*
Enhanced features in Maple 10
** New features in Maple 10
Mathematics
Maple includes over 3,500 computational
functions to deliver the richest set of computation tools for any
area in mathematics, science, or engineering.
MAJOR TOPICS INCLUDE:
Algebra
• Exact symbolic arithmetic with real and complex numbers
• Factor, expand, combine*, and simplify* algebraic expressions
• Sequences and series
Calculus*
• Compute derivatives, integrals, and limits
• Continuity testing
• Asymptotic expansion, and directional and multidirectional
limits
Differential
Equations
• Exact and numerical solutions of ODEs and ODE systems*
• Exact and numerical solutions of PDEs and PDE systems*
• Exact and numerical solutions of Boundary Value Problems
for PDEs
• Numerical solutions for Differential Algebraic ODE initial
value problems (DAEs)
• Differential elimination for ODE and PDE systems
• Structural analysis and order-reduction of ODEs and PDEs
• Interactive Maplet™ Assistant for numeric and symbolic
solutions of ODEs and ODE systems
Linear
Algebra*
• Over 100 commands for constructing, solving, programming,
and querying topics in linear algebra
• Symbolic and numeric computations
• Eigenvalues and eigenvectors, both classical and generalized
• Sophisticated algorithms for modular linear algebra
• Many matrix factorizations and system solvers
• State-of-the-art numerical methods for dense and sparse
systems with a high degree of user control
Solvers
• Solve equations and systems of algebraic equations symbolically
and numerically for closed form and approximate solutions*
• Inequalities and systems of inequalities
• ODEs, PDEs and DAEs
• Numerous specialized solvers including routines for equations
over the integers, equations over the integers mod m, recurrence
equations, differential equations, series solutions and q-difference
equations
Statistics**
• Wide range of common statistical tasks, such as quantitative
and graphical data analysis, simulation and curve fitting
• Over 35 continuous and discrete probability distributions
and tools for creating custom distributions
• Interactive data analysis assistant
• Statistical plots including box plots, bar charts, histograms,
probability plots and scatter plots
• Tools for fitting linear and nonlinear models to data points
and performing regression analysis
• Statistical Process Control (SPC) package with 11 different
statistical control charts for process control variables and attributes
Vector
Calculus*
• Directional derivatives, gradients, Hessian matrices and
Laplacians of a function
• Curl and divergence of a vector field
• Jacobian and Wronskian matrices of a list of functions
• Cross products and dot products of vectors and differential
operators
OTHER TOPICS INCLUDE:
Abstract
Algebra
• Groups, polynomials ideals, greatest common divisors, finite
rings and fields
Algebraic
Curves
• Holomorphic differentials and genus of an algebraic curve
•
Normal forms for elliptic and hyperelliptic curves
Combinatorial
Functions
• Permutations and combinations
• Construction of random combinations, partitions and permutations
• Stirling numbers of the first and second kind, polynomials
and Fibonacci numbers
Combinatorial
Structures
• Computation and solution of a system of generating function
equations associated with an attribute grammar
• Generation of random combinatorial objects and counting
the objects of a given size
Complex
Arithmetic and Functions
• Complex numbers, fractions, constants and variables
Curve
Fitting
• B-spline basis functions, polynomial interpolation, least-squares
approximation, rational interpolation and splines
Differential
Algebra
• Manipulation and reduction of differential equations
• Development of the solutions into formal power series
Differential
Forms
• Create, manipulate and compute with differential forms
Discrete
Transforms
• Fast Fourier transform and inverse transform of single or
multidimensional data
Euclidean
Geometry
• Close to 300 commands for constructing, computing, plotting
and translating 2-D and 3-D objects
Financial
Mathematics
• Annuities and growing annuities, cash flows, perpetuities
and growing perpetuities, and level coupons
• Amortization, Black-Scholes option pricing, effective rate,
future value, present value and yield to maturity
Gaussian
Integers
• Chinese remainder, GCD, and LCM of Gaussian integers
• Gaussian integer factorization
• Extended Euclidean algorithm for Gaussian integers
Generating
Functions*
• Tools for determining and manipulating generating functions,
including ordinary and exponential generating functions
• Tools for determining a probable generating function from
initial terms
Graph
Theory
• Over 75 commands to create and study networks
Groebner Bases* and
Polynomial Ideals**
• Groebner bases over commutative and non-commutative domains
• Ideal membership and containment
• Radical, prime and primary decompositions
• Hilbert series, polynomials and dimensions
Group
Theory
• 34 commands, including calculating the elements of a permutation
group, order computations and finding a permutation of a group
Integral
Transforms
• Laplace, inverse Laplace, Fourier sine, Hankel, Hilbert,
inverse Mellin and Z transforms
Lie
Symmetries
• Lie group symmetry methods for differential forms
Linear
Functional Systems of Equations*
• Transformations of a matrix recurrence system into an equivalent
system with nonsingular leading and trailing matrices
• Rational and formal power series solutions of a linear functional
system of equations with polynomial coefficients
Linear Operators
• Numerous commands to manipulate d’Alembertian terms
• Conversions among Ore polynomial structures, linear ODEs,
linear recurrence equations and factored OrePoly structures
