Maple 11 New Features

Mathematical Computations


Differential Equations
Exact Solutions
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Ability to compute elliptic solutions to various classes of nonlinear first and second order ODEs

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Entirely new set of algorithms for finding exact solutions to PDEs based on symmetry calculations

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The PDETools package contains 20 new commands based on the symmetry approach, including some original algorithms

Plotting of Differential Equations
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Interactive Differential Equation plotting assistant

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Assistant contains a database of parametrized physical systems that can be used as a starting point for exploration

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Enhancements to DEPlot command:

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Animation capability with respect to both solution curves and field arrows

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New arrow types, including two which follow along curved field lines

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Ability to color the plot based on field magnitude

For more information, see updates/Maple11/de.


New Packages


Graph Theory
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Supports directed graphs, undirected graphs, and graphs with edge weights, and includes over 150 functions and over 35 predefined special graphs

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Visualization of graphs in two and three dimensions

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Includes tools for the import and export of graph data using other standard formats

Physics
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Includes 3D nonprojected vectors, noncommutative variables, spacetime tensors including the indexed differentiation operator, Einstein's summation convention for repeated indices, and standard mathematical physics objects

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Supports the use of standard notation and allows you to define a framework of notational conventions and spacetime properties

Differential Geometry
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Supports computation in the areas of calculus on manifolds , tensor analysis, calculus on jet spaces, Lie algebras and Lie groups, and transformation groups

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Includes a extensive reference material on Differential Geometry and its applications

For more information on new packages, see updates/Maple11/newpackages.


Enhanced Packages


Groebner
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Uses the renowned FGb library, the world’s fastest Groebner bases engine

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New computation and manipulation tools, including a command that suggests the best variable order to use

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Additional options and calling sequences

Linear Algebra
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New subpackage for computing with generic implementations of algorithms in linear algebra over fields, integral domains and rings, and Euclidean domains

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Additional commands for augmented matrices and square matrices

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The CompanionMatrix command has been extended to accept a matrix polynomial as input, expressed in terms of any of a large number of orthogonal bases

Linear Recurrence Equations (LREtools)
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New command for computing hypergeometric solutions of a linear difference equation with hypergeometric coefficients

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Extended commands to determine analyticity of the solution of a linear difference equation in the complex plane, and to handle desingularization of a linear difference operator with respect to both the leading and the trailing coefficients simultaneously

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Formulas for the values at a point now work even when the evaluation point is an algebraic number

Number Theory
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Implements the Index Calculus method for computing discrete logarithms

Polynomial Ideals
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Tools for decomposing ideals into ideals of distinct dimension and for computing the number of solutions over the algebraic closure of the coefficient field

Regular Chains
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Implements a new probabilistic modular algorithm for triangularization that, under certain conditions, is asymptotically faster than the usual approach

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New command for changing the variable ordering of a regular chain while maintaining the same saturated ideal

Statistics
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The frequency plot command has a new option to specify how to handle nonnumeric data

SumTools
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New tools for hypergeometric and indefinite sums

VectorCalculus
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New structures for rooted and position vectors

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Tools for plotting space curves, creating vector spaces at a point, and determining the properties of the new vector structures

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New option for evaluating the directional derivative

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Improved implementation of nonCartesian coordinates

For more information, see updates/Maple11/enhancedpackages.
General
Symbolic
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New command for solving linear integral equations

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The integration capabilities have been extended to perform indefinite integration in the presence of special functions in general, and to handle certain types of integrands containing doubly periodic functions

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The diff command can now compute derivatives of the four Weierstrass functions when the discriminant is equal to zero

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The solve command can now return complete solutions to linear and nonlinear inequalities involving parameters, in the form of piecewise expressions

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The sum command has been enhanced to handle unknown functions. The convert/sum command can now transform expressions into formal power series around a point

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Improved mod command can now handle inputs with more than one RootOf object

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The simplex[convexhull] command has new output options, including plot

For more information, see updates/Maple11/symbolics.
Numeric
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New option for Maple procedures causes hardware floatingpoint arithmetic to be used wherever possible during the execution of the procedure, resulting in a dramatic increase in performance for numerically intensive procedures.

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When writing procedures intended for execution in the evalhf environment, it is now possible to include calls to Maple functions that are not directly supported within evalhf

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Improvements to capabilities and efficiency of numeric integration and summation

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New RootFinding commands can be used to iterate through the zeros of a function in the positive real direction and to isolate real roots of real univariate polynomials and polynomial systems

For more information, see updates/Maple11/numerics.
Efficiency
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Now includes the best certified polynomial real root finder, incorporating the RS library, which is guaranteed to find real roots of polynomial systems. Implemented as part of the RootFinding package and also used in fsolve, which is now more efficient in finding real solutions of univariate polynomials

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The default stiff numerical ODE solver and the default stiff/nonstiff numerical DAE solvers have been made more efficient with respect to large problems

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The Multiply command for modp1 polynomials now uses Karatsuba's algorithm for polynomials of sufficiently high degree

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The Matrix and Vector construction and concatenation shortcut notations, <,> and <>, have been made much more efficient

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Changes to the Maple argument processing mechanism and the allocation of storage for procedure arguments have improved performance and reduced memory requirements for virtually all Maple procedure calls

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The evala command uses more efficient data representations and algorithms for computations involving polynomials with algebraic number coefficients. As a result, gcd computations for such polynomials have become significantly faster in many cases

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Native 64bit Windows® version

For more information, see updates/Maple11/efficiency.


