ITC Research Computing Support Whats New in Maple 9

1
ITC Research Computing SupportWhats New in
Maple 9

• By Kathy Gerber
• Research Computing Support Center
• Phone [phone] F Fax [phone]
• E-Mail Res-Consult_at_Virginia.EDU
• http//www.itc.Virginia.edu/researchers

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New Maple Users

• Complete the Quick New Users Tour, a focused
  overview of the Maple system (about 10 minutes).
• Complete the New Users Tour, an in-depth,
  comprehensive overview of the Maple system.
• Refer to the How to Perform Basic Tasks, a quick
  summary of the most common Maple commands,
  syntax, and more. Notes for Maple 8
  http//www.itc.virginia.edu/research/talks/html/ma
  ple8.html

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Three InterfacesClassical Interface
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Command Line Interface
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New Interface

• Java-based
• Slow !!
• Both the Classic and Standard interfaces have
  access to the full mathematical engine of Maple 9
  and take advantage of the new functionality in
  Maple 9.
• If your system has less than the recommended
  amount of physical memory, Maple suggests that
  you use the Classic Worksheet version of Maple 9.
• According to Maple, the new Standard Worksheet
  interface provides more flexible formatting with
  fonts and colors, better menu organization,
  easier management of sections and subsections,
  free-form sketch regions, and many other
  improvements.
• Some find it too slow to be useful.

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Worksheet Format
Maple 9 worksheets are saved in a new XML-based
format. The new file extension for these
worksheets is .mw. Maple 9 can read worksheets
from previous releases of Maple. The Save as
Maple 8 Worksheet option exists for cases where
the worksheet also needs to be read by older
releases of Maple it creates a worksheet file in
the .mws format. Note that whenever an older
release of Maple reads a worksheet created in a
new release, newer features will not be available
and command results may change.
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Inserting Images
UNIX and Macintosh based users can now insert
images directly into worksheets. Previously, this
was available only to Windows users. A variety
of formats, such as .jpeg, .tif, and .pnm, are
supported. Images are incorporated by using the
Insert dialog. This dialog is accessed by
selecting Insert from the main menu and then
Image.
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OpenMaple Application Programming Interface (API)
to Maple
OpenMaple is a suite of functions that allows
you to access Maple algorithms and data
structures in your compiled C program.
OpenMaple provides the ability to start a Maple
session, evaluate commands, manipulate native
Maple data structures, and control output.
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define_external

• Method to connect to a custom external wrapper
  library
• Before any C or Fortran function can be used with
  define_external, it must first be compiled into a
  shared library. Java functions must be compiled
  into .class files.
• Built-in functions for converting a native C data
  structure to a Maple object and vice versa.

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Code Generation for MATLAB and Visual Basic

• The CodeGeneration package contains two new
  target languages, MATLAB and Visual Basic.
• The code translators for Java, C, and Fortran are
  improved.
• The new extensibility subpackage allows you to
  modify the built-in translators and create new
  translators for other languages.

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Assumption Changes

• In Maple 9, some assumptions have been removed.
  These are
• x0 and 0/x do not automatically simplify to 0
  if the value of x renders this simplification
  invalid. If x is an unassigned name, the
  simplification proceeds.
• 0x does not automatically simplify to 0 unless
  x is an unassigned name.
• x/x does not automatically simplify to 1. This
  is invalid if, for example, x is a function that
  produces random numbers.
• xx does not automatically simplify to x2.
  This is invalid if, for example, x is a function
  that produces random numbers.
• Constant operators do not simplify to numbers.
  For example, x - 1 does not simplify to 1.
• Expressions such as x - f(x) do not simplify
  to f. This is invalid if f can also take fewer or
  greater than one argument.
• Procedure bodies, in which the computations
  involve floating-point numbers, are not
  simplified. Simplification may involve
  transformations not valid when the procedure is
  invoked, for example, for the particular
  arguments passed to the procedure or for the
  environment in which the procedure is called. In
  particular, the value of Digits may be different.

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Interactive ODE Analyzer

• Launch with dsolveinteractive()

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Function Advisor

• FunctionAdvisor()
• Based on "The function wizard project A Computer
  Algebra Handbook of Special Functions,
  Cheb-Terrab, E.S.

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Initially known mathematical functions

• Mathematical functions that are known to Maple,
  in that they have simplification procedures
  defined and/or are known to one or more of diff,
  evalc, evalf, expand, series, simplify
• Search help for inifcn and ininames

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GNU GMP

• The GNU Multiple Precision (GMP) library is a
  portable library written in C for arbitrary
  precision arithmetic on integers, rational
  numbers, and floating-point numbers. Maple 9 uses
  GMP library for integer arithmetic when operands
  are greater or equal to 10kernelopts(gmpthreshold
  ).
• The default on Windows is 108.

