query: Characteristic polynomial $g(x)$ of $\alpha$ over $K$ of a finite extension field $F$
positive_passages.docid: 21578
positive_passages.text: Showing the minimal polynomial for an element in an extension field is the same as the minimal polynomial of a linear transformation.
negative_passages.docid: 129109
negative_passages.text: Is the set of polynomial with coefficients on $\mathbb{Q}$ enumerable?
negative_passages.docid: 28803
negative_passages.text: Extension of degree 2 with characteristic not 2
negative_passages.docid: 65661
negative_passages.text: Decomposition of a homogeneous polynomial
negative_passages.docid: 38489
negative_passages.text: Degree of the extension $\mathbb{Q}(\sqrt{a+\sqrt{b}})$ over $\mathbb{Q}$
negative_passages.docid: 31142
negative_passages.text: Why does $K \leadsto K(X)$ preserve the degree of field extensions?
negative_passages.docid: 26999
negative_passages.text: How is the degree of the minimal polynomial related to the degree of a field extension?
negative_passages.docid: 21853
negative_passages.text: When are minimal and characteristic polynomials the same?
negative_passages.docid: 149364
negative_passages.text: Characteristic polynomial of an inverse
negative_passages.docid: 100899
negative_passages.text: Coefficients of the characteristic polynomial
negative_passages.docid: 51770
negative_passages.text: Number of elements in a finite field extension for finite fields
negative_passages.docid: 42677
negative_passages.text: Proving $(\alpha + \beta)^{p^n} = \alpha^{p^n} + \beta^{p^n}$ in a finite field
negative_passages.docid: 24919
negative_passages.text: $\mathbb{Q}(\zeta_{10}) $ degree of field extension over $\mathbb{Q}$
negative_passages.docid: 146591
negative_passages.text: Inseparable polynomial over a non-perfect field
negative_passages.docid: 18282
negative_passages.text: Finding the minimal polynomial, the eigenvalues, and the characteristic polynomial of $T(A)=A+A^t$
negative_passages.docid: 20613
negative_passages.text: Units (invertibles) of polynomial rings over a field
negative_passages.docid: 10885
negative_passages.text: Existence of irreducible polynomials over finite field