Mathworks SYMBOLIC MATH TOOLBOX RELEASE NOTES

Symbolic Math Toolbox™ Release Notes

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Symbolic Math Toolbox™ Release Notes

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. No part of this manual may be photocopied or reproduced in any form without prior written consent from The MathW orks, Inc.

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Summary by Version ............................... 1

Version 5.4 (R2010a) Symbolic Math Toolbox

Software

Version 5.3 (R2009b) Symbolic Math Toolbox

Software

Version 5.2 (R2009a) Symbolic Math Toolbox

Software

Version 5.1 (R2008b) Symbolic Math Toolbox

Software

Version 5.0 (R2008a+) Symbolic Math Toolbox

Software

........................................ 5

........................................ 11

........................................ 15

........................................ 20

........................................ 21

Contents

Version 4.9 (R2007b+) Symbolic M ath Toolbox

Software

Version 3.2.3 (R2008a) Sym bolic Math Toolbox and

Extended Symbolic Math Toolbox Software

Version 3.2.2 (R2007b) Symbolic Math Toolbox and

Extended Symbolic Math Toolbox Software

Version 3.2 (R2007a) Symbolic Math Toolbox and

Extended Symbolic Math Toolbox Software

Version 3.1.5 (R2006b) Symbolic Math Toolbox and

Extended Symbolic Math Toolbox Software

Version 3.1 (R14) Symbolic Math Toolbox and Extended

Symbolic Math Toolbox Software

........................................ 22

........ 30

........ 31

........ 32

........ 33

................. 34

iii

Compatibility Summary for Symbolic Math Toolbox

and Extended Symbolic Math Toolbox Software

.... 39

iv Contents

SummarybyVersion

This table provides quick access to what’s new in each version. For clarification, see “Using Release Notes” on page 3 .

Symbolic Math Toolbox™ Release Notes

Version (Release)

Latest Versi V5.4 (R2010a

V5.3 (R2009b)

V5.2 (R2009a)

V5.1 (R2

008b)

New Features and Changes

Yes

)

Details

Yes Details

No No

Version Compatibilit Consideratio

Yes Summary

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 22.

Fixed Bugs and Known Problems

Bug Reports Includes fix

Bug Reports Includes fixes

Bug Repor Includes

Bug Reports Includes fixes

fixes

Related Documentation at Web Site

Printable R elease Notes: PDF

Current product documentation

Symbolic Math Toolbox™ Release Notes

Version (Release)

V5.0 (R2008a+)

V4.9 (R2007b+)

V3.2.3 (R2008a)

V3.2.2 (R2007b)

New Features and Changes

No No

Version Compatibility Considerations

Fixed Bugs and Known Problems

Bug Reports Includes fixes

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 22.

Yes Details

Yes Summary

Bug Reports Includes fixes

No No Bug Reports

Includes fixes

No No Bug Reports

Includes fixes

Related Documentation at Web Site

V3.2 (R2007a)

V3.1.5 (R2006b)

V3.1.4 (R2006a)

V3.1.3 (R14SP3)

V3.1.2 (R14SP2)

Yes Details

No Bug Reports

Includes fixes

Yes Summary

Bug Reports Includes fixes

No No Bug Reports

Includes fixes

No No

No bug fixes

No No Bug Reports

Includes fixes

SummarybyVersion

Version (Release)

V3.1.1 (R14SP1)

V3.1 (R14)

New Features and Changes

No No

Yes Details

Version Compatibility Considerations

Fixed Bugs and Known Problems

No bug fixes

Related Documentation at Web Site

Using Release Notes

Use release notes when upgrading to a newer version to learn about:

• New features

• Changes

• Potential impact on your existing files and practices

Review the release notes for other MathWorks™ products required for this product (for example, MATLAB bugs, or compatibility considerations in other products impact you.

If you are upgrading from a software version other than the m ost recent one, review the current release notes and all interim versions. For example, when you upg rade from V1.0 to V1.2, review the release notes for V1.1 and V1.2.

or Simulink®). Determine if enhancements,

What Is in the Release Notes

New Features and Changes

• New functionality

• Changes to existing functionality

Version Compatibility Con si derations

When a new feature or change introduces a reported incompatibility between versions, the Compatibility Considerations subsection explains the impact.

Symbolic Math Toolbox™ Release Notes

Compatibility issues reported after the product release appear under Bug Reports at The MathWorks™ Web site. Bug fixes can sometimes result in incompatibilities, so review the fixed bugs in Bug Reports for any compatibility impact.

Fixed Bugs and Known Problems

The MathWorks offers a user-searchable Bug Reports database so you can view Bug Reports. The development team updates this database at release time and as more information becomes available. Bug Reports include provisions for any known workarounds or file replacem ents. Information is available for bugs existing in or fixed in Release 14SP2 or later. Information is not avail able for all bugs in earlier releases.

Access Bug Reports using y our MathWorks Account.

