Mathematica 's functions for solving differential equations can be applied to many different classes of differential equations, including ordinary differential equations ...

LatticeData[lattice, " property"] gives the specified property for a lattice.LatticeData[n] gives a list of named lattices of dimension n.

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

Any combination of equations or inequalities can be thought of as implicitly defining a region in some kind of space. The fundamental function of Reduce is to turn this type ...

New functions CountRoots, IsolatingInterval, and RootIntervals have been added to the built-in Mathematica kernel. IsolatingInterval includes the functionality of ...

One of the important features of Mathematica is that it can do symbolic, as well as numerical calculations. This means that it can handle algebraic formulas as well as ...

If you represent the n^th term in a sequence as a[n], you can use a recurrence equation to specify how it is related to other terms in the sequence. RSolve takes recurrence ...

GenericCylindricalDecomposition[ineqs, {x_1, x_2, ...}] finds the full-dimensional part of the decomposition of the region represented by the inequalities ineqs into ...

Simplifying expressions. Mathematica does not automatically simplify an algebraic expression like this. Simplify performs the simplification.

RootLocusPlot[g, {k, k_min, k_max}] generates the root locus plot of a rational function g of k ranging from k_min to k_max.RootLocusPlot[sys, ...] plots the root loci of a ...