query: The degree of splitting field of $X^4-2$ over $\mathbb Q$
positive_passages.docid: 22632
positive_passages.text: Galois group of $x^4-2$
negative_passages.docid: 126127
negative_passages.text: A field extension of prime degree
negative_passages.docid: 46572
negative_passages.text: Degree of a splitting field is no greater than $n!$
negative_passages.docid: 24168
negative_passages.text: A characterisation of quadratic extensions contained in cyclic extensions of degree 4
negative_passages.docid: 43987
negative_passages.text: Decomposition of the tensor product $\mathbb{Q}_p \otimes_{\mathbb{Q}} \mathbb{Q}[i]$ into a product of fields
negative_passages.docid: 155771
negative_passages.text: Product of degree of two field extensions of prime degree
negative_passages.docid: 46648
negative_passages.text: How to prove the existence of a splitting field?
negative_passages.docid: 26069
negative_passages.text: Why is $X^4-16X^2+4$ irreducible in $\mathbb{Q}[X]$?
negative_passages.docid: 87467
negative_passages.text: Finding some missing subfields of a splitting field of $x^4-7$
negative_passages.docid: 145594
negative_passages.text: Splitting of prime ideals in algebraic extensions
negative_passages.docid: 77620
negative_passages.text: Irreducible polynomials over $\mathbb Q$ and $\mathbb Z $
negative_passages.docid: 147459
negative_passages.text: Find a non-constructible algebraic number of degree $4$ over $\Bbb Q$
negative_passages.docid: 145140
negative_passages.text: Subfield of $\mathbb{Q}(\sqrt[n]{a})$
negative_passages.docid: 143831
negative_passages.text: Showing $\mathbb{Q}$ is homeomorphic to $\mathbb{Q}^2$
negative_passages.docid: 20097
negative_passages.text: Cardinality of the quotient ring $\mathbb{Z}[x]/(x^2-3,2x+4)$
negative_passages.docid: 95602
negative_passages.text: Computing the Galois group of $x^4+ax^2+b \in \mathbb{Q}[x] $
negative_passages.docid: 114295
negative_passages.text: Find all the middle fields of the splitting field of $x^4-2$ over $\mathbb{Q}$