Maple 2023 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, Maple 2023 improves fundamental routines that are used regularly both by customers and by other Maple commands, as well as enhancing support for a variety of more specialized areas of mathematics.

• Maple 2023 provides much simpler answers for many indefinite integrals of algebraic functions whose answers used to run over many lines, or even many screens. This improvement is achieved through the use of the Blake’s heuristic method, which expresses some algebraic integrands in more elementary forms. This technique results in much simpler, much more compact answers to integration problems that are easier to understand and work with.
• The int command now exposes more internal routines for indefinite integration through the method option.  It is now possible to directly call the integration by parts routine Parts and a parallel version of the Risch algorithm ParallelRisch, if desired.
• Assumption handling for integration has been enhanced. The definite integration method that works via MeijerG convolutions now does a better job of checking conditions on parameters so that they are only applied under proper assumptions. It also tells the user the conditions under which the method could have produced an answer, so if the problem does meet those conditions they can add assumptions to obtain the result.
• The solve command can now handle problems expressed as element-wise relations between vectors or matrices, instead of requiring you to rewrite the problem as a list of relations between the corresponding entries.
• The simplify command has been significantly improved, with a particular focus on trigonometric simplification.
• The IntegerHull command in the PolyhedralSets package has been extended to support both bounded and unbounded higher dimensional polyhedral sets.
• The new ZPolyhedralSets subpackage of the PolyhedralSets package is a collection of commands for working with Z-polyhedral sets, which are the intersections of a polyhedral set with an integer lattice.
• The parametric option to the limit command has been extended to handle more cases where the expansion point may lie on the branch cut of a mathematical function for some real parameter values.
• A new, faster method for isolating the complex roots of a univariate polynomial with complex numeric coefficients has been added to the RootFinding:-Isolate command, which in turn means that fsolve is also faster in these cases.
• The collocation method in intsolve has been improved, resulting in more and better approximations to solutions of integral equations.
• The MultivariatePowerSeries package deals with multivariate power series in a lazy fashion, meaning that extra terms for a given result can be computed quickly. In Maple 2023, this package can now deal with multivariate Puiseux series and univariate polynomials over multivariate Puiseux series.

Learn more...

Visualization improvements in Maple 2023 include enhanced plotting tools and significant performance enhancements.

• The Plot Builder is a convenient tool for creating a wide variety of customized plots and animations without worrying about the underlying commands, and now you can also use it to build interactive plot explorations where parameters are controlled by sliders or dials.
• Create 2-D and 3-D interactive plots whose values can be changed interactively, without using a single command.
• Select the range for each of your chosen interactive parameters, as well as the interactive components you wish to use to control them, such as sliders or dials.
• Customize the appearance of the plot, including colors, line styles, gridlines, axes style, title, and more, without having to know the syntax for setting plot options.
• View the Maple command that will produce the same interactive plot that you created, if desired, for easy reuse in your own code.
• Color bars have been added to 2-D contour and density plots to show the values of the gradations.
• Fourteen new colormaps are now available as ColorTools palettes that can easily be used with the colorscheme option for plot commands that accept it. These include a new colorblind-friendly linear colormap, cyclical colormaps for data that cycles, and divergent colormaps.
• More plot commands are responsive to the global color settings.
• The adaptive plotting engine is faster and uses less memory.

Learn more...

• Maple language files, which are typically saved with the file extension .mpl, can now be opened directly in Maple’s code editor, where you can view and edit the file using the editor’s syntax highlighting, command completion, and automatic indenting.
• Code edit regions allow you to include Maple commands, functions, and procedures in your document while taking advantage of standard code editing tools like syntax highlighting and automatic indenting. Maple 2023 includes many improvements that make it even easier to enter and run your Maple code in code edit regions.
  • You can now use the palettes in code edit regions to make entering complicated or unfamiliar Maple syntax simple. When you are in a code edit region, clicking on a button on the Expression, Calculus, Matrix, or other palettes will insert the corresponding Maple syntax for that item. You can then easily edit the resulting Maple expression to change the values of any placeholders.
  • It is easier to add units to your calculations and code. You can insert units into the code edit region using the Units palette or hotkeys, just as you would elsewhere in your document.
  • The Find and Replace feature in Maple has been improved so that code edit regions are now included in the search, even if the code edit region is collapsed.
  • You can now set code edit regions to accept Python code. See the Connectivity section for details.