Version 5.4 (R2010a) Symbolic Math Toolbox™ Software

Version 5.4 (R2010a) Symbolic Math Toolbox Software

This table summarizes what’s new in Version 5.4 (R2010a):

New Features and Changes

Yes Details below

New features and changes introduced in this version are:

• “When Opening Notebook, MuPAD Can Jump to Particular Locations”

on page 6

• “simscapeEquation Function Generates Simscape Equations from Symbolic

Expressions” on page 6

• “New Calling Syntax for the sort Function” on page 6

• “Changes in the symengine Function” on page 7

• “64-Bit GUI Support for Macintosh” on page 7

• “New MuPAD Print Pr eview Dialog” on page 7

• “Improved Configure MuPA D Dialog Box” on page 7

Version Compatibility Considerations

Yes–Details labeled as

Compatibility Considerations,

below. S e e als o Summary

Fixed Bugs and Known Problems

Bug Reports Includes fixes

Related Documentation at Web Site

Printable Release Notes: PDF

Current product documentation

• “MuPAD Support for Basic Arithmetic Operations for Lists” on page 7

• “Improved Performance When Operating on Matrices with Symbolic

Elements” on page 7

• “Enhanced MuPAD divide Function” on page 7

• “Improved Performance for Operations on Polynomials” on page 8

• “MuPAD coeff Function Accepts the New All Option” on page 8

• “MuPAD expand Function Accepts the New ArithmeticOnly Option” on

page 8

Symbolic Math Toolbox™ Release Notes

• “MuPAD expand Function Now Expands Powers of Products” on page 8

• “New Calling Syntax for MuPAD rationalize Function ” on page 9

• “Enhanced MuPAD simplify and Simplify Functions” on page 9

• “MuPAD subs Function Accepts the New EvalChanges Option” on page 9

• “MuPAD Solv er for Ordinary Differential Equations Handles More

Equation Types” on page 9

• “The digits and v pa Functions: Compatibility Considerations” on page 9

• “Functions and Function Elements Being Removed” on page 10

When Opening Notebook, MuPAD Can Jump to Particular Locations

The mupad command that opens a M uPAD®notebook now supports references to particular places inside a notebook. You can create a link target inside a notebook and refer to it when opening a notebook.

simscapeEquation Function Generates Sim scape Equations from Symbolic Expressions

The new simscapeEquation command represents symbolic expressions in the form of Simscape™ equations. For more information, see Generating Simscape Equations in the Symbolic Math Toolbox™ documentation.

New Calling Syntax for the sort Function

The sort function that sorts the element of symbolic arrays and polynomials has the new syntax and set of options.

Compatibility Considerations

In previo us releases, the sort function flattened symbolic matrices to vectors before sorting the elements. Now the column or each row of a symbolic matrix. If you want to obtain the same results as in the previo us release, flatten the symbolic matrix before sorting it:

sort(A(:)).

sort function sorts the elements of each

Version 5.4 (R2010a) Symbolic Math Toolbox™ Software

Changes in the sy

The toolbox no lo engine.

64-Bit G UI Sup

MuPAD now supp Editor and Deb

New MuPAD Pri

Adjusting M Preview dia between pag and print t

Improved C

Specifyi and Edito configu

ng the default settings for graphical user interfaces, such as notebooks

r and Debugger windows, has become easier with the improved

ration dialog box.

MuPAD Su

nger supports the ability to choose an alternative symbolic

port for Macintosh

orts 64-bit graphical user interfaces (such as notebooks and

ugger windows) for a 64-bit Macintosh

nt Preview Dialog

uPAD documents for printing is easier with the new Print

log. You can view one or several pages, zoom in and out, switch

e orientations, adjust the page settings without closing the dialog,

he page or save it to PDF format

onfigure MuPAD Dialog Box

pport for Basic Arithmetic Operations for

Lists

Basic a

rithmetic operations now work for lists.

mengine Function

operating system .

Impro with S

MuPA oper

Enh

Enh div

ved Performance When Operating on Matrices

ymbolic Elements

D demon strates better performance when handling some linear algebra

ations on matrices containing symbolic elements.

anced M uPAD divide Function

anced MuP AD

ision of multivariate polynomials.

divide function computes the quotient and remainder for

Symbolic Math Toolbox™ Release Notes

Improved Performance for Operations on Polynomials

Improved performance for conversion s involving polynomials. Improved performance for operations on polynomials including evaluation, multiplication, and division.

Compatibility Considerations

If the coefficients of a polynomial contain the variables of the polynomial itself, the form of results returned by the MuPAD from previous releases. In previous releases, the coefficients to monomials. Now the of the original expression as coefficients in the resulting polynomial. To get the same behavior as in previous releases, use polynomial into an expression, and then call the the following call exercises the old behavior:

MuPAD coeff Function Accepts the New All Option

The coeff function accepts the newAll option. With this option, coeff returns all coefficients of a polynomial including those equal to 0.

poly function can differ

poly function converted such

poly function can return the coefficients

expr to convert an original

poly function. For ex ample ,

poly(expr(p), [y, x]).

MuPAD expand Function Accepts the New ArithmeticOnly Option

The expand function accepts the new ArithmeticOnly option. The option allows you to expand a sum w ithout expanding trigonometric expressions and special functions in its terms. Technically, the option omits overloading the

expand function for each term of the original expression.

MuPAD expand Function Now Expands Powers of Products

The expand function now expands powers of products such as (xy)nfor positive x and y. When called with the

function expands the power of products for arbitrary terms.

