NumberFieldDiscriminant[a] gives the discriminant of the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

Built into Mathematica is the world's largest collection of both numerical and symbolic equation solving capabilities—with many original algorithms, all automatically ...

NumberFieldRegulator[a] gives the regulator of the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

ToNumberField[a, \[Theta]] expresses the algebraic number a in the number field generated by \[Theta]. ToNumberField[{a_1, a_2, ...}, \[Theta]] expresses the a_i in the field ...

Subresultants[poly_1, poly_2, var] generates a list of the principal subresultant coefficients of the polynomials poly_1 and poly_2 with respect to the variable var.

Mathematica's handling of polynomial systems is a tour de force of algebraic computation. Building on mathematical results spanning more than a century, Mathematica for the ...

A core activity in exploratory experimental mathematics is recognition of numbers: going backward from a number to find out how it can be generated. Mathematica provides ...

Counting roots of polynomials. CountRoots accepts polynomials with Gaussian rational coefficients. The root count includes multiplicities. This gives the number of real roots ...

Packing a large number of sophisticated algorithms—many recent and original—into a powerful collection of functions, Mathematica draws on almost every major result in number ...

Mathematica represents Boolean expressions in symbolic form, so they can not only be evaluated, but also be symbolically manipulated and transformed. Incorporating ...