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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.

Ci

LegendreP

LegendreQ

LerchPhi

Whittaker

wronskian

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

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