User manual THE MATHWORKS SYMBOLIC MATH TOOLBOX RELEASE NOTES

[. . . ] Symbolic Math ToolboxTM Release Notes How to Contact MathWorks Web Newsgroup www. mathworks. com/contact_TS. html Technical Support www. mathworks. com comp. soft-sys. matlab suggest@mathworks. com bugs@mathworks. com doc@mathworks. com service@mathworks. com info@mathworks. com Product enhancement suggestions Bug reports Documentation error reports Order status, license renewals, passcodes Sales, pricing, and general information 508-647-7000 (Phone) 508-647-7001 (Fax) The MathWorks, Inc. 3 Apple Hill Drive Natick, MA 01760-2098 For contact information about worldwide offices, see the MathWorks Web site. Symbolic Math ToolboxTM Release Notes © COPYRIGHT 2004­2010 by The MathWorks, Inc. The software described in this document is furnished under a license agreement. The software may be used or copied only under the terms of the license agreement. [. . . ] Major enhancements to object-oriented programming capabilities enable easier development and maintenance of large applications and data structures. For a full description of object-oriented features, see the MATLAB Object-Oriented Programming documentation. Compatibility Considerations It is no longer possible to add methods to @sym by creating a @sym directory containing custom methods. For an empty x, sym(x) returns a symbolic object of the same size as x. In previous releases, sym(x) returned a symbolic object of size 0-by-0 for an empty x. generate::MATLAB Function Converts MuPAD Expressions to MATLAB Code The new generate::MATLAB command converts MuPAD expressions, equations, and matrices to MATLAB formatted strings. MuPAD IgnoreAnalyticConstraints Option Specifies That Core Functions Apply Common Algebraic Assumptions to Simplify Results The new IgnoreAnalyticConstraints option allows the use of a set of simplified mathematical rules when solving equations, simplifying expressions, or integrating. For example, this option applies practical, but not generally correct rules for combining logarithms: ln(a) + ln(b) = ln(a b) 22 Version 5. 2 (R2009a) Symbolic Math ToolboxTM Software MuPAD Outputs Contain Abbreviations for Better Readability The new default format of presenting results enhances readability of long output expressions by using abbreviations. MuPAD Solver for Ordinary Differential Equations Handles More Equation Types The solver now can handle more than 200 additional types of second-order ordinary differential equations. The solver demonstrates improved performance. MuPAD limit Function Now Can Compute Limits for Piecewise Functions The enhanced limit function computes limits of piecewise functions including bidirectional and one-sided limits. New and Improved MuPAD Special Functions MuPAD includes the following new special functions: · laguerreL represents Laguerre's L function. · erfc(x, n) returns iterated integrals of the complementary error function. · meijerG represents the Meijer G function. The hypergeom special function demonstrates better performance. New Calling Syntax for Test Report Function prog::tcov The prog::tcov function that inspects the data collected during the code execution has the new syntax and set of options. Compatibility Considerations The new syntax is not valid in MuPAD versions earlier than 5. 2. MuPAD 5. 2 does not support the earlier syntax. 23 Symbolic Math ToolboxTM Release Notes New Demos To see new demos that use MuPAD Notebook Interface, type mupadDemo at the MATLAB command line or click MuPAD Notebooks Demo. 24 Version 5. 1 (R2008b) Symbolic Math ToolboxTM Software Version 5. 1 (R2008b) Symbolic Math Toolbox Software This table summarizes what's new in Version 5. 1 (R2008b): New Features and Changes No Version Compatibility Considerations No Fixed Bugs and Known Problems Bug Reports Includes fixes Related Documentation at Web Site No There are no new features or changes in this version. Note If you are upgrading from a version before 4. 9, see the release notes for "Version 4. 9 (R2007b+) Symbolic Math Toolbox Software" on page 27. 25 Symbolic Math ToolboxTM Release Notes Version 5. 0 (R2008a+) Symbolic Math Toolbox Software This table summarizes what's new in Version 5. 0 (R2008a+): New Features and Changes No Version Compatibility Considerations No Fixed Bugs and Known Problems Bug Reports Includes fixes Related Documentation at Web Site No There are no new features or changes in this version. Note If you are upgrading from a version before 4. 