# Advanced Math

Maple 18 includes numerous cutting-edge updates in a variety of branches of mathematics:

### Fractals

Maple 18 features a new package for generating Fractals. This includes various fractal generators, such as BurningShip, Julia, Lyapunov, Mandelbrot, and Newton. For more, see Fractals in Maple 18.

 BurningShip Julia Lyapunov Mandelbrot Newton

### Graph Theory

 Several improvements and enhancements have been made to the GraphTheory package including the new Latex command for generating code for displaying a graph using the LaTeX picture environment.    For more, see Updates to Graph Theory.

### There are numerous improvements for Group Theory, including a new library of Perfect Groups. Other new commands include:

• AbelianInvariants: Compute the Abelian invariants of a finitely presented group.
• CycleIndexPolynomial: Return the degree of a permutation group.
• PresentationComplexity: Return a measure of the complexity of a presentation of a finitely presented group.
• Simplify: Simplify the presentation for a group.
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For more details, see Updates to Group Theory.

### Numerical Integration with Cuba Library

Maple 18 provides more methods for numerical integration, adding four routines for high-dimensional numerical integration that rely on the Cuba library for multidimensional numerical integration.

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### QDifferenceEquations

The QDifferenceEquations package includes two new commands for working with q-difference operators.

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Closure computes the closure in the ring of linear q-difference operators with polynomial coefficients.

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Desingularize computes a multiple of a given q-difference operator with fewer singularities.

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For details, see Q-Difference Equation in Maple 18.

### RootOf

There have been several ease of use enhancements made to the function RootOf, including with numeric, interval, and index selectors.

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For more on improvements to RootOf in Maple 18, see the RootOf updates page.

## Ready for the next step?

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