Linear
Programming
• Solve linear programs using symbolic and numeric methods,
including simplex
Linear Recurrence
Equations
• Polynomial, rational and hypergeometric solutions of linear
recurrence equations
• Solutions of divide and conquer recurrence equations
Logic
• Commands for manipulating Boolean expressions
Numerical
Approximations
• Infinite precision numerical computations
• Chebyshev-Pade and minimax rational approximation
• Conversion of rational functions to continued-fraction form
and Polynomials to Horner form
Number
Theory
• Primality testing
• Computation of the nth Fermat number and the nth Mersenne
prime
• Computation of the nth convergent, denominator, and numerator
of simple and regular continued fractions
Optimization*
• Numeric methods for the solution of optimization problems
• Interactive Optimization assistant for defining, solving
and visualizing** problems
• Solvers for linear, quadratic and nonlinear programs, including
constrained and unconstrained problems
• Solvers for linear and nonlinear least-squares problems
• Solvers for integer linear programs**
Orthogonal
Polynomials
• Commands to generate the nth Gegenbauer, Hermite, Laguerre,
Legendre and Jacobi polynomials
P-adic
Numbers
• Commands for p-adic evaluation, expansion and functions
• Computation of the order and the leading coefficient of
a p-adic expansion of a rational function
Polynomials
• Factor, expand, manipulate, and compute properties of polynomials
Q-Difference
Equations*
• Solve linear q-difference equations with polynomial coefficients
Rational
Normal Forms
• Computation of polynomial and rational normal forms, canonical
forms of rational functions, and minimal representations of hypergeometric
terms
Real
Domain Computations
• Restrict calculations to the domain of real numbers
Series
Expansions
• Compute Taylor, Puiseux and asymptotic series expansions
Scientific
Constants
• Support for over 70 scientific constants including the Newtonian
constant of gravitation, magnetic flux quantum, and conductance
quantum
• Properties of all elements and isotopes of the Periodic
Table
• Tools for building custom scientific constants
Scientific
Error Analysis
• Representation and construction of numerical quantities
that have a central value and associated error
Special
Functions*
• Over 100 special functions
• Includes Airy Ai and Bi wave functions, Bessel, Chebyshev,
Ei, Si, Ci, Li, error function, Gamma, Zeta, Heun**, Legendre, Jacobi
functions
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Statistical
Process Control**
• Supports 11 different control charts for process control
variables and attributes, including EWMA, S, MA and X-bar charts
• Visualize both numeric and non-numeric quality characteristics
Symbolic-Numeric
Algorithms for Polynomials
• Algebraic manipulation of numeric polynomials
Tensors
• Routines that deal with tensors, their operations and their
use in General Relativity, both in the natural basis and in a moving
frame
Tolerances**
• Perform best- and worst-case computations with quantities
involving tolerances, using standard notation
• Tolerances understood by arithmetic operators and by many
built-in functions, including square roots, exponentials, trigonometric
and special functions
Units and
Dimensions
• Support for over 500 units and dimensions defined using
exact conversions
• Systems of units include Atomic, CGS, Electromagnetic, Electrostatic,
FPS, MKS, MTS and SI
• Over 50 base quantities include acceleration, area, dynamic
viscosity, electric resistance, energy, heat transfer, light, magnetic
flux and mass
• Ability to add and remove systems and dimensions
Variational
Calculus
• Euler-Lagrange equations and first integrals
• Solve Jacobi differential equation for conjugate points
• Weierstrass excess function
Mathematics Education
Maple includes educational packages and resources
to assist students by furthering their understanding of concepts
presented in mathematics courses.
Precalculus*
• Study lines, polynomials, rational functions, compositions
of functions and more, using interactive tutors and visualization
routines
Calculus
• Single step through differentiation, integration and limit
problems
• Visualization routines display a function and its derivative,
Taylor series approximation, Newton’s method, approximating
integrals, antiderivatives, surfaces of revolution and more
• Explore these Calculus 1 concepts using interactive tutors*
Linear Algebra
• Single step through Gaussian elimination; Gauss- Jordan
elimination; and the computation of the inverse, eigenvalues and
eigenvectors of a matrix
using interactive tutors*
• Visualization routines display the cross product of two
vectors, a system of 2-D or 3-D linear equations, the projection
of a vector onto a subspace and more
• Over 65 routines for computing with matrices and vectors
Multivariate
Calculus
• Interactive tutors* allow you to work through the standard
problems of multivariate calculus in a visually directed manner
• Visualization routines to aid in the understanding of concepts
including Taylor approximation, change of variables, centre of mass,
gradient, Jacobian, surface area
Vector Calculus**
• Computations, visualizations and interactive problem solving
involving the calculus of functions from Rn to Rm
• Interactive tutors for exploring space curves and vector
fields through plots and animations
• Supports 5 predefined coordinate systems
Dictionary*
• Over 5,000 definitions of mathematical and engineering terms
and concepts incorporated into the Help system
• Includes over 300 figures to clearly explain the concepts
Graphing Calculator**
• Traditional graphing calculator interface
• Standalone or over a MapleNet™
installation
Maple T.A.
