New Features in Maple 2024 - Technical Computing Software for Engineers, Mathematicians, Scientists, Teachers and Students (2024)

Maple 2024 includes a very large number of improvements that strengthen the math engine, expanding Maple’s abilities to handle new areas of mathematics and solve harder problems, faster. In addition to the mathematical improvements described in more detail elsewhere,

improves many fundamental routines that are used regularly both by customers and by other Maple commands, and enhances support for a variety of more specialized areas of mathematics.

• New cutting-edge algorithms enable Maple to find and approximate all complex roots of multivariate polynomial systems and guarantee the accuracy of the results, and to solve the univariate case significantly 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 to trigonometric simplification that result in more compact, simpler forms of the answer.
• Core algorithm improvements in simplification were also made for sums, products, integrals, limits, piecewise expressions, radicals, min and max, elliptic functions, logarithms and dilogarithms, binomial, Beta, and GAMMA.
• A new SolveTools:-DisplaySolutions command reformats the results from calling solve with the allsolutions option to make them much more readable, 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 fsolve command now uses RootFinding:-Isolate for computing roots of univariate polynomials of degree greater than two, providing easy access to the fastest solvers by default.
• A new pattern matching method for definite summation problems returns closed forms for several definite sums which earlier versions were unable to compute.
• The intsolve command now supports special nodes, custom nodes, and custom basis functions for the collocation method.
• Several improvements have been made to IntegrationTools:-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, and signum commands.
• The min and max commands are now better at recognizing whether inputs are real.
• Verification of two expressions up to sign differences has undergone some significant improvements, including verification of relations and new options for function symmetries.
• The results of converting between mathematical functions are better simplified.
• Various small improvements were made to many commonly used functions, including int, dsolve, factor, lcm/gcd, collect, product, expand, and more!

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

• The new AI Formula Assistant helps you find and understand formulas and equations. In response to your query, it delivers a curated selection of relevant options with clear explanations of their functions and parameters. Once you’ve made your selection, you can easily insert your chosen formula as a Maple expression into your document.
• 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 to accomplish a specific task, and more!

Maple 2024 includes many useful enhancements suggested by customers.

• With Maple 2024, you can call even unfamiliar commands correctly on the first try, without having to consult the help pages to get the right arguments in the right order, thanks to automatic argument completion.
• After you enter a command name, in many useful cases, Maple will automatically offer a list 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 the variables 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 when working 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 the matrix browser, while still maintaining a compact view of the matrix.
• 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, for preference 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 on plots and images, now supports arc segments.

Maple 2024 includes many new and improved visualization tools for creating, exploring, and customizing 2-D and 3-D visualizations.

• Support for colorbars has been substantially expanded:
• The colorbars for density and contour plots can be customized in many more ways, including changing labels and fonts.
• You can now add colorbars to plots created with plot3d that use a custom gradient or coordinate colorscheme.
• Colorbars are now available and displayed by default on matrix plots, surface data plots, complex plots, and spectrograms.
• For completely customized plots, color bars can be created individually with the new plottools:-colorbar command, and then added to the plot using plots:-display.
• Plots of many piecewise functions now show discontinuities by default, without using the discont option.
• Maple automatically chooses a plotting domain that includes most of the interesting features of the plot. This functionality was further improved in Maple 2024, most notably for piecewise functions.
• When you use a slider to change the parameter in a plot exploration, the viewing range will now grow as 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 creating interactive plot explorations.
• The complexplot command can now create phase plots when given a complex range, and the complexplot3d command now lets you select custom 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.

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 can provide step-by-step solutions for solving equations, differentiation, integration, inverting matrices, and more. In Maple 2024, this collection has been expanded to include partial fraction decomposition. In addition, many of the worked solutions are even better, especially when solving equations involving absolute values or logarithms.
• The Check My Work feature, which analyzes each step 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 and golden angles using interactive visualizations.

Maple provides tools for creating documents and interactive applications programmatically. Once you have developed and tested your applications in Maple, you have the choice of sharing them as Maple documents or deploying them to Maple Learn.

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

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

A matroid is an object which encodes independence structure on a set. Examples include linear independence, algebraic independence, and graph independence. The Matroids package enables you to construct matroids, generate matroids of specific 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 hypergraph is a generalized graph, consisting of a finite set of vertices and a collection of subsets of those vertices, called hyperedges. The package provides efficient commands to create, manipulate, and draw hypergraphs, and determine their properties.

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

• The new AllGraphs command returns an iterator you can use to step through all graphs matching a particular set of criteria, such as the number of vertices and edges, if the graphs must be connected, and if the next graph should not be isomorphic to any previous graph returned by the iterator.
• New commands let you find the condensation of a graph, construct a relation graph, compute the Wiener index of a graph, test whether a set is a dominating set of a graph, test if a given graph is an Archimedean graph, construct the moral graph given a directed graph, find an asteroidal triple in a graph, 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 command has been extended to work on all graphs.
• The EdgeConnectivity and VertexConnectivity commands have been updated to use MinCut so that they can now also return cut-sets.
• The Distance and ShortestPath commands now use the edge weights of a weighted matrix, and new options to compute the distance and shortest path in the underlying graph.
• The collection of special graphs supported by the GraphTheory package has been further expanded to include the Archimedean graphs, such as the Icosidodecahedron, Truncated Tetrahedron, Cuboctahedron, and Great Rhombicosidodecahedron, as well as the Möbius ladder graph and Wagner graph.

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

• The new ResponseSpectrum command is used to plot the response of a structure or system to varying frequencies of ground motion or input excitation.
• The IntegrateData command has been updated to include options for specifying the initial area and to 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.

The Maple Quantum Chemistry Toolbox from RDMChem, a separate add-on product to Maple, is a powerful environment for the computation and visualization of the electronic structure of molecules. In Maple 2024, this toolbox has significant new features and enhancements that enable you to:

• Compute electronic energies and properties with a new generalization of density functional theory that captures static correlation.
• Run the CoupledCluster and NuclearGradient commands on Windows that were previously available only on macOS and Linux.
• Harness artificial intelligence (AI) through a new command Chat that, when prompted with a word or phrase, can provide invaluable information about molecules and compounds, electronic structure methods, as well as other scientific words 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 and improvements throughout the package.

Maple’s extensive support for units has been further 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 arguments with units, and will raise an error if the units are inconsistent.
• 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.

• Computations on matrices whose entries have units are significantly faster thanks to a new indexing 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 with floating-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 all complex roots of a univariate polynomial with numeric or complex numeric coefficients is considerably faster in most cases and is now the default when the ‘complex’ option is specified.
• The EvaluateAtRoot command in the RootFinding package has a new avoidsymbolic option that allows you to skip the symbolic processing used to ascertain whether the given root is an exact zero of 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 that answer more quickly.
• Significant performance improvements have been 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.