WHAT’S NEW | www.maplesoft.com

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TM

WHAT’S NEW
Maple 2024™

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WHAT’S NEW | www.maplesoft.com

What’s New in Maple 2024
TM

The most powerful and comprehensive environment for exploring, visualizing, andsolving even the most difficult math problems just got even better!
Commands Just Got Easier

Cutting Edge Complex Solvers

By popular request! With Maple 2024, you can calleven unfamiliar commands correctly on the first try,
without having to consult the help pages to get theright arguments in the right order. Just enter thecommand with the help of command completion,then automatic argument completion takes over toguide you through the rest.

New cutting-edge algorithms enable Maple to findand approximate all complex roots of multivariate
polynomial systems and guarantee the accuracyof the results, and to solve the univariate casesignificantly faster.

AI Formula AssistantGet the formulas and equations youneed with the help of powerful AI
technology. In response to your search, you will
get a choice of relevant options, explanations as
to what each one is for and what the parameters
represent, and an easy way to insert the selected
formula into your document as a Maple expression.

Check My Work
The Check My Work feature, which analyses eachstep of a student’s fully worked solution and helps
them identify where they went wrong, has been
expanded to also cover problems in factoring,
simplification, and limits.

Simplify Made (Even More) Simple
The simplify command now expresses many
trigonometric expressions more simply by using thefull range of standard trig functions, rather thanwriting everything in terms of sin and cos.

WHAT’S NEW | www.maplesoft.com

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Step-by-Step Solutions

Expanded Unit Support

The step-by-step solutions in Maple have been
improved to provide even better worked solutions,especially for solving equations, and now handle
even more problems.

Maple’s facilities for working with units are stronger
than ever, with support for units in the Statistics
package, faster operations on matrices containing
units, and the addition of the IPS (inch-poundsecond) system.

Enhanced Signal Processing
New and improved signal processing tools let you
manipulate, visualize, and explore signals in moreways, more efficiently.

Matroid and Hypergraphs
A new package for Matroids and Hypergraphs
supports the thriving research field of Matroid
Theory, an area of study with applications in graphtheory, linear algebra, geometry, topology, network
theory, and more

Scrollable Matrices
You can now browse the contents of large matrices
directly inside your document, instead of launchinga separate matrix browser.

Visualization
Key improvements include better handling of
discontinuities in piecewise functions by default,
and color bar support for many more 2-D and
3-D plots.

More Math, Faster Math
The math engine in Maple has been updated incountless ways so that it can solve more problems,
faster.

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WHAT’S NEW | www.maplesoft.com

Advanced Math
Maple 2024 includes a very large number of
improvements that strengthen the math engine,
expanding Maple’s abilities to handle new areasof mathematics and solve harder problems, faster.
In addition to the mathematical improvements
described in more detail elsewhere, Maple 2024
improves many fundamental routines that are used
regularly both by customers and by other Maple
commands, and enhances support for a variety ofmore specialized areas of mathematics.
• New cutting-edge algorithms enable Maple to findand approximate all complex roots of multivariate
polynomial systems and guarantee the accuracyof the results, and to solve the univariate casesignificantly faster.
• The simplify command expresses many
trigonometric expressions more simply by using
the full range of standard trig functions, rather
than writing everything in terms of sin and cos,and includes many additional improvements totrigonometric simplification that result in morecompact, simpler forms of the answer.

• A new pattern matching method for definite
summation problems returns closed forms forseveral definite sums which earlier versions wereunable to compute.
• The intsolve command now supports special
nodes, custom nodes, and custom basis functions
for the collocation method.
• Several improvements have been made toIntegrationTools:-Change, which can handle more
problems and provide more guidance when the
problem is ill-formed.
• Improvements to assumption handling provide
better results from the is, coulditbe, argument, andsignum commands.

• Core algorithm improvements in simplification
were also made for sums, products, integrals,
limits, piecewise expressions, radicals, min andmax, elliptic functions, logarithms and dilogarithms,
binomial, Beta, and GAMMA.

• The min and max commands are now better atrecognizing whether inputs are real.

• A new SolveTools:-DisplaySolutions commandreformats the results from calling solve with theallsolutions option to make them much morereadable, including using piecewise formatting,
employing standard notation to represent the
integers and naturals numbers instead of _Z and_N, and eliminating _B variables entirely.

