AlgebraicNumberDenominator[a] gives the smallest positive integer n such that n a is an algebraic integer.

The systems of equations that govern certain phenomena (in electrical circuits, chemical kinetics, etc.) contain a combination of differential equations and algebraic ...

AlgebraicNumber[\[Theta], {c_0, c_1, ..., c_n}] represents the algebraic number in the field \[DoubleStruckCapitalQ][\[Theta]] given by c_0 + c_1 \[Theta] + ... + c_n ...

AlgebraicNumberTrace[a] gives the trace of the algebraic number a.

In general, a system of ordinary differential equations (ODEs) can be expressed in the normal form, The derivatives of the dependent variables x are expressed explicitly in ...

The representation of algebraic numbers. When you enter a Root object, the polynomial that appears in it is automatically reduced to a minimal form. This extracts the pure ...

AlgebraicNumberPolynomial[a, x] gives the polynomial in x corresponding to the AlgebraicNumber object a.

Although Diophantine equations provide classic examples of undecidability, Mathematica in practice succeeds in solving a remarkably wide range of such equations—automatically ...

With its convenient symbolic representation of algebraic numbers, Mathematica's state-of-the-art algebraic number theory capabilities provide a concrete implementation of one ...

AlgebraicNumberNorm[a] gives the norm of the algebraic number a.