Learn more...

In addition to the interface changes described in various other sections of this document, Maple 2023 includes several interface enhancements that are in direct response to customer requests.

• You can now have more than one help page open at a time. The help system now opens help pages in tabs, making it much easier to consult content from multiple help pages.
• When you load packages using the Tools > Load Package menu, the with command that loads the package is now always visible in your document, even in Document mode. 
• New context panel menu operations are available for inserting rows and columns in a matrix before the cursor position as well as after, deleting rows and columns of a matrix, and adding additional branches to piecewise expressions.
• You can easily copy the full topic name of a help page to the clipboard, making it simpler to create a hyperlink to that page in your document. 
• It is now easier to delete entries from a custom palette.

Learn more...

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, where students can access them through a web browser. Maple 2023 includes additional tools that help you create more applications, more easily.

Practice Quizzes

• A new Quiz Builder comes loaded with sample quizzes and makes it easy to create your own custom quiz questions. The Quiz Builder makes it easier to choose your question types, add hints, provide feedback, show the solution, and generate new problems.
• You can now create practise questions that ask students to provide all the steps of the solution, and then provides feedback on each step, not just the final answer.
• Quizzes can now have titles in addition to the question text.

Template Gallery
A new template gallery provides examples that make it easier to create more complex Math Apps and interactive applications that require programming, such as interactive clickable plots, quizzes that offer students unlimited practice and provide feedback, examples that provide solution steps, and more.

• Over 44 templates and modifiable examples cover functions, geometry, calculus, and other topics.
• Examples demonstrate how to implement clickable plots, self-grading practise quizzes, solution steps, and other advanced features.
• The Maple code used for those applications can be easily viewed, copied, and modified, so you can customize specific applications or use the code as a starting point for your own work.

Tools
The DocumentTools:-Canvas package, which provides a framework for building applications programmatically, has been expand to allow for greater control over the application’s appearance and make some common tasks easier.

• Canvas elements have more options to control appearance, such as font size, color, slider controls, and custom attributes. 
• New script commands make it easier to clear a single group, reset the entire document, or convert text with embedded MathML into plain text.

Learn more...

Maple 2023 includes enhancements to its core teaching and learning functionality, including step-by-step solutions and resources for teaching undergraduate physics.

• Maple can provide step-by-step solutions for solving equations, differentiation, integration, inverting matrices, and more, and in Maple 2023, that collection has been further expanded to include implicit differentiation and completing the square.
• Maple 2023 adds a new option to the LongDivision command, which shows full solutions to long division problems, to include a summary line with the final answer including any remainders.
• A large collection of Classical Mechanics examples that align with popular textbooks make it very easy for instructors and students to focus on the important concepts rather than the algebraic manipulations. The material covers key topics including equations of motion, laws of conservation, canonical transformation, and rigid-body motion. 

Other improvements directly relevant to education are described elsewhere in this document. These include using the Plot Builder to create explorations of graphs, a quiz builder, and expanded tools and resources for creating and sharing interactive content with students.

Learn more...

A substantial effort was put into Graph Theory for Maple 2023, including improved ability to solve traveling salesman problems, support for multigraphs, new commands for graph computation, and advances in visualization.

• The TravelingSalesman command now makes use of Concorde, a well-known library implementing highly efficient heuristics for solving instances of the traveling salesman problem. This addition considerably increases the size of problems that TravelingSalesman is able to handle.
• The GraphTheory package now supports multigraphs, in which there may be multiple edges between the same pair of vertices.
• Additional graph product operations are now supported: conormal, lexicographic, modular, and strong.
• The collection of special graphs supported by the GraphTheory package has been further expanded (to 119 types of graphs!) with the addition of bouquet, dipole, Hamming, house, windmill, and bishop’s graphs.

Learn more...