Assessment Tools**
• Question authoring environment provides templates for creating
common question types, such as fill-in- the-blank, Maple-graded
and multiple-choice questions
• Questions can include algorithmically generated content
• Questions can contain plots, hints, feedback and algorithmically-generated
variables.
• Assignments are used inside Maple, printed, or exported
to Maple T.A.
Programming
Flexible programming language, tools and base routines.
• Advanced programming language
• Procedural and functional programming
• Operator overloading
• Exception handling
• Debugging, profiling and library management tools
• Analysis of the code complexity of a Maple procedure and
module
• Ability to create new worksheets, programs, packages, modules
and help pages
• Source code of most routines available for viewing
• Assumptions on variables
• Create and manipulate many kinds of objects, including sets,
strings, lists, arrays* and libraries
• Tools for manipulating mathematical objects, including polynomials**,
integrals** and sums*
• Extend existing types
• Generate and manipulate Maple worksheets through its XML
representation
• Compiler package for dramatic speed-up of numerical computations**
Custom Interfaces
Maple lets you create custom user interfaces to access built-in
and user-written routines.
Maplet Application
• Create custom Java™-based graphical user interfaces
to access the Maple kernel and libraries, or user-written Maple
functions
• Graphical elements include text areas, buttons, equation
editors, slider bars, tool tips, plotting windows and numerous built-in
dialogues
• Can be created programmatically or through the point-and-click
Maplet Builder**
• Perform calculations and display graphs without seeing the
Maple code
Context-Sensitive
Menu
• Design a context menu or edit an existing menu
Visualization
Maple includes a comprehensive set of visualization tools to make
problem exploration easier.
• 2-D and 3-D graphs
• 2-D and 3-D animations
• 2-D and 3-D implicit plots
• Conformal mapping
• 2-D and 3-D contour plots
• Vector fields
• 2-D and 3-D complex plots
• ODE and PDE plots
• Light modelling, legends, axis control*, titles, glossiness**,
gridlines** and transparency
• Scale and pan 2-D and 3-D plots and animations
• Real-time rotation of 3-D plots
• Interactive control of parameters through slider controls
• Wide variety of coordinate systems
• Layering of graphics and animations of different types
• Standard geometric objects, regular solids and polyhedra,
including ellipses, hyperbolae, polygons, cones, spheres, torii,
dodecahedra, icosahedra and tetrahedra
• Over 40 visualization routines display concepts presented
in calculus, precalculus, multivariate calculus and linear algebra
courses
• Plot builder assistant for creating and modifying plots
and animations
User Interface
Maple includes many features to automate tasks and interact with
Maple without knowledge of Maple commands and syntax.
• Sophisticated 2-D maths editing**
• Context menus*
• Over 20 palettes** for expressions, symbols, matrices, operators
and more
• Comprehensive word-processing** for creating professional
reports
• Spell-checker containing standard maths terms
• Command completion*
• Automatic equation labelling**
• Tables**, sketch regions, symbolic spreadsheets, embedded
GUI components**
• Over 40 interactive tutors* display concepts presented in
precalculus, calculus, multivariate calculus, vector calculus**
and linear algebra courses
• Over 200 task templates for fill-in-the-blank problem solving**
• Task assistants for many tasks including analyzing ODEs
and ODE systems, creating plots and matrices and converting units
• Document blocks** to write content with live calculations
while hiding computation details
• Help Navigator* for searching help pages, tasks, tutors,
definitions and manuals
Connectivity
Maple adheres to international standards for data communication
by enhancing tool interoperability and Web connectivity.
• Access Maple algorithms and data structures in compiled
C, Java and Visual Basic® programs using OpenMaple™
• MathML 2.0 presentation and content support
• Import and export of XML documents
• TCP/IP socket connectivity
• External calling to Java, C, and Fortran
• Code Generation
° Generate Visual Basic, MATLAB®,
Java, C and Fortran code
° Override or add to code translations
specified in the existing definition or specify an entirely new
language definition
• Link to MATLAB
° From within Maple, use MATLAB
to compute Cholesky factorization, determinants, dimensions, eigenvalues,
LU decompositions
° Call out to MATLAB to compute
and retrieve the results of MATLAB expressions.
• Link to Microsoft® Excel 2000, Excel XP, and Excel 2003*
on Windows
° Access the Maple kernel from
within Excel
° Copy and paste between Maple
and Excel
° Function Wizard steps through
the creation of a Maple function
• Mathematica® Notebook conversion and command translation
tools
• Export worksheets to HTML, XML, MathML, LaTeX and RTF
• Export plots to BMP, DXF, EPS, GIF, HPGL, JPEG, PCX, POV,
TEK and WMF
• Import, manipulate and export WAV, JPEG and TIFF data files**
• Import data* from ASCII, CSV, Matrix Market, MATLAB and
more
• Direct links to the Maple Application Centre™,
Maple Student Centre™, Maplesoft™ corporate Web site,
and more
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