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Improved Symbolics in Maple V Release 5

Table of Contents:

1. General

2. Evaluation (eval, evala)

Evaluation at a point, using the second argument of eval, has been added. Note that this is defined quite generally, and can deal with expressions where subs was incorrect.

Functions with special support for evaluation at a point:

diff, Diff,

int, Int,

limit, Limit,

product, Product,

sum, Sum,

the inttrans functions and piecewise.

In addition, a new command, intat, for "evaluating integrals at a point" has been added.

The internals of evala have been substantially improved. It is now faster and more powerful.

The evala command can now handle more expressions by operating recursively.

3. Simplification (simplify)

The simplify command has been extended to interpret the following functions.







4. Conversions (convert)

  • convert(..., Sum): Convert MeijerG functions to sums.
  • convert(..., dawson): Convert to a Dawson integral. Dawson's integral is defined as
  • convert(..., erfi): Convert to an expression in terms of the imaginary error function erfi.
  • convert(..., sincos): Specify only those terms that depend upon a specified variable which are to be converted, using an optional third parameter.
  • convert(...., StandardFunctions): Convert functions represented in terms of hypergeometric functions and Meijer G functions to a form in terms of standard special and elementary functions.
  • convert(..., MeijerG): Convert special functions to a form using MeijerG functions.
  • convert(..., Riccati) and convert(..., linearODE): Convert a linear second order homogeneous ODE into a first order Riccati type ODE and vice-versa; see convert,ODEs.

5. New Functions

Special Functions

Many new special functions have been added in Release 5.

Other Functions

6. Changes to Functions

  • The C procedure, which compiles Maple expressions to C code, is now in the codegen package.
  • The C procedure can still be loaded using readlib.
  • C handles ceil, floor, round, trunc
  • The fortran procedure, which compiles Maple into fortran code, is now part of the codegen package.
  • However, fortran can be accessed without using readlib or with in Release 5.

7. The Integrator

  • int of DESol
  • int of surd
  • lots of improvements on inttrans
  • the definite integrator has been substantially improved for the cases where the integrand can be converted to a MeijerG function and the usual theorems for integration of such functions apply
  • elliptic integration - Improved with symbolic parameters
  • An integral that previous versions of Maple could not evaluate can now be solved in R5 in two different ways.

8. The Differential Equation solvers

  • The differential equation solver dsolve has been substantially rewritten. It is now much more powerful, and uses several new techniques for finding closed form solutions.
  • The most noticable improvements are in the areas of non-linear ODEs and ODEs with special function solutions.
  • The partial differential equation solve pdesolve is now obsolete, and has been replaced by the much more powerful pdsolve.
  • There is now a wealth of tools available to manipulate, explore and solve differential equations and related objects in the packages PDEtools and DEtools.

9. Pattern Matcher

  • applyrule - applying rules
  • compiletable - table lookup
  • patmatch - pattern matching
  • tablelook - table lookup
  • define - define characteristics of an operator name
  • definemore - define characteristics of an operator name