IgnoreAnalyticConstraints option , the

Version 5.4 (R2010a) Symbolic Math Toolbox™ Software

New Calling Syntax for MuPAD rationalize Function

The rationalize function that transforms an arbitrary expression into a rational expression has the new syntax and set of options.

Compatibility Considerations

The new syntax is not valid in MuPAD versions earlier than 5.4. The old syntax is supported in MuPAD 5.4, but will be removed in a future release.

Enhanced MuPAD simplify and Simplify Functions

Enhanced simplification functions, simplify and Simplify,demonstrate better results for expressions involving trigonometric a nd hy p erbolic functions, square roots, and sums over roots of unity.

MuPAD subs Function Accepts the New EvalChanges Option

The subs function now accepts the new EvalChanges option. By default, subs does not evaluate an expression after making substitutions. With this option,

subs evaluates all subexpressions that contain substitutions.

MuPAD Solver for Ordinary Differential Equations Handles More Equation Types

Enhanced MuPAD solver handles more second-order linear and first-order nonlinear ordinary differential equations. The solver demonstrates improved performance.

The digits and vpa Functions: Compatibility Considerations

It is no longer po ssible to set the number of digits to 1 when using the digits and vpa functions. The Sy m bo lic Math Toolbox software version number 4.9 and lower allowed you to set the number of digits to 1.

Symbolic Math Toolbox™ Release Notes

Functions and Fu

Function or Function Element Name

MuPAD Domain

Dom::Ideal

MuPAD stud Library

MuPAD

relation option

simplify

Global property

What Happens When You Use the Function or Element?

Errors

ent

Errors None

Warns

nction Elements Being Removed

Use This Instead

groebner

plot::Int

egral

and linalg

Assumptions on each variable

Compatibility Considerations

Represent ide as lists, and use function of the

groebn

package ins

Use

plot::Integral

and the linalg package instead.

No replac

ement

Make assump each va instea

tions on riable

als

tead.

Version 5.3 (R2009b) Symbolic Math Toolbox™ Software

Version 5.3 (R2009b) Symbolic Math Toolbox Software

This table summarizes what’s new in Version 5.3 (R2009b):

New Features and Changes

Yes Details below

New features and changes introduced in this version are described here:

• “Support for Windows x64 and 64-Bit Macintosh” on page 12

• “sym and syms Use Reserved Words as Variable Names” on page 12

• “The Toolbox Now Displays Floating-Point Results with Their Original

Precision” on page 12

• “New MuPAD Preference Pref::outputDigits Controls Floating-Point

Outputs” on page 13

• “Solver for Ordinary Differential Equations Handles More Equation Types”

on page 13

• “MuPAD limit Function Supports Limits for Incomplete Gamma Function

and Exponential Integral Function” on page 13

Version Compatibility Considerations

Yes–Details labeled as

Compatibility Considerations,

below. S e e als o Summary

Fixed Bugs and Known Problems

Bug Reports Includes fixes

Related Documentation at Web Site

Printable Release Notes: PDF

Current product documentation

• “Enhanced Simplificat ion Routines for MuPAD Special Functions” on

page 13

• “Enhanced MuPAD combine Function for Logarithms” on page 13

• “MuPAD normal Function Accepts New Options” on page 13

• “Functions and Function Elements Being Removed” on page 13

Symbolic Math Toolbox™ Release Notes

Support for Windows x64 and 64-Bit Macintosh

The toolbox now supports 64-bit Windows®and M acin tosh ope rating systems. If you work in the MuPAD Notebook Interface on a 64-bit Macintosh operating system, MuPAD runs a 64-bit engine w ith 32-bit graphical user interfaces, such as notebooks and Editor and Debugger windows.

sym and syms Use Reserved Words as Variable Names

sym and syms commands now treat reserved MuPAD words, except pi,as

variable names.

Compatibility Considerations

In previous releases, the reserved words returned MuPAD values. If your code uses the reserved words as MuPAD commands, modify your code and use the

evalin command with the reserved word as a name. For example, use

evalin(symengine,'beta').

The Toolbox Now Displays Floating-Point Results with Their Original Precision

The toolbox now d isplay s the floating-point results with the original precision with which the toolbox returned them.

Compatibility Considerations

In previous releases, the toolbox displayed floating-point results with the current precision. You must update the existing code that relies on the output precision for displaying floating-point numbers. Use precision you need before computing such results. The toolbox displays the results with the same number of digits it used to compute the results. The toolbox also can increase the specified precision of calculations by several digits.

In previous releases,

N*2^(e - 52)) N0.Nowsym(A, 'f') displays results in the rational form that actually

represents the double-precision floating-point numbers.

sym(A, 'f') represented numbers in the form (2^e +

or -(2^e + N*2^(e - 52)) , with integers for N and e,and

digits to set the

Version 5.3 (R2009b) Symbolic Math Toolbox™ Software

New MuPAD Preference Pref::outputDigits Controls Floating-Point Outputs

New preference Pref::outputDigits controls the precision MuPAD uses to display floating-point results.

Solver for Ordinary Differential Equations Handles More Equation Types

Enhanced solvers handle more equation types of second-order homogeneous linear ordinary differential equations. The solver demonstrates improved performance.

MuPAD limit Function Supports Limits for Incomplete Gamma Function and Exponential Integral Function

Enhanced limit function now can compute limits for incomplete Gamma function and exponential integral function.

