NumberFieldSignature[a] gives the signature of the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

Mathematica incorporates the latest algorithms—some original to Wolfram Research—for evaluating mathematical constants to any number of digits of precision. For basic ...

Mathematica has been used to make many important discoveries in discrete mathematics over the past two decades. Its integration of highly efficient and often original ...

If you use a text-based interface to Mathematica, then the input you give must consist only of characters that you can type directly on your computer keyboard. But if you use ...

 

GroebnerBasis[{poly_1, poly_2, ...}, {x_1, x_2, ...}] gives a list of polynomials that form a Gröbner basis for the set of polynomials poly_i. GroebnerBasis[{poly_1, poly_2, ...

Mathematica contains the world's largest collection of number theoretic functions, many based on specially developed algorithms.

Eigenvalues and eigenvectors. The eigenvalues of a matrix m are the values λ_i for which one can find nonzero vectors v_i such that m.v_i λ_iv_i. The eigenvectors are the ...

SemialgebraicComponentInstances[ineqs, {x_1, x_2, ...}] gives at least one sample point in each connected component of the semialgebraic set defined by the inequalities ineqs ...

Algebraics represents the domain of algebraic numbers, as in x \[Element] Algebraics.