New Features of Maple 9.5

Mathematical Computations

Graphical User Interface

Differential Equations Exact Solutions New algorithms for solving Riccati type ODEs, second order linear ODEs of Mathieu type, polynomial solutions for nonlinear ODEs and systems of ODEs, linear and nonlinear PDEs and systems of PDEs New methods for initial value ODE problems, and piecewise ODEs Hypergeometric solutions free of integrals for linear ODEs Efficiency improvements for difficult first order Abel type ODE problems Numeric Solutions Three new numerical solution methods for Differential Algebraic ODE initial value problems (DAEs), both stiff and non-stiff Maplet assistant extended to allow interactive solving of DAE problems Optimisation option for large or complex systems can increase calculation speed by up to 30 times New implicit option for the stiff IVP solver is useful for large, dense ODE systems Differential Equation Tools Seven new commands, some based on original algorithms, were added to DEtools PDEtools now includes a command for computing traveling wave solutions Method for using algebraic triangular techniques were added to diffalg package New Packages Optimisation Numeric methods for solutions of optimization problems Easy-to-use interactive Maplet assistant Arbitrary-precision solutions Solvers for linear, quadratic and nonlinear programs, including constrained and unconstrained problems Solvers for linear and nonlinear least-squares problems Logic The Logic package is a collection of commands for manipulating and transforming expressions using two-valued Boolean logic Simplify logical expressions, test two expressions for equivalence, convert logical expressions to algebraic expressions modulo 2, and perform a variety of other logical operations RootFinding The RootFinding package enhances Maple's ability to compute and locate roots numerically Computes zeros of analytic functions and solutions of two or more bivariate polynomials Enhanced Packages Groebner Now includes two algorithms to compute the reduced Groebner basis of a toric ideal LREtools Determine necessary conditions for the solution of a linear recurrence equation to be analytic, in terms of the initial values Finds all d'Alembertian solutions of a linear recurrence equation Determine if it is possible to construct a desingularizable operator with polynomial coefficients for the linear recurrence, and compute it if it exists QDifferenceEquations Sum the solutions of a q-shift operator using the methodof accurate q-summations Compute a series solution of a linear q-difference equation Extend a series solutions of a linear q-difference equation to a higher degree Finds all q-hypergeometric solutions of a given linear q-difference equation SolveTools Extended to include functions to solve inequalities Linear inequalities with respect to one variable Linear univariate and multivariate systems of inequalities SumTools Functionality involving sums of hypergeometric type sums has been extended General Symbolic Calculations Enhancements have been made to many top-level routines for symbolic calculations and manipulations, including the functions for: Integration Summation Simplification Combinations Series expansions Conversions Function decomposition routines performs rational function decomposition on overdetermined systems in the presence of parameters The FunctionAdvisor command has been enhanced regarding the computation of non-trivial specializations of mathematical functions for particular values of their parameters Efficiency Improvements Significant improvements have been made in the efficiency and accuracy of the routines that calculate elliptic and Jacobi functions Maple 9.5 has more efficient computation of the quotient of sparse polynomials Conversions between D and diff notation for derivatives are now much faster Numeric linear algebra calculations on Windows®, Macintosh® and Linux® use state-of-the art routines optimized for each platform   Education Dictionary Over 5000 mathematical and engineering terms and definitions are fully incorporated into the Help system Includes over 300 figures to clearly explain the concepts Definitions can be accessed as help pages using an alphabetical listing in the Maple Help system, or through links in a worksheet or help page Short definitions are conveniently displayed as pop-ups Student[MultivariateCalculus] The Student[MultivariateCalculus] package will assist with the teaching and learning of multivariate calculus Interactive routines use Maplet technology to assist you to work through the standard problems of multivariate calculus in a visually directed manner Visualisation routines are provide to aid in the understanding of concepts including Taylor approximation, change of variables, center of mass, gradient, Jacobian, surface area and more Student Packages Student package tutors are now easily accessible from the Tools menu Most interactive tutors now include an option to see the equivalent Maple command Student[Precalculus] now includes more functions for visual explorations of topics in greater depth, including a routine to explore lines

Usability Maple 9.5 adds the ability to dock your palettes to the edges of your workspace Improved palettes use meaningful placeholder names. Expressions can be dragged from the palette into the workspace Improved command completion facilities automatically display the full command when a unique completion is detected The Tools menu provides quick access to the Maple Assistants, such as the Unit Converter, Plot Builder and ODE Analyser, and to the Maple Tutors associated with the Student packages, including Linear Algebra and Multivariate Calculus The Options dialog has been redesigned to allow easier and more consistent access to the settings and control over more items Document Formatting You can emphasize information in your worksheets by using the Text Highlight feature Maple 9.5 allows you to include superscript and subscript characters in your worksheets You can now easily control the number of displayed terms of an expression and digits of a number. A threshold can be set at which elision is invoked as well as the number of leading and trailing terms or digits Two new types of hyperlinks are supported: a link to a definition contained in the math dictionary and a link to a Maplet Graphics The Interactive Plot Builder has been expanded to allow easier creation of a greater variety of plots The Plot Builder now supports plotting multiple expressions simultaneously, and allowing interactive adding of expressions to be plotted Animations can be created using the Plot Builder Plots created with slider controls for parameters permit a plot to be adjusted interactively Maple 9.5 provides slider control for viewing individual frames of an animated plot Oscillate control allows you to play animations backward and forward Point-probe cursor makes is easy to identify the coordinates of a particular point on a 2-D plot Scale and pan 2-D and 3-D plots and animations   Programming and Connectivity OpenMaple™ OpenMaple allows access to Maple using C and now Java and Visual Basic programs Maple Library Archive All components of a Maple library can now be saved in a single file Other types of files can be saved inside the archive for convenient sharing of related materials Debugging A program that is already running can be debugged by clicking on a Debug button inside the worksheet If a computation cannot be interrupted, you are now given the option of restarting the maths engine MapleNet™ Maplet applications created in Maple 9.5 can easily be deployed to MapleNet   New Packages and Functions Mathematica® Conversion Tools Automatically convert Mathematica notebooks to Maple worksheets Translate commands from Mathematica’s syntax to Maple syntax Maplet assistant makes translating commands and documents easy Context Menus The new context menu package provides new easy-to-use tools to control and customize Maple context-sensitive menus Replace the default context menu, add new entries to the existing context menu, or alter the criteria under which entries are displayed in a menu Cache This package contains function to manipulate a new cache data structure. A cache table allows both permanent and temporary storage inside the same data structure Used as a remember table, the important items can be stored permanently while temporary items can be replaced to avoid wasting memory Package Unloading The unwith command allows you to reverse the effects of a with for module-based packages Modules and Operators Modules can now be applied to objects Modules can control how they are printed Routines can be defined that will run when a module is loaded or unloaded The list of overloadable operators has been extended to include list construction, set construction, function application, and index application Overloaded operators and functions can be controlled by the argument type   Enhanced Packages and Functions Code Generation The new CodeGeneration[Save] command allows user-contributed language definitions to be saved in a Maple archive more easily Inert Representation The ToInert command for converting to an inert representation of a Maple object has been extended to allow for finer control over which objects to convert Partial Fraction Decomposition Partial fraction decomposition now has a convenient programmer interface Polynomial Tools Four more tools have been added for calculating Taylor shift distances, shiftless decompositions, greatest factorial factorisations and gcd-free bases String Tools Includes a function for seeding the random string generator Note: Not all features are available on all machine configurations.

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