In calculus even more than other areas, Mathematica packs centuries of mathematical development into a small number of exceptionally powerful functions. Continually enhanced ...

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

When a differential system has a certain structure, it is advantageous if a numerical integration method preserves the structure. In certain situations it is useful to solve ...

NumberFieldIntegralBasis[a] gives an integral basis for the field \[DoubleStruckCapitalQ][a] generated by the algebraic number a.

Mathematica normally assumes that all your variables are global. This means that every time you use a name like x, Mathematica normally assumes that you are referring to the ...

Mathematica provides many functions to group terms in a polynomial, extract and sort the monomials, display them in various ways, and even process them as arbitrary ...

Mathematica has sophisticated built-in automatic numerical precision and accuracy control. But for special-purpose optimization of numerical computations, or for studying ...

NumberFieldNormRepresentatives[a, m] gives a list of representatives of classes of algebraic integers of norm \[PlusMinus]m in the field \[DoubleStruckCapitalQ][a] generated ...

Mathematica can work with polynomials whose coefficients are in the finite field Z_p of integers modulo a prime p. Functions for manipulating polynomials over finite fields. ...

RootReduce[expr] attempts to reduce expr to a single Root object.