Enhanced Simplification Routines for MuPAD Special Functions

Enhanced simplification routines for MuPAD hypergeom, mejerG,andbessel special functions.

Enhanced MuPAD combine Function for Logarithms

Enhanced combine function demonstrates better performance for logarithms.

MuPAD normal Function Accepts New Options

The normal command now accepts the options NoGcd, ToCancel, Rationalize,

Recursive,andIterations. The options control costly operations, such as

recognizing greatest common d ivisors an d algebraic dependencies.

Functions and Function Elements Being Removed

Symbolic Math Toolbox™ Release Notes

Function or Function Element Name

MuPAD Domain

Dom::Ideal

MuPAD student Library

d in char(A, d)

MuPAD

relation option

simplify

What Happens When You Use

Use This

Instead the Function or Element?

Warns

groebner

plot::Integral

and linalg

Warns None

Compatibility Considerations

Represent ideals as lists, and use functions of the

groebner

package instead.

Use

plot::Integral

and the linalg package instead.

No replacement

Version 5.2 (R2009a) Symbolic Math Toolbox™ Software

Version 5.2 (R2009a) Symbolic Math Toolbox Software

This table summarizes what’s new in Version 5.2 (R2009a):

New Features and Changes

Yes Details below

New features and changes introduced in this version are described here:

• “dsolve Accepts the New Option IgnoreAnalyticConstraints” on page 16

• “emlBlock Function Generates Embedded MATLAB Function Blocks from

Symbolic Objects” on page 16

• “matlabFunction Improves Control over Input and Output Parameters”

on page 16

• “Enhancements to Object-Oriented Programming Capabilities” on page 17

• “generate::MATLAB Function Con verts MuPAD Expressions to MATLAB

Code” on page 17

• “MuPAD IgnoreAnalyticConstraints Option Specifies That Core Functions

Apply Common Algebraic Assumptions to Simplify Results” on page 17

Version Compatibility Considerations

Yes–Details labeled as

Compatibility Considerations,

below. S e e als o Summary

Fixed Bugs

and Known

Problems

Bug Reports

Includes fixes

Related Documentation at Web Site

Printable Release Notes: PDF

Current product documentation

• “MuPAD Outputs Contain Abbreviation s for Better Readability” on page 18

• “MuPAD Solv er for Ordinary Differential Equations Handles More

Equation Types” on page 18

• “MuPAD limit Function Now Can Compute Limits for Piecewise Functions”

on page 18

• “NewandImprovedMuPADSpecialFunctions”onpage18

• “New Calling Syntax for Test Report Function prog::tcov” on page 18

Symbolic Math Toolbox™ Release Notes

• “New Demos” on page 19

dsolve Accepts the New Option IgnoreAnalyticConstraints

The dsolve command now accepts the option IgnoreAnalyticConstraints. The option controls the level of mathematical rigor that the solver uses on the analytical constraints on the solution. By default, the solver ignores all analytical constraints.

Compatibility Considerations

The results of the dsolve command can differ from those returned in the previous release. If you want to obtain the same solutions as in the previous release, set the value of the option

emlBlock Function Generates Embedded MATLAB Function Blocks from Symbolic Objects

The new emlBlock command converts symbolic expressions to Embedded MATLAB installation, even those without a Symbolic Math Toolbox license. For more information, see Generating Embedded MATLAB Blocks in the Symbolic Math Toolbox documentation.

IgnoreAnalyticConstraints to none.

Function Blocks. You can use these blocks in any Simulink

matlabFunction Improves Control over Input and Output Parameters

matlabFunction now accepts multiple expressions and cell arrays of symbolic

arrays as input parameters. The function now allows you to specify the names of the output parameters.

Compatibility Considerations

In previous releases, the default name of an output variable was RESULT. Now the default names of the output variables coincide with the names you use to call default output name methods:

matlabFunction. You must update existing code that relies on the

RESULT. You can change your code using any of these

Version 5.2 (R2009a) Symbolic Math Toolbox™ Software

• DefinethenameofanoutputvariableasRESULT.

• Change the name of an input variable to

• Throughout your code change the variable name from

name.

RESULT.

RESULT to the input

Enhancements to Object-Oriented Programming Capabilities

The Symbolic Math Toolbox product uses some object-oriented programming features to implement symbolic objects. 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 previous releases, empty

x, sym(x) returns a symbolic object of the same size as x.In

sym(x) returned a symbolic object of size 0-by-0 for an

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( ) ln( ) ln( )ab ab+=⋅

Symbolic Math Toolbox™ Release Notes

MuPAD Outputs Contain Abbreviations for Better Readability

Thenewdefaultformatofpresentingresults 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 l imit 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 n ew syntax is not v alid in MuPA D versions earlier than 5.2. MuPAD 5.2 does not support the earlier syntax.

Version 5.2 (R2009a) Symbolic Math Toolbox™ Software

New Demos

To see new demos that use MuPAD Notebook Interface, type mupadDemo at the M AT LAB command line or click MuPAD Notebooks D emo.

Symbolic Math Toolbox™ Release Notes

Version 5.1 (R2008b) Symbolic Math Toolbox Software

This table summarizes what’s new in Version 5.1 (R2008b):

New Features and Changes

No No Bug Reports

There are no new features or changes in this version.