User Interface


Usability
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Selfdocumenting context menus automatically create a record of your actions

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Customizable Favorites palette for frequently used items

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The Backsolver assistant allows you to instantly solve for any variable in your formula, given the values of the other parameters

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The Special Functions assistant gives you easy access to over 20 different properties of over 200 special functions

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The Scientific Constant assistant provides access to a database of scientific constants with over 20,000 values of physical constants and properties of chemical elements

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Over 35 new pointandclick task templates for Calculus and Algebra

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The Error Message Guide explains over 30 of the most common error messages, including details on how to correct or avoid the problem

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The handwriting recognition feature lets you try out a preview version of developing technology for understanding handwritten mathematics

For more information, see updates/Maple11/gui.
Document Creation
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Slide show mode turns a Maple document into a slideshow for presentations

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Annotations for providing supplementary information through comments added to text and math

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Enhanced numeric formatting supports many formats including scientific notation, currencies, engineering notation, and custom

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Interdocument equation references allow you to access mathematical expressions from another document

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Drawing canvas includes shapes, lines, arrows, text, outline and fill color control, alignment tools, grid controls, and a favorites palette

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Annotating plots and images: All drawing tools can be used directly on 2D plots and images

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Document block enhancements include the display of warnings and all output

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Markers are available for additional features such as annotations and numeric formatting

For more information, see updates/Maple11/gui.
Visualization
2D plots render faster and use less memory
2D Plot Annotations
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Typeset text and mathematical expressions can be displayed in plots, including in titles, legends, labels, tickmark labels, and axes labels

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Extensive plot annotation tools include sketching, typing, and drawing of lines, arrows and shapes on plots, using the drawing canvas tools

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Increased user control over tickmark spacing and the generation of subticks.

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New line styles and symbols for plotting curves and points

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International (nonEnglish) characters permitted where text is normally allowed

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A wider range of fonts can be used within plots

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More legend placement options, long strings can be used, and the formatting of multiple legends has been enhanced

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Extended color names and control over the default colors of curves

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Enhanced context menus for plotting options

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The numeric range for a 2D plot has greatly increased

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Improved export to Windows Meta Files (WMF format)

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New commands for plotting the 3D intersection of surfaces, and animation with trace.

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Improved commands for plotting 2D implicit curves and density plots

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Highlighting has improved, both for rollover and selection.

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Arrays of plots are now displayed as a table allowing greater control over the individual plots.

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Improvements to Pan and Scale. Text in plots now takes account of the Zoom factor

For more information, see updates/Maple11/graphics.


Connectivity


Excel Integration
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Easy import and export of Microsoft® Excel® data files

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Integrated with the Data Import Assistant and the Matrix Browser

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Commands for programmatic import and export

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Complete and partial file import

For details, see ExcelTools[Export] and Browse Matrix.
External Calling
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New command has been added to the C external API allowing external compiled code to abort long running computations when a user clicks the Stop button or presses CtrlC.

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Support for external calling to Fortran libraries has been extended to include the Intel® Fortran compiler on Windowsbased machines

Matlab Link
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The Matlab package supports a wider range of data conversions, including strings and structs

Image Tools
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Runs faster and uses less memory

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More support for image previewing

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Over 20 new commands, including conversions between different color representations, rotation, flipping, stacking, and padding of images

For more information, see updates/Maple11/efficiency, updates/Maple11/programming, updates/Maple11/language.


Programming


Threads Package
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Provides userlevel routines for multithreaded programming while on multicore computers

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Executes functions in a new thread

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Supports condition variables for synchronization of execution

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Uses mutexes to control access to data structures

Parameter Declarations and Argument Processing
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Ability to specify alternate spellings of keyword parameters

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Explicitly declared dependent types

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A single parameter can be declared to match a sequence of zero or more arguments of a specified type

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Optional parameters can raise an exception if the next argument does not match the declared type

Embedded Components
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Greatly simplified mechanism for extracting and setting values

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Option to GetProperty command extracts the contents of a Math Expression component and returns an evaluated Maple expression

ListTools
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Allows you to split a list into sublists of a given length

StringTools
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Contains more than 15 new commands, including fence matching and functions used in cryptanalysis

For more information, see updates/Maple11/programming