The new Quantifier Elimination package offers a set of routines for quantifier elimination over the real numbers, as well as auxiliary tools for working with Tarski and other related formulae. Algorithms used by the package include Virtual Term Substitution, as well as Cylindrical Algebraic Decomposition using the Lazard projection with equational constraints, which is useful in quantifier elimination as well as in exploring real algebraic geometry. Lastly, a poly-algorithm offers a new way to use Virtual Term Substitution in conjunction with Cylindrical Algebraic Decomposition for both regular and incremental quantifier elimination.

Learn more...

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

• The Quantize command is used to replace real-valued data in a container with values from a codebook, and display the original and quantized signals together.
• The SavitzkyGolayFilter command applies the Savitzky-Golay filter to a signal, whose applications include smoothing noisy data and estimating derivatives of data. The filter is also known as Polynomial Smoothing, Least-Squares Smoothing, and Locally Weighted Scatterplot Smoothing (LOWESS).
• The Convolution command has been updated to include shape options full, same, and valid.
• The FFT and InverseFFT commands in the SignalProcessing package now support padding and truncation.
• Several commands in the SignalProcessing package, including DynamicTimeWarping and MUSIC, now use compiled C code and so run much faster.
• Most SignalProcessing commands can now be run natively on Silicon CPUs, greatly reducing the need to switch processors and often providing faster computations.

Learn more...

Maple provides a state-of-the-art environment for algebraic computations in physics, with emphasis on ensuring that the computational experience is as natural as possible. Maple 2023 provides many improvements that support both computation and physics education.

• Courseware support for undergraduate mechanics provides material for an extensive topic list, including equations of motion, conservation laws, oscillations, rigid body motion, and more. It contains typical symbolic problems and shows how they can be solved in Maple, demonstrating how computer algebra can support the learning activity.
• A new LagrangeEquations command receives an expression representing a Lagrangian and returns a sequence of Lagrange equations.
• A general Substitute command performs a wide variety of mathematical substitutions.
• New commands for factoring expressions provide more control over the final form of the factors.
• You can now use any symbol as a coordinate system label, not just single capital letters.
• Expanded documentation provides even more examples of how the package can be used in different scenarios.

Learn more...

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 2023, this toolbox has significant new features and enhancements.

• Search the scientific literature for new journal articles and preprints without leaving Maple.
• Explore algorithms and computations for quantum computers with the new QuantumComputing subpackage.
• Fly through a molecule or an orbital in 3-D with new fly-though molecular animations.
• Import molecular geometries and skeletal structures for nearly 100 million chemical structures using SMILES formulas.
• Customize your own Hamiltonian in variational calculations of the 2-RDM.
• Teach Fermi’s Golden rule using the latest addition to the collection of built-in lessons for classroom learning and self-study in undergraduate-to-graduate chemistry and physics.

Learn more...

• The underlying engine that solve uses for systems of linear equations with rational coefficients has been improved for many types of systems.
• When initializing hardware-float matrix, vector, and array data structures, Maple will now use hardware float computations whenever possible when computing the entries, resulting in dramatic speed-ups in initialization time in some cases.
• The Units package, and in particular the Units:-Simple subpackage, have received several upgrades that make them faster, sometimes several orders of magnitude faster.
• The new adaptive plotting engine, first introduced in Maple 2022, has been sped up significantly.
• The ThermophysicalData package, which contains functions for computing thermophysical, thermodynamic, and thermochemical properties, provides faster computations involving water and steam properties.
• The evalhf subsystem has been extended to handle all built-in (kernel) procedures that process arbitrary inputs and return hardware values, allowing a wider variety of code to be used inside evalhf.
• Importing comma-separated value (CSV) files on Windows is now faster.
• Two new commands, integerdivq2exp and integermul2exp, provide what are considered hardware bit-shift operations, and are fast methods for dividing or multiplying an integer by a power of 2. 

Learn more...

• The new OpenMaple API for Python is an interface for the Python programming language that allows you to perform Maple computations and access Maple algorithms and data structures from a Python session on the same machine. 
• Code Edit Regions can now be used to write and execute Python code from inside Maple more easily. When the Python language is set, the code edit region uses Python syntax highlighting, and when it is executed, the code is run using the underlying Python session associated with the Python package.
• The new OpenAPI package provides a way to automatically generate Maple packages to interface with HTTP APIs that conform to the REST (REpresentational State Transfer) architectural style, starting from an OpenAPI specification.

Learn more...