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GNU Multiprecision Library

• Maple commands that directly benefit from the GMP
  library.
  
• (addition) - (subtraction)
  (multiplication) / (division)
  (exponentiation) iquo
  (quotient) irem (remainder)
  isqrt (square root) igcd
• ilcm (least common multiple) ! (factorial)
  isprime (primality test)
  
• The following Maple commands indirectly benefit
  from the GMP because they use the previous
  commands extensively.
• add mult mod nextprime
  prevprime ithprime
• trunc round frac floor
  ceil ifactor

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Speed Increase

• The following example runs in 160 seconds on
  Maple 8 but only in 6 seconds on Maple 9.
• add(1/k2, k1..100000)

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Linear Algebra
The Basic Linear Algebra Subprograms (BLAS)
libraries for Sun and Linux platforms now have
built-in architecture-specific optimizations, as
well as expected updates resulting from an
upgrade to newer versions of ATLAS BLAS. Run time
for multiplication of two 1000x1000 random
float8 matrices Platform/Arch
Maple 8 Maple 9 Linux/PII
8.45 7.46 Linux/PIII 4.38
4.35 Linux/P4 1.96
0.99 Linux/Athlon 3.62 2.55
Linux/Athlon XP 1.77 0.98
Sun/Sparc 45.74 42.28
Sun/Ultra 5.11 3.14
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New Packages in Maple 9
Student Packages Precalculus and Linear
Algebra ScientificErrorAnalysis DiscreteTransforms
ArrayTools FileTools CodeTools IntegerRelations g
fun MathematicalFunctions QDifferenceEquations LRE
toolsHypergeometricTerm
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Student
Two new packages have been added to the Student
package Precalculus and LinearAlgebra
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Discrete Transforms

• The new Discrete Transforms package computes
  the fast Fourier transform (and inverse
  transform) of single or multi-dimensional data.
• The FourierTransform and InverseFourierTransform
  functions work in hardware precision, so are
  limited to 15 Digits of accuracy, but run in
  compiled code, so are very fast.

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Array Tools

• The new ArrayTools package provides low-level
  manipulation of rectangular Arrays, Vectors, and
  Matrices, and rectangular Array, Vector, and
  Matrix data aliasing. This package is provided
  primarily for programming purposes.
• Examples of the capabilities that this package
  provides are
• Efficient data filling (ArrayToolsFill).
• Raw data copying of portions of one Array to
  another (ArrayToolsCopy).
• In-place data reordering (ArrayToolsDataTranspos
  e)
• Aliasing the data (or part of the data) of an
  Array to another Array with, for example,
  different ordering, indices, or dimensions
  (ArrayToolsAlias)

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File Tools
The FileTools package is a collection of file
manipulation utilities. It contains submodules
for both text and binary.
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Code Tools

• The CodeTools package contains subpackages and
  functions to help improve the efficiency and
  quality of Maple code.

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Integer Relations

• identify - find a closed form for a decimal
  approximation of a number. Attempts to convert a
  floating point number to a symbolic value.
• freeze, thaw - replace an expression by a name
  (not new)

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Generating Functions

• The new gfun package produces and manipulates
  generating functions.
• The package provides tools to compute with
  generating functions defined by equations. For
  example, given two generating functions defined
  by linear differential equations with polynomial
  coefficients, there is a procedure that computes
  the differential equation satisfied by their
  product.

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Mathematical Functions

• In addition to using mathematical functions
  computationally, you also need general
  information about their properties, for example,
  definitions, identities, integral forms, and
  series expansions. You can refer to a handbook
  like Abramowitz Stegun for general information,
  but it does not indicate, for example, the
  definition used in the Maple system.
• You can use the MathematicalFunctions package and
  related FunctionAdvisor command as simple
  interfaces to the information appropriate to the
  Maple implementation.

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Upcoming Talks
On Wednesday, November 5, the topic will be
"Getting Started with HPC Tools Tricks" This
talk is an introduction to using
the High-Performance Computing (HPC) platforms at
UVa. Then on Wednesday, November 12 at 330,
the colloquium will be "Introduction to
Mathematica 5.0" For details about this talk,
please see this month's newsletter at
http//www.itc.virginia.edu/research/news/newslett
erOct03.htmlseminars As always, the notes
from the talks will be available shortly
after each talk on the Web at
http//www.itc.virginia.edu/research/talks