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A Heronian triangle is a triangle having rational side lengths and rational area. The triangles are so named because such triangles are related to Heron's formula ...

The minimal polynomial of an algebraic number zeta is the unique irreducible monic polynomial of smallest degree p(x) with rational coefficients such that p(zeta)=0 and whose ...

Let c and d!=c be real numbers (usually taken as c=1 and d=0). The Dirichlet function is defined by D(x)={c for x rational; d for x irrational (1) and is discontinuous ...

The problem of finding the connection between a continuous function f on the boundary partialR of a region R with a harmonic function taking on the value f on partialR. In ...

A polynomial is said to be irreducible if it cannot be factored into nontrivial polynomials over the same field. For example, in the field of rational polynomials Q[x] (i.e., ...

If a is an element of a field F over the prime field P, then the set of all rational functions of a with coefficients in P is a field derived from P by adjunction of a.

The number q in a fraction p/q.

A polynomial form which is the sum of two polynomial forms involving separate sets of variables.

A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

The number p in a fraction p/q, i.e., the dividend.