9, see the release notes for "Version 4. 9 (R2007b+) Symbolic Math Toolbox Software" on page 27. 26 Version 4. 9 (R2007b+) Symbolic Math ToolboxTM Software Version 4. 9 (R2007b+) Symbolic Math Toolbox Software This table summarizes what's new in Version 4. 9 (R2007b+): New Features and Changes Yes Details below Version Compatibility Considerations Fixed Bugs and Known Problems Related Documentation at Web Site No Bug Reports Yes­Details Includes fixes labeled as Compatibility Considerations, below. See also Summary. New features and changes introduced in this version are described here: · "MuPAD Engine Replaces Maple Engine" on page 27 · "New MuPAD Language and Libraries Supplant Extended Symbolic Math Toolbox Software" on page 32 · "New MuPAD Help Viewer (GUI)" on page 32 · "New MuPAD Notebook Interface (GUI)" on page 33 · "New MuPAD Editor and Debugger (GUI)" on page 33 · "New Functionality for Communication Between MATLAB Workspace and MuPAD" on page 33 · "New symengine Command for Choosing a Maple Engine" on page 34 · "New matlabFunction Generates MATLAB Functions" on page 34 MuPAD Engine Replaces Maple Engine The default Symbolic Math Toolbox engine is now the MuPAD engine. For more information, see the "MuPAD in Symbolic Math Toolbox" chapter in the Symbolic Math Toolbox User's Guide. 27 Symbolic Math ToolboxTM Release Notes Compatibility Considerations The new engine causes many computed results to differ from those returned by previous versions of Symbolic Math Toolbox software. · Many computations return in a permuted order (such as a + b instead of b + a). · Some computations return in a different, mathematically equivalent form (such as (cos(x))^2 instead of 1 - (sin(x))^2). · diff(dirac(t)) returns dirac(t, 1) instead of dirac(1, t). · sym(x, 'f') no longer produces strings of the form hex digits*2^n. Instead the strings have the form (2^e+N*2^(e-52)), where N and e are integers. · For toolbox calculations, some symbols can only be used as symbolic variables, and not in strings: E, I, D, O, beta, zeta, theta, psi, gamma, Ci, Si, and Ei. This is because those symbols represent MuPAD reserved words, and are interpreted as the MuPAD word if you pass them as strings. The words Ci, Si, Ei represent special mathematical functions: the cosine integral, sine integral, and exponential integral respectively. · Error and warning message IDs may have changed. [. . . ] See also Summary. New features and changes introduced in this version are described here: Change in call to code generation package using the maple function Calling a function in code generation package using Maple software now requires you to explicitly include the package name. For example, maple('codegen[fortran](x^2-4)'); The generated code output using these methods is unaffected by this change. Compatibility Considerations In previous versions, functions in the code generation package of Maple software were made automatically available using the Maple with command, and did not require the package name. For example maple('fortran(x^2-4)'); This sometimes caused a conflict when assigning to Maple variables having the same name as a function in the code generation package. 38 Version 3. 1 (R14) Symbolic Math ToolboxTM and Extended Symbolic Math ToolboxTM Software Version 3. 1 (R14) Symbolic Math Toolbox and Extended Symbolic Math Toolbox Software This table summarizes what's new in version 3. 1 (R14): New Features and Changes Yes Details below Version Compatibility Considerations No Fixed Bugs and Known Problems No Related Documentation at Web Site No New features and changes introduced in this version are described here: · "Rounding Operations" on page 39 · "Quotient and Remainder for Division of Integers and Polynomials" on page 40 · "Dirac and Step Functions" on page 40 · "Sorting Symbolic Expressions" on page 41 · "Coefficients of Multivariable Expressions" on page 41 · "Multidimensional Symbolic Arrays" on page 42 · "Conversion to Nondouble Numeric Data Types" on page 42 · "Logarithms to Base 2 and Base 10" on page 43 · "Modulus After Division" on page 43 Rounding Operations The following new functions perform rounding operations on symbolic arrays: · ceil -- Round a number x to the nearest integer greater than or equal to x. · floor -- Round a number x to the nearest integer less than or equal to x. 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