Note If you are upgrading from a version befo re 4.9, see the release notes for “Version 4.9 (R2007b+) Symbolic Math Toolbox Software” on page 22.

Version Compatibility Considerations

Fixed Bugs

and Known

Problems

Includes fixes

Related Documentation at Web Site

Printable Release Notes: PDF

Current product documentation

Version 5.0 (R2008a+) Symbolic Math Toolbox™ Software

Version 5.0 (R2008a+) Symbolic Math Toolbox Software

This table summarizes what’s new in Version 5.0 (R2008a+):

New Features and Changes

No No Bug Reports

There are no new features or changes in this version.

Note If you are upgrading from a version befo re 4.9, see the release notes for “Version 4.9 (R2007b+) Symbolic Math Toolbox Software” on page 22.

Version Compatibility Considerations

Fixed Bugs

and Known

Problems

Includes fixes

Related Documentation at Web Site

Printable Release Notes: PDF

Current product documentation

Symbolic Math Toolbox™ Release Notes

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

New features and changes introduced in this version are described here:

• “MuPAD Engine Replaces Maple Engine” on page 22

• “New MuPAD Language and Libraries Supplant Extended Symbolic Math

Toolbox Software” on page 27

• “New MuPAD Help Viewer (GUI)” on page 27

• “New MuPAD Notebook Interface (GUI)” on page 28

• “New MuPAD Editor and Debugger (GUI)” on page 28

• “New Functionality for Communication Between MATLAB Workspace and

MuPAD” on page 28

• “New symengine Command for Choosing a Maple Engine” on page 29

Version Compatibility Considerations

Yes–Details labeled as

Compatibility Considerations,

below. S e e als o Summary.

Fixed Bugs

and Known

Problems

Bug Reports

Includes fixes

Related Documentation at Web Site

Printable Release Notes: PDF

Current product documentation

• “New matlabFunction Generates MATLAB Functions” on page 29

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.

Version 4.9 (R2007b+) Symbolic Math Toolbox™ Software

Compatibility Considerations

The new engine causes many computed results to differ from those returned by previous versions of Symbolic Math Toolbox software.

General Differences.

• Many computations return in apermutedorder(suchas

b+a).

a+binstead of

• Some computations return in a different, mathematically equivalent form

(such as

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

(cos(x))^2 instead of 1 - (sin(x))^2).

(2^e+N*2^(e-52)),whereN and e are

integers.

• For toolbox calculations, some symbols can only be used a s symbolic

variables, and not in strings:

Ci, Si,andEi. This is because those symbols represent MuPAD reserved

E, I, D, O, beta, zeta, theta, psi, gamma,

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 w arning message IDs may have changed.

• Performance of numerical in te gration is slower t ha n in prev io us versions.

• Subexpressions, calculated by the

subexpr function, may be different than

in previous versions.

• The

pretty function no longer uses partial subexpressions (with syntax %n).

Calculus.

•

Int no longer evaluates some integrals, including many involving Bessel

functions.

•

symsum(sin(k*pi)/k,0,n) no longer evaluates to pi.

Symbolic Math Toolbox™ Release Notes

Linear Algebra.

• The output of

mathematically equivalent.

• The

•

Simplification.

• The

• Subexpressions no longer have partial subexpressions (previous syntax

• The

eig function may return eigenvalues in a different order than previous

versions. Expressions returned by versions.

jordan function may return diagonal subblocks in a different order

than previous versions.

svd may return singular values in a different order than previous versions.

coeffs function may return multivariable terms in a different order

than in previous versions.

expand function may return some trig and exponential expressions

differently than in previous versions.

simplify function involving radicals and powers make fewer

assumptions on unknown symbols than in previous versions.

subexpr function may choose a different subexpression to be the

common subexpression than in previous versions.

solve function returns solutions with higher multiplicity only when

solving a single polynomial.

colspace may differ from previous versions, but it is

eig may be larger than in previous

%n).

•

acot(-x) = -acot(x) instead of pi - acot(x) as in previous versions.

acoth(-x) = -acoth(x) instead of 2*acoth(0) - acoth(x) as in

•

previous versions.

• The

simple function has several differences:

- The 'how' value combine(trig) has been replaced with

combine(sincos), combine(sinhcosh),andcombine(ln).

- The 'how' values involving convert have been replaced with rewrite.

- Anew'how' value of mlsimplify(100) indicates the MuPAD function

Simplify(...,Steps=100) simplified the expression.

Version 4.9 (R2007b+) Symbolic Math Toolbox™ Software

- Simplifications such as (sin(x)^2)^(1/2) to sin(x) arenolonger

performed, since the MuPAD language is careful not to make assumptions about the sign of

Conversion.

sin(x).

• Arithmetic involving the

vpa function uses the current number of digits

of precision. Variable precision arithmetic may have different rounding behaviors, and answers may differ in trailing digits (trailing zeros are now suppressed).

• The

char function returns strings using MuPAD syntax instead of Maple™

syntax.

• Testing equality does not compare strings as in previous versions; the

symbolic engine equality test is used.