• The results of converting between mathematical
functions are better simplified.

• The fsolve command now uses RootFinding:-Isolate
for computing roots of univariate polynomials ofdegree greater than two, providing easy access tothe fastest solvers by default.

• Verification of two expressions up to signdifferences has undergone some significant
improvements, including verification of relations
and new options for function symmetries.

• Various small improvements were made to many
commonly used functions, including int, dsolve,
factor, lcm/gcd, collect, product, expand, and more!

WHAT’S NEW | www.maplesoft.com

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Maple and AI

User Interface

Maple 2024 leverages the latest advancements in
AI technology to provide you with the formulas,equations, explanations, and Maple commands thatyou need.

Maple 2024 includes many useful enhancementssuggested by customers.

• The new AI Formula Assistant helps you find andunderstand formulas and equations. In response
to your query, it delivers a curated selectionof relevant options with clear explanations of
their functions and parameters. Once you’ve
made your selection, you can easily insert yourchosen formula as a Maple expression into yourdocument.
• The NaturalLanguage package provides commands
you can use to explore the use of large language
models, such as GPT-4 and ChatGPT from
OpenAI, to process natural language in Maple.
You can ask the AI to explain a concept, provide
additional details, find a Maple command toaccomplish a specific task, and more!

• With Maple 2024, you can call even unfamiliar
commands correctly on the first try, without
having to consult the help pages to get the rightarguments in the right order, thanks to automaticargument completion.
• After you enter a command name, in many
useful cases, Maple will automatically offer alist of suggested arguments to that function,
including variables and options.
• You can select the one you want using the
Tab key, so you can continue typing smoothly
without having to reach for a mouse or hotkey.
• As appropriate, the suggestions will use thevariables already defined in your document,
and/or provide examples you can then modify.
• Combined with command and symbol
completion, you can now enter full command
names, arguments, and options, with
substantially fewer keystrokes and no mistakes.
• Argument suggestions are available whenworking in standard math notation, Maple
syntax, and in code edit regions.
• You can now scroll through large matrices directly
inside your document, as well as by opening thematrix browser, while still maintaining a compact
view of the matrix.

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WHAT’S NEW | www.maplesoft.com• A new character formatting option lets you
strikethrough text in your document.
• You can change the font used in Code Edit
Regions by modifying the Code style font, forpreference reasons or to facilitate printing and
PDF export when needed.
• The Drawing tool, which enables you to create
diagrams and sketches in Maple as well as draw onplots and images, now supports arc segments.

Visualization
Maple 2024 includes many new and improved
visualization tools for creating, exploring, andcustomizing 2-D and 3-D visualizations.
• Support for color bars has been substantiallyexpanded:• The color bars for density and contour plots
can be customized in many more ways,
including changing labels and fonts.
• You can now add color bars to plots createdwith plot3d that use a custom gradient orcoordinate color scheme.
• Color bars are now available and displayed
by default on matrix plots, surface data plots,
complex plots, and spectrograms.
• For completely customized plots, color bars canbe created individually with the new plottools:colorbar command, and then added to the plotusing plots:-display.
• Plots of many piecewise functions now show
discontinuities by default, without using thediscont option.
• Maple automatically chooses a plotting domainthat includes most of the interesting features ofthe plot. This functionality was further improved in
Maple 2024, most notably for piecewise functions.

• When you use a slider to change the parameter ina plot exploration, the viewing range will now growas needed so that the changes to the plot range
are more apparent.
• Improvements to the interactive Plot Builder
include easier entry of view ranges and intelligent
selection of the plotting variables when creatinginteractive plot explorations.
• The complexplot command can now create
phase plots when given a complex range, andthe complexplot3d command now lets you selectcustom colormaps to represent the argument of
the function being plotted.
• It is now easy to use the many built-in color maps
in your own custom coloring schemes.
• The new plottools:-pyramid command can be used
to create pyramids with any 2-D polygon as a base.

