The Cache package is a set of functions for manipulating the new Cache data structure.  A Cache can be used like a table; however, a Cache stores two types of elements, permanent and temporary. Permanent elements are like those of a table, once inserted they remain in the table until removed.  Temporary elements are stored as long as the Cache has space to store them.  When a new temporary element is inserted, an older one may be removed.

Caches are primarily intended to be used as remember tables.  Elements that are added automatically are added as temporary. This restricts the remember table to store only recently accessed elements.  Important remember table entries can be stored as permanent entries, assuring that they are not automatically removed.

The ContextMenu package provides tools to control and customize Maple context-sensitive menus.  It supersedes the context package. A context-sensitive menu is generated when a user right-clicks (Control-click on Macintosh platforms) a Maple expression.

The information necessary to build context-sensitive menus is encapsulated in context menu modules.  The module corresponding to the built-in context menu is available as ContextMenu[CurrentContext]. To build a new context menu module, which replaces the default, see ContextMenu[New].

Within a context menu module, you can add new entries to the context menu or alter the criteria under which entries are displayed in a menu. For more information, see ContextMenu[CurrentContext].

The Logic package is a collection of commands for manipulating and transforming expressions using two-valued Boolean logic.

With the Logic package, you can simplify logical expressions, test two expressions for equivalence, convert logical expressions to algebraic expressions modulo 2, and perform a variety of other logical operations.  In the following example, the dual of a logical expression is computed using the Logic[Dual] command.

with(Logic):

Dual( (x &and y) &implies z );

$\neg \left(z\Rightarrow \left(x\vee y\right)\right)$

The MmaTranslator package converts Mathematica commands and notebooks to Maple commands and worksheets.

You can use the FromMma and FromMmaNotebook commands or the Mathematica to Maple Translator Maplet application for the translation.

For more information, see MmaTranslator.

The Optimization package is a collection of commands for numerically solving optimization problems, which involve minimization or maximization of an objective function possibly subject to constraints.  The package takes advantage of built-in library routines provided by the Numerical Algorithms Group (NAG).  Key features are described as follows.

The package provides the ability to solve linear programs, quadratic programs, nonlinear programs, and both linear and nonlinear least-squares problems. For non-convex problems, local solutions are computed.  Both unconstrained and constrained problems are accepted.

An Interactive Maplet application provides and easy-to-use interface to all of the computation routines in the Optimization package, including the Minimize and Maximize commands. Alternatively, users can take full advantage of the solvers' capabilities by calling the specialized routines: LPSolve for linear programs, QPSolve for quadratic programs, NLPSolve for nonlinear programs, and LSSolve for least-squares problems. The following examples demonstrate the Minimize and QPSolve commands.  The solution consists of the final objective function value followed by a point at which this value is attained.

with(Optimization);

$\left[\mathrm{ImportMPS}\,\mathrm{Interactive}\,\mathrm{LPSolve}\,\mathrm{LSSolve}\,\mathrm{Maximize}\,\mathrm{Minimize}\,\mathrm{NLPSolve}\,\mathrm{QPSolve}\right]$

Minimize(sin(x)/x, x=1..10);

$\left[\mathrm{-0.217233628211222}\,\left[x=4.49340945753529\right]\right]$

QPSolve(2*x+5*y+3*x^2+3*x*y+2*y^2, {x-y>=2});

$\left[\mathrm{-3.53333333333333}\,\left[x=0.466666666666667\,y=\mathrm{-1.60000000000000}\right]\right]$

The Optimization package commands allow a simple and natural way to express the objective function and the constraints using algebraic expressions. Alternative forms of input using procedures, Vectors, and Matrices are available, which provide greater flexibility and efficiency. For a summary of the various ways in which the optimization problem can be expressed, see Optimization[InputForms]. In addition, the package features the Optimization[ImportMPS] command for importing linear programs in MPS format.

Computations can be performed using hardware floating-point data or arbitrary-precision software floating-point data.  The Optimization commands automatically select the most appropriate floating-point computation environment and attempt to solve the problem as efficiently as possible. For details concerning numeric computation in the Optimization package, see the Optimization[Computation] help page.

For a brief introduction to the Optimization package, see the examples[Optimization] worksheet.

The RootFinding package enhances Maple's ability to compute and locate roots numerically. The package contains four commands. The RootFinding[Analytic] and RootFinding[AnalyticZerosFound] commands compute the zeros of an analytic univariate function. The RootFinding[BivariatePolynomial] command computes the solutions of two or more bivariate polynomials. The RootFinding[Homotopy] command finds numerical approximations to roots of systems of polynomial equations.

A new package for multivariate calculus is available in the Student package. The Student[MultivariateCalculus] package assists with the teaching and learning of the calculus of functions from $R^n$ to $R$.  Interactive tutors are provided covering the basic concepts, and a range of commands are included that allow exploration of these and other concepts in greater depth.

For more information, see Student[MultivariateCalculus].