• Saving and loading symbolic expressions is compatible with previous

versions, except when the symbolic contents use syntax o r functions that differ between Maple or M u PAD engines. For example, suppose you save the symbolic object

sym('transform::fourier(f,x,w)'), which has

MuPAD syntax. You get a MATLAB error if you try to open the object while using a Maple engine.

• LaTeX output from the

• C and Fortran code generated with the

latex function may look different than before.

ccode and fortran functions may

be different than before. In particular, generated files have inte rmediate expressions as “optimized” code. For more information, see the “Generating C or Fortran Code” section of the User’s Guide.

•

pretty output may look different than before.

Equation Solving.

•

solve re tu rns solu tion s with h ig h er multiplicity only when solving a single

polynomial.

•

solve may return a different number of solutions than before.

• Some calls to

dsolve that used to return results involving lambertw now

return no solution.

•

dsolve can now use the variable C.

Symbolic Math Toolbox™ Release Notes

• Some dsolve results are more complete (more cases are returned).

• Some

•

dsolve results are less complete (not all previous answers are found).

finverse may be able to find inverses for different classes of functions

than before.

• When

finverse fails to find an explicit inverse, it produces different

output than before.

Transforms.

• Fourier and inverse Fourier transforms return the MuPAD form

transform::fourier when they cannot be evaluated. For example,

h = sin(x)/exp(x^2); FF = fourier(h)

FF = transform::fourier(sin(x)/exp(x^2), x, -w)

The reason for this behavior is the MuPAD definition of Fourier transform and inverse Fourier transform differ from their Symbolic Math Toolbox counterparts by the sign in the exponent:

Symbolic Math

MuPAD definition

Toolbox definition

Fourier transform

Inverse Fourier transform

Fw f xe dx

fx Fwe dw

() ()=

() ( )=

∞

∫

−∞



−∞

iwx

−

∞

iwx

∫

Fw f xe dx

fx Fwe dw

() ()=

() ( )=

∞

iwx

∫

−∞

∞

∫



−∞

−

iwx

• Several Fourier transforms can no longer be calculated, especially those

involving Bessel functions.

•

ztrans and iztrans may return more complicated expressions than before.

Version 4.9 (R2007b+) Symbolic Math Toolbox™ Software

SpecialMathematicalFunctions.

• The three-parameter Riemann Zeta function is no longer supported.

• heaviside(0) = 0.5; in previous versions it was undefined.

maple.

• The

maple, mhelp,andprocread functions error, unless a Maple engine is

installed and selected with

symengine.

New MuPAD Language and Libraries Supplant Extended Symbolic Math Toolbox Software

The functionality of the MuPAD language, together with the included libraries, goes far beyond that of the previous Symbolic Math Toolbox software. However, it is not identical to that of the previous Extended Symbolic Math Toolbox™ software. The differences between these software packages are beyond the scope of these release notes.

You can access the MuPAD language in several ways:

• To learn the commands, syntax, and functionality of the language, use the

MuPAD Help browser, or read the Tutorial.

• Use a MuPAD notebook, which contains an integrated help system for

the language syntax.

• Use the new

language at the MATLAB command line. More detail is available in the “Calling M uPAD Functions at the MATLAB Command Line” section of the User’s Guide.

evalin function or feval function to access the MuPAD

New MuPAD Help Viewer (GUI)

The MuPAD help viewer contains complete documentation of the MuPAD language, and of the MuPAD Notebook Interface. For more information, see the “G etting Help for MuPAD” section of the User’s Guide.

Symbolic Math Toolbox™ Release Notes

New MuPAD Notebook Interface (GUI)

A MuPAD notebook is an interface for p erf orm i ng symbolic math computations with embedded math notation, graphics, animations, and text. It also enables you to share, document, and publish your calculations and graphics. For example, the MuPAD help view er is essentially a special MuPAD notebook. For m ore information, s ee the “Calculating in a MuPAD Notebook” section of the User’s Guide.

New MuPAD Editor and Debugger (GUI)

The MuPAD Editor GUI enables you to write custom symbolic functions and libraries in the MuPAD language. The Debugger enables you to test your code. F or more information, consult the MuPAD help viewer.

New Functionality for Communication Between MATLAB Workspace and MuPAD

Function

doc(symengine,...)

evalin(symengine,...)

feval(symengine,...)

getVar

mupad

mupadwelcome

reset(symengine,...)

setVar

symvar

Use

Access the MuPAD Help browser.

Use MuPAD functionality in the MATLAB workspace.

Copy expressions residing in a MuPAD notebook into the MATLAB workspace.

Launch a MuPAD notebook .

Access MuPAD GUIs .

Clear the MuPAD engine for the MATLAB workspace.

Copy expressions residing in the MATLAB workspace into a MuPAD notebook.

Produce a list of symbolic objects in an expression.

Version 4.9 (R2007b+) Symbolic Math Toolbox™ Software

For more information, see the “Integration of MuPAD and MATLAB” section of the User’s Guide.