WHAT’S NEW | www.maplesoft.com

Using Maple 2022 or earlier?
If you aren’t at Maple 2023 already, upgrading to Maple 2024 will also get you
all the great improvements from the intervening releases. Here’s a sampling of
improvements that could be of interest no matter what kind of math you do:• The Maple Help Browser now opens each help page in a separate tab,so you can have more than one help page open at the same time and flip
between them easily. (Maple 2023)• Plots that automatically put the most interesting features front and center(Maple 2021), and that handle discontinuities without being told (yes, tan(x)now looks right by default – no more vertical lines!) (Maple 2022)• Massively improved printing and document export, including PDF export(Maple 2020), LaTeX export (Maple 2021), and a Layout Mode so you don’t
need to keep consulting Print Preview over and over again (Maple 2022)• Improvements to help students become productive even more easily,
including guidance when they accidentally enter the exponential e andderivate operator d incorrectly, helpful explanations for more error messages,
and a redesigned Start Page designed to introduce new users to the basics
quickly (Maple 2020)
To see all the improvements you’ll get when you upgrade to Maple 2024 from anearlier version, visit www.maplesoft.com/maplehistory.

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WHAT’S NEW | www.maplesoft.com

Education

Build and Share Interactive Content

Maple 2024 includes many improvements to support
teaching and learning of mathematics, engineering,and science, including tools to help students when
they get stuck on a problem.

Maple provides tools for creating documents andinteractive applications programmatically. Onceyou have developed and tested your applicationsin Maple, you have the choice of sharing themas Maple documents or deploying them to
Maple Learn .

• Maple can provide step-by-step solutions forsolving equations, differentiation, integration,
inverting matrices, and more. In Maple 2024, thiscollection has been expanded to include partial
fraction decomposition. In addition, many of theworked solutions are even better, especially whensolving equations involving absolute values orlogarithms.
• The Check My Work feature, which analyzes eachstep of a student’s fully worked solution and helps
them identify where they went wrong, has been
expanded to also cover problems in factoring,
simplification, and limits.
• New Math Apps explore tangent planes andgolden angles using interactive visualizations

TM• A new layout engine in Maple 2024 results inmore attractive, compact applications.
• When you give your students a practice quiz
involving money, percentages, etc. you may wantappropriate symbols such as $ and % to be usedin the question and beside the response. In
Maple 2024, the PracticeSheet command has new
options that adds these additional symbols in thegenerated question content and response areas.

Matroids and Hypergraphs
New packages for matroids and hypergraphs
support the thriving research field of matroid
theory, an area of study with applications in graphtheory, linear algebra, geometry, topology, network
theory, and more.

WHAT’S NEW | www.maplesoft.com

A matroid is an object which encodes
independence structure on a set. Examples include
linear independence, algebraic independence, andgraph independence. The Matroids package enables
you to construct matroids, generate matroids ofspecific types, test their properties, and compute
their rank, characteristic polynomials, bases,
hyperplanes, ground sets, and much more.
The Hypergraph package is the computational
backbone of the Matroids package. A hypergraphis a generalized graph, consisting of a finite setof vertices and a collection of subsets of thosevertices, called hyperedges. The package provides
efficient commands to create, manipulate, and draw
hypergraphs, and to determine their properties.

9• The Distance and ShortestPath commands now use
the edge weights of a weighted matrix, and new
options to compute the distance and shortest pathin the underlying graph.
• The collection of special graphs supportedby the GraphTheory package has been further
expanded to include the Archimedean graphs,
such as the Icosidodecahedron, TruncatedTetrahedron, Cuboctahedron, and Great
Rhombicosidodecahedron, as well as the Möbius
ladder graph and Wagner graph.

Signal Processing

Graph Theory

New signal processing tools let you create,combine, and analyze signals in more ways, more
efficiently.

A substantial effort was put into Graph Theory for
Maple 2024, including new commands for graphtesting and generation.

• The new ResponseSpectrum command is used
to plot the response of a structure or system tovarying frequencies of ground motion or input
excitation.

• The new AllGraphs command returns an iterator
you can use to step through all graphs matchinga particular set of criteria, such as the numberof vertices and edges, if the graphs must beconnected, and if the next graph should not be
isomorphic to any previous graph returned by theiterator.
• New commands let you find the condensation ofa graph, construct a relation graph, compute the
Wiener index of a graph, test whether a set is adominating set of a graph, test if a given graph is
an Archimedean graph, construct the moral graphgiven a directed graph, find an asteroidal triple in agraph, and verify if a graph contains an asteroidal
triple.
• The new MinCut command uses the flow output
to compute a cut-set, and the MaxFlow commandhas been extended to work on all graphs.
• The EdgeConnectivity and VertexConnectivity
commands have been updated to use MinCut sothat they can now also return cut-sets.

