Complex Polynomial Systems (Mathematica Tutorial)

The Mathematica functions Reduce, Resolve, and FindInstance allow you to solve a wide variety of problems that can be expressed in terms of equations and inequalities. The ...

$MaxRootDegree (Built-in Mathematica Symbol)

$MaxRootDegree specifies the maximum degree of polynomial to allow in Root objects.

Nonlinear PDEs (Mathematica Tutorial)

The general first-order nonlinear PDE for an unknown function u(x,y) is given by Here F is a function of uu(x,y), p ( ∂u(x,y) ) / ( ∂x ) , and q ( ∂u(x,y) ) / ( ∂y ) . The ...

Resolve (Built-in Mathematica Symbol)

Resolve[expr] attempts to resolve expr into a form that eliminates ForAll and Exists quantifiers. Resolve[expr, dom] works over the domain dom. Common choices of dom are ...

QuotientRemainder (Built-in Mathematica Symbol)

QuotientRemainder[m, n] gives a list of the quotient and remainder from division of m by n.

Getting Started (Mathematica Overview)

Your First Mathematica Calculations Arithmetic Defining Variables

ComposeSeries (Built-in Mathematica Symbol)

ComposeSeries[series_1, series_2, ...] composes several power series.

UpSet (Built-in Mathematica Symbol)

lhs ^= rhs assigns rhs to be the value of lhs, and associates the assignment with symbols that occur at level one in lhs.

KnotData (Built-in Mathematica Symbol)

KnotData[knot, " property"] gives the specified property for a knot.KnotData[knot] gives an image of the knot.KnotData["class"] gives a list of knots in the specified class.

Solving Frobenius Equations and ... (Mathematica Tutorial)

A Frobenius equation is an equation of the form where a_1, …, a_n are positive integers, m is an integer, and the coordinates x_1, …, x_n of solutions are required to be ...