Maple 11 New Features
Links to All Updates Pages
Ability to compute elliptic solutions to various classes of nonlinear first and second order ODEs
Entirely new set of algorithms for finding exact solutions to PDEs based on symmetry calculations
The PDETools package contains 20 new commands based on the symmetry approach, including some original algorithms
Plotting of Differential Equations
Interactive Differential Equation plotting assistant
Assistant contains a database of parametrized physical systems that can be used as a starting point for exploration
Enhancements to DEPlot command:
Animation capability with respect to both solution curves and field arrows
New arrow types, including two which follow along curved field lines
Ability to color the plot based on field magnitude
For more information, see updates/Maple11/de.
Supports directed graphs, undirected graphs, and graphs with edge weights, and includes over 150 functions and over 35 pre-defined special graphs
Visualization of graphs in two and three dimensions
Includes tools for the import and export of graph data using other standard formats
Includes 3D non-projected vectors, noncommutative variables, spacetime tensors including the indexed differentiation operator, Einstein's summation convention for repeated indices, and standard mathematical physics objects
Supports the use of standard notation and allows you to define a framework of notational conventions and spacetime properties
Supports computation in the areas of calculus on manifolds , tensor analysis, calculus on jet spaces, Lie algebras and Lie groups, and transformation groups
Includes a extensive reference material on Differential Geometry and its applications
For more information on new packages, see updates/Maple11/newpackages.
Uses the renowned FGb library, the world’s fastest Groebner bases engine
New computation and manipulation tools, including a command that suggests the best variable order to use
Additional options and calling sequences
New subpackage for computing with generic implementations of algorithms in linear algebra over fields, integral domains and rings, and Euclidean domains
Additional commands for augmented matrices and square matrices
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)
New command for computing hypergeometric solutions of a linear difference equation with hypergeometric coefficients
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
Formulas for the values at a point now work even when the evaluation point is an algebraic number
Implements the Index Calculus method for computing discrete logarithms
Tools for decomposing ideals into ideals of distinct dimension and for computing the number of solutions over the algebraic closure of the coefficient field
Implements a new probabilistic modular algorithm for triangularization that, under certain conditions, is asymptotically faster than the usual approach
New command for changing the variable ordering of a regular chain while maintaining the same saturated ideal
The frequency plot command has a new option to specify how to handle non-numeric data
New tools for hypergeometric and indefinite sums
New structures for rooted and position vectors
Tools for plotting space curves, creating vector spaces at a point, and determining the properties of the new vector structures
New option for evaluating the directional derivative
Improved implementation of non-Cartesian coordinates
For more information, see updates/Maple11/enhancedpackages.
New command for solving linear integral equations
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
The diff command can now compute derivatives of the four Weierstrass functions when the discriminant is equal to zero
The solve command can now return complete solutions to linear and non-linear inequalities involving parameters, in the form of piecewise expressions
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
Improved mod command can now handle inputs with more than one RootOf object
The simplex[convexhull] command has new output options, including plot
For more information, see updates/Maple11/symbolics.
New option for Maple procedures causes hardware floating-point arithmetic to be used wherever possible during the execution of the procedure, resulting in a dramatic increase in performance for numerically intensive procedures.
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
Improvements to capabilities and efficiency of numeric integration and summation
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.
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
The default stiff numerical ODE solver and the default stiff/nonstiff numerical DAE solvers have been made more efficient with respect to large problems
The Multiply command for modp1 polynomials now uses Karatsuba's algorithm for polynomials of sufficiently high degree
The Matrix and Vector construction and concatenation shortcut notations, <,> and <|>, have been made much more efficient
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
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
Native 64-bit Windows® version
For more information, see updates/Maple11/efficiency.
Self-documenting context menus automatically create a record of your actions
Customizable Favorites palette for frequently used items
The Backsolver assistant allows you to instantly solve for any variable in your formula, given the values of the other parameters
The Special Functions assistant gives you easy access to over 20 different properties of over 200 special functions
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
Over 35 new point-and-click task templates for Calculus and Algebra
The Error Message Guide explains over 30 of the most common error messages, including details on how to correct or avoid the problem
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.
Slide show mode turns a Maple document into a slide-show for presentations
Annotations for providing supplementary information through comments added to text and math
Enhanced numeric formatting supports many formats including scientific notation, currencies, engineering notation, and custom
Inter-document equation references allow you to access mathematical expressions from another document
Drawing canvas includes shapes, lines, arrows, text, outline and fill color control, alignment tools, grid controls, and a favorites palette
Annotating plots and images: All drawing tools can be used directly on 2-D plots and images
Document block enhancements include the display of warnings and all output
Markers are available for additional features such as annotations and numeric formatting
2-D plots render faster and use less memory
2-D Plot Annotations
Typeset text and mathematical expressions can be displayed in plots, including in titles, legends, labels, tickmark labels, and axes labels
Extensive plot annotation tools include sketching, typing, and drawing of lines, arrows and shapes on plots, using the drawing canvas tools
Increased user control over tickmark spacing and the generation of subticks.
New line styles and symbols for plotting curves and points
International (non-English) characters permitted where text is normally allowed
A wider range of fonts can be used within plots
More legend placement options, long strings can be used, and the formatting of multiple legends has been enhanced
Extended color names and control over the default colors of curves
Enhanced context menus for plotting options
The numeric range for a 2-D plot has greatly increased
Improved export to Windows Meta Files (WMF format)
New commands for plotting the 3-D intersection of surfaces, and animation with trace.
Improved commands for plotting 2-D implicit curves and density plots
Highlighting has improved, both for rollover and selection.
Arrays of plots are now displayed as a table allowing greater control over the individual plots.
Improvements to Pan and Scale. Text in plots now takes account of the Zoom factor
For more information, see updates/Maple11/graphics.
Easy import and export of Microsoft® Excel® data files
Integrated with the Data Import Assistant and the Matrix Browser
Commands for programmatic import and export
Complete and partial file import
For details, see ExcelTools[Export] and Browse Matrix.
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 Ctrl-C.
Support for external calling to Fortran libraries has been extended to include the Intel® Fortran compiler on Windows-based machines
The Matlab package supports a wider range of data conversions, including strings and structs
Runs faster and uses less memory
More support for image previewing
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.
Provides user-level routines for multi-threaded programming while on multi-core computers
Executes functions in a new thread
Supports condition variables for synchronization of execution
Uses mutexes to control access to data structures
Parameter Declarations and Argument Processing
Ability to specify alternate spellings of keyword parameters
Explicitly declared dependent types
A single parameter can be declared to match a sequence of zero or more arguments of a specified type
Optional parameters can raise an exception if the next argument does not match the declared type
Greatly simplified mechanism for extracting and setting values
Option to GetProperty command extracts the contents of a Math Expression component and returns an evaluated Maple expression
Allows you to split a list into sub-lists of a given length
Contains more than 15 new commands, including fence matching and functions used in cryptanalysis
For more information, see updates/Maple11/programming
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