• The IntegrateData command has been updated toinclude options for specifying the initial area andto return running totals.
• The IntegrateData and IntegrateData2D commands
now accept units in the data containers and step
sizes.
• The heavy computations used by the
FindPeakPoints command run significantly faster.

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WHAT’S NEW | www.maplesoft.com

Units
Maple’s extensive support for units has beenfurther expanded to include faster computations,tighter integration with core functionality, and a
new unit system.
• When working with matrices with entries involving
units, Maple can now perform operations much
faster than before.
• Many commands in the Statistics package
involving description statistics, random variables,and distributions can now handle argumentswith units, and will raise an error if the units areinconsistent.

Quantum Chemistry Toolbox
The Maple Quantum Chemistry Toolbox from
RDMChem, a separate add-on product to Maple,
is a powerful environment for the computationand visualization of the electronic structure ofmolecules. In Maple 2024, this toolbox has
significant new features and enhancements thatenable you to:• Compute electronic energies and properties witha new generalization of density functional theory
that captures static correlation.
• Run the CoupledCluster and NuclearGradientcommands on Windows that were previously
available only on macOS and Linux.
• Harness artificial intelligence (AI) through a newcommand Chat that, when prompted with a wordor phrase, can provide invaluable information
about molecules and compounds, electronic
structure methods, as well as other scientificwords or concepts.
• Learn or teach about the role of chemistry in art
through a new curricular set of lessons entitled
The Chemistry of Art.
• Take advantage of additional enhancements andimprovements throughout the package.

• Maple supports many systems of units, such as
SI and FPS, and in Maple 2024, you can now also
work easily in the IPS (inch-pound-second) system.

Programming• By customer request, the series command now
supports an option to return the results as astandard polynomial data structure with no orderterm, rather than as a series data structure.
• The normal and expand commands now map overthe elements of an array.
• When appropriate, you can use evalhf on
expressions that contain calls to your own custom
procedures, and in Maple 2024, the scope has
been expanded to include procedures that employ
try/catch statements.
• Maple 2024 makes it easier to provide an indexing
function to an array, to control how values areinserted and extracted.
• The rules around handling aliased arrays when thesource or aliased array grows have been refined
to provide more insight into when the efficiency
advantages are lost.

WHAT’S NEW | www.maplesoft.com• The new elementwise command applies all theoperations in a given expression to the elementsof a matrix, list or other container, rather than tothe container itself. This command is an alternative
to the ~ syntax, and can be simpler and moreintuitive to use in some cases.
• A new option to the convert command lets you
rewrite expressions involving logarithms to use a
specified logarithmic base.
• Maple now supports Fenwick trees, which arebinary indexed trees for quickly computing sumsof values in an array that undergoes changes.

• Significant performance improvements havebeen made to the QuantifierElimination package,
including faster evaluation at sample points
and caching of intermediate results. Other
improvements in this package include better
display of various data structures and additional
options to control the output of the new GetCells
method.
• The ceil, floor, and round functions are 1.5-2x
faster for some numeric arguments.

• The piecewise function can now handle conditions
involving Maple objects.

Performance• Computations on matrices whose entries haveunits are significantly faster thanks to a newindexing function that allows a matrix, vector, or
array to keep the units separate from the data.
This way, fast hardware algorithms can be used on
the data portion for optimal performance.
• When constructing matrices and vectors withfloating-point entries, Maple now calls directly
to the hardware/evalhf implementation of
known functions as much as possible, resulting
in faster, and in some cases dramatically faster,
initializations.
• A new solver for isolating and approximating allcomplex roots of a univariate polynomial withnumeric or complex numeric coefficients is
considerably faster in most cases and is now thedefault when the ‘complex’ option is specified.
• The EvaluateAtRoot command in the RootFinding
package has a new avoidsymbolic option thatallows you to skip the symbolic processing used toascertain whether the given root is an exact zeroof a constraint. While in general this option will
reduce the function’s ability to reach a conclusion,
when it can find the answer, it will find thatanswer more quickly.

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We’re More than
Just Maple
Did you know? In addition
to Maple, the Maplesoft
Mathematics Suite offers avariety of other complementary
software products, including
online and mobile solutions, that
help you teach and learn mathand math-related courses.

www.maplesoft.com/suite

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