02:22:22

447

Views

Does there exist a finite set of polynomials which do not have roots over any prime field?

Published on 23 Sep 2014 - 2:22

score 69 · Answer 13 · 2014-09-27 13:16:05

69

Views

If $\deg(f) > p^k$ then $f$ as an irreducible divisor of degree $> k$

Published on 27 Sep 2014 - 13:16

score 69 · Answer 14 · 2014-09-28 03:46:24

69

Views

The irreducibility of the polynomial $x^p\pm px-t$, where $t$ is an integer, $p$ is a prime number.

Published on 28 Sep 2014 - 3:46

score 115 · Answer 15 · 2014-10-01 02:46:11

115

Views

Roots of irreducible polynomials in a finite field

Published on 01 Oct 2014 - 2:46

List Question

Polynomial transformation of the roots of another irreducible polynomial.

Prove that $f=X^3-\sqrt{3}$ is irreducible in $\mathbb{Q}(3^{1/4})$

When are the coordinates of the intersection points of plane curves actually algebraic conjugates

Can the product of only some of the algebraic conjugates be an integer?

Polynomial factοrisation

If $f(x+a)$ is irreducible over $F$ then $f(x)$ is irreducible over $F$

SAGE: Is it possible to extract the irreducible factor of a polynomial for the purpose of constructing a Number Field?

$\mathbb{Q}[x,y]/(f(x,y))$ is not a field for any irreducible $f(x,y) \in \mathbb{Q}[x,y]$.

Field extension of degree 3 and polynomial roots

Prove that $f(x)=x^4+8x^3+x^2+2x+5$ is irreducible in $\mathbb Q[x]$

Factorization into irreducible factors

Does there exist a finite set of polynomials which do not have roots over any prime field?

If $\deg(f) > p^k$ then $f$ as an irreducible divisor of degree $> k$

The irreducibility of the polynomial $x^p\pm px-t$, where $t$ is an integer, $p$ is a prime number.

Roots of irreducible polynomials in a finite field

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