New symengine Command for Choosing a Maple Engine

If y ou own a compatible version of a M aple software, you can choose to have Symbolic Math Toolbox software use the Maple engine instead of a MuPAD engine. You might want to do this if you have existing Maple programs. Choose the engine by entering brings up a GUI for making your choice.

symengine at the MATLAB command line; this

New matlabFunction Generates MATLAB Functions

The new matlabFunction generates MATLAB functions from symbolic expressions. a function handle. You can use the generated function handles and files in any MATLAB installation, even those without a Symbolic Math Toolbox license. For more information, see “Generating MATLAB Functions” in the User’s Guide.

matlabFunction writes the generated code to a file or creates

Symbolic Math Toolbox™ Release Notes

Version 3.2.3 (R2008a) Symbolic Math Toolbox and Extended Symbol

ic Math Toolbox Software

This table summ

New Features and Changes

No No Bug Reports

There are no new features or changes in this version.

arizes what’s new in Version 3.2.3 (R2008a):

Version Compatibility Considerations

Fixed Bugs

and Known

Problems

Includes fixes

Related Documentation at Web Site

Version 3.2.2 (R2007b) Symbolic Math Toolbox™ and Extended Symbolic Math Toolbox™ Software

Version 3.2.2 (R2007b) Symbolic Math Toolbox and Extended Symbol

ic Math Toolbox Software

This table summ

New Features and Changes

No No Bug Reports

There are no new features or changes in this version.

arizes what’s new in Version 3.2.2 (R2007b):

Version Compatibility Considerations

Fixed Bugs

and Known

Problems

Includes fixes

Related Documentation at Web Site

Symbolic Math Toolbox™ Release Notes

Version 3.2 (R2007a) Symbolic Math Toolbox and Extended Symbol

ic Math Toolbox Software

This table summ

New Features and Changes

Yes Details below

New features and changes introduced in this version are described here:

arizes what’s new in Version 3.2 (R2007a):

Version Compatibility Considerations

No Bug Reports

Fixed Bugs

and Known

Problems

Includes fixes

Related Documentation at Web Site

Maple10 A ccess Added for Linux 64–bit Processors and Intel Macintosh Platforms

MATLAB now supports Maple Version 10 on 32-bit Windows, 32- and 64-bit

Linux

platforms, and the Intel®and PowerPC®Macintosh platforms.

Version 3.1.5 (R2006b) Symbolic Math Toolbox™ and Extended Symbolic Math Toolbox™ Software

Version 3.1.5 (R2006b) Symbolic Math Toolbox and Extended Symbol

ic Math Toolbox Software

This table summ

New Features and Changes

Yes Details below

New features and changes introduced in this version are described here:

arizes what’s new in version 3.1.5 (R2006b):

Version Compatibility Considerations

Yes–Details labeled as

Compatibil Considerat

below. S ee Summary.

ity ions,

also

Fixed Bugs

and Known

Problems

Bug Reports

Includes fixes

Related Documentation at Web Site

Change in call to code gen eration package using the maple function

Calling a function in code generationpackageusingMaplesoftwarenow requires you to explicitly include the package name. For example,

maple(

The generated code output using these methods is unaffected by this change.

'codegen[fortran](x^2-4)');

Compa

In previous versions, functions in thecodegenerationpackageofMaple software were made automatically available using the Maple and did not require the package name. For example

This sometimes caused a conflict when assigning to Maple variables having thesamenameasafunctioninthecodegenerationpackage.

tibility Considerations

le('fortran(x^2-4)');

map

with command,

Symbolic Math Toolbox™ Release Notes

Version 3.1 (R14) Symbolic Math Toolbox and Extended Symbolic Math To

olbox Software

This table summ

New Features and Changes

Yes Details below

New features and changes introduced in this version are described here:

• “Rounding Operations” on page 34

• “Quotient and Remainder for Division of Integers and Polynomials” on

page 35

• “Dirac and Step Functions” on page 35

• “Sorting Symbolic Expressions” on page 36

• “Coefficients of Multivariable Expressions” on page 36

• “Multidimensional Symbolic Arrays” on page 37

• “Conversion to Nondouble Numeric Data Types” on page 37

• “Logarithms to Base 2 and Base 10” on page 38

• “Modulus After Division” on page 38

arizes what’s new in version 3.1 (R14):

Version Compatibility Considerations

No No No

Fixed Bugs

and Known

Problems

Related Documentation at Web Site

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.

fix — Round toward zero.

•

floor — Round a number x to the nearest integer less than or equal to x.

•

frac — Compute the fractional part of a number.

•

round — Round a number to the nearest integer.

•

Version 3.1 (R14) Symbolic Math Toolbox™ and Extended Symbolic Math Toolbox™ Software

For example,

x = sym([2.5; -9.639]) [fix(x) floor(x) round(x) ceil(x) frac(x)]

5/2

-9639/1000

ans = [2,2,3,3,1/2] [ -9, -10, -10, -9, -639/1000]

Quotient and Remainder for Division of Integers and Polynomials

The new function quorem computes the quotie n t and remainder for division of integers and polynomials. For example,

syms x y p = x^3-2*x+5 [q,r] = quorem(x^5,p)

p= x^3-2*x+5

q= x^2+2

-5*x^2-10+4*x

Dirac and Step Functions

The following new functions compute the Dirac delta and Heaviside functions:

•

dirac — Compute the Dirac delta function.

heaviside — Compute the Heaviside step function.

