Number Theoretic Functions (Mathematica Guide)

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

JacobiZeta (Built-in Mathematica Symbol)

JacobiZeta[\[Phi], m] gives the Jacobi zeta function Z(\[Phi] \[VerticalSeparator] m).

LogGamma (Built-in Mathematica Symbol)

LogGamma[z] gives the logarithm of the gamma function log \[CapitalGamma](z).

NevilleThetaN (Built-in Mathematica Symbol)

NevilleThetaN[z, m] gives the Neville theta function \[CurlyTheta]_n (z \[VerticalSeparator] m).

NevilleThetaS (Built-in Mathematica Symbol)

NevilleThetaS[z, m] gives the Neville theta function \[CurlyTheta]_s (z \[VerticalSeparator] m).

Algebraic Number Fields (Mathematica Tutorial)

Mathematica provides representation of algebraic numbers as Root objects. A Root object contains the minimal polynomial of the algebraic number and the root number—an integer ...

Numerical Evaluation & Precision (Mathematica Guide)

In two decades of intense algorithmic development, Mathematica has established a new level of numerical computation. Particularly notable are its many original highly ...

Polynomial Systems (Mathematica Guide)

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 ...

JacobiSN (Built-in Mathematica Symbol)

JacobiSN[u, m] gives the Jacobi elliptic function sn(u | m).

Cryptographic Number Theory (Mathematica Guide)

Mathematica's extensive base of state-of-the-art algorithms, efficient handling of very long integers, and powerful built-in language make it uniquely suited to both research ...