•

For example,

Symbolic Math Toolbox™ Release Notes

dirac([-1 0 1])

ans =

0 Inf 0

heaviside([-1 0 1])

ans =

0 NaN 1

Sorting Symbolic Expressions

The new function sort sorts symbolic expressions. For example,

symsabcdex sort([a c e b d])

ans = [a,b,c,d,e] sort([a c e b d]*x.^(0:4).')

ans = x^4*d+x^3*b+e*x^2+x*c+a

Coefficients of Multivariable Expressions

The new function coeffs computes coefficients of a multivariate polynomial. For example,

syms c t x y t = 2 + (3 + 4*log(x))^2 - 5*log(x); coeffs(expand(t))

ans = [ 11, 19, 16]

z = 3*x^2*y^2 + 5*x*y^3 [c,t] = coeffs(z,y)

z= 3*x^2*y^2+5*x*y^3

Version 3.1 (R14) Symbolic Math Toolbox™ and Extended Symbolic Math Toolbox™ Software

c= [ 3*x^2, 5*x]

t= [ y^2, y^3]

Multidimensional Symbolic Arrays

The new function reshape reshapes symbolic arrays. For example,

syms x A = reshape(x.^(1:9),1,3,3)

A(:,:,1) = [ x, x^2, x^3]

A(:,:,2) = [ x^4, x^5, x^6]

A(:,:,3) = [ x^7, x^8, x^9]

Conversion to Nondouble Numeric Data Types

The following new functions enable you to convert symbolic arrays to nondouble numeric data types:

•

int8 — Convert a sy mbolic matrix to signed 8-bit integers.

int16 — Convert a symbolic matrix to signed 16-bit integers.

•

int32 — Convert a symbolic matrix to signed 32-bit integers.

•

int64 — Convert a symbolic matrix to signed 64-bit integers.

•

single — Convert a number to single precision.

•

uint8 — Convert a symbolic matrix to unsigned 8-bit integers.

•

uint16 — Convert a symbolic matrix to unsigned 16-bit integers.

•

uint32 — Convert a symbolic matrix to unsigned 32-bit integers.

•

uint64 — Convert a symbolic matrix to unsigned 64-bit integers.

•

Symbolic Math Toolbox™ Release Notes

Logarithms to Ba

The following ne arrays to bas e 2 a

•

log10 —Compute

•

log2 —Compute

Modulus Afte

The new funct

syms x mod(x^3-2*x+999,10)

ans = x^3+8*x+9

w functions enable you to compute the logarithm of symbolic

nd base 10:

base 10 logarithm.

base 2 logarithm.

r Division

ion m od computes modulus after division. For example,

se 2 and Base 10

Compatibility Summary for Symbolic Math Toolbox™ and Extended Symbolic Math Toolbox™ Software

Compatibility Summary for Symbolic Math Toolbox and Extended Symbolic Math Toolbox Software

This table summarizes new features and changes that might cause incompatibilities when you upgrade from an earlier version, or wh en you use files on multiple versions. Details are provided with the description of the new feature or change.

Version (Release) New Features and Changes with

Version Compatib ility Impact

Latest Version V5.4 (R2010a)

V5.3 (R2009b) See the Compatibility

See the Compatibil ity

Considerations subheading

for each of these new features or

changes:

• “New Calling Syntax for the sort

Function” on page 6

• “Improved Performance for

Operations on Polynomials” on page 8

• “New Calling Syntax for MuPAD

rationalize Function” on page 9

• “The digits and vpa Functions:

Compatibility Considerations” on page 9

• “Functions and Function

Elements Being Removed” on page 10

Considerations subheading

for each of these new features or

changes:

• “sym and syms Use Reserved

Words as Variable Names” on page 12

Symbolic Math Toolbox™ Release Notes

Version (Release) New Features and Changes with

V5.2 (R2009a) See the Compatibility

Version Compatib ility Impact

• “The Toolbox Now Displays

Floating-Point Results with Their Original Precision” on page 12

• “Functions and Function

Elements Being Removed” on page 13

Considerations subheading

for each of these new features or

changes:

• “dsolve Accepts the New Option

IgnoreAnalyticConstraints” on page 16

• “matlabFunction Improves

Control over Input and Output Parameters” on page 16

• “Enhancements to

Object-Oriented Programming Capabilities” on page 17

• “New Calling Syntax for Test

Report Function prog::tcov” on page 18

V5.1 (R2008b)

V5.0 (R2008a+)

None

V4.9 (R2007b+) See the Compatibility

Considerations subheading

for each of these new features or

changes:

• “MuPAD Engine Replaces Maple

Engine” on page 22

Compatibility Summary for Symbolic Math Toolbox™ and Extended Symbolic Math Toolbox™ Software

Version (Release) New Features and Changes with

Version Compatib ility Impact

V3.2.3 (R2008a)

V3.2.2 (R2007b)

V3.2 (R2007a)

None

V3.1.5 (R2006b) See the Compatibility

Considerations subheading

for each of these new features or

changes:

• “Changeincalltocodegeneration

package using the maple function” on page 33

V3.1.4 (R2006a)

V3.1.3 (R14SP3)

V3.1.1 (R14SP1)

V3.1 (R14)

None

Mathworks SYMBOLIC MATH TOOLBOX RELEASE NOTES

Specifications and Main Features

Frequently Asked Questions

User Manual