Maple

Most computations in science and engineering, as well as many other applications, are done using quantities that have units associated with them. Maple has many tools to help you keep track of your units and avoid the problems that come from getting them wrong. Maple 2018 provides substantial improvements to unit support in Maple, with even deeper integration of units with the Maple computation engine, as well as improved interface tools for attaching and converting units to your quantities.

• More top level computation functions can now accept expressions involving units as arguments, and return results that include in the appropriate unit information:
  • Solve equations numerically or symbolically (fsolve, solve)
  • Solve optimization problems using a variety of solvers (Optimization package)
  • Solve integrals numerically or symbolically (int)
• When working with units, the solve command returns solutions faster, gives more meaningful error messages, and gives you finer control over the units in the result by allowing you to explicitly specify the units of symbolic parameters.
• The units formatting dialog has been redesigned and moved to the context panel, so it can be accessed more easily, and fewer mouse clicks are required for each unit change.
• Unit and numeric formatting can now be done much more efficiently through the context panel rather than by navigating through two different dialogs.
• The list of suggested unit conversions offers better choices.
• Suggested unit conversions are now presented using standard math notation so they are more recognizable.

Maple offers several different approaches that enable you to share your work without allowing full access to your work. New in Maple 2018 is the ability to encrypt your procedures, which provides a way to share executable procedures with others while protecting your IP.

• An encrypted procedure acts and behaves like any normal procedure in Maple, but its definition cannot be viewed.
• Encrypted procedures are shared through library archive files (.mla) so the user never has access to the original source.
• Viewing the encrypted procedure, for example using eval or print, results in only the display of the encrypted definition.
• The debugger cannot be used to step through encrypted procedures.

In addition to the many mathematical advances detailed elsewhere, Maple 2018 also includes improvements across many other areas of the mathematics engine.

• More integration problems can be solved because of enhancements made to several different solving methods.
• The simplify command is more powerful, with improvements to dealing with logarithms, exponentials, trigonometric expressions, and more.
• When working with assumptions, the is and coulditbe commands both offer improved handling of inequalities, and is also performs more simplifications and takes into account more function properties.
• The sum command has been improved for the case of hypergeometric sums with more than one parameter.
• Generalized polylogarithms, multiple polylogarithms, and multiple zeta functions were added as high level functions.
• Two new commands for performing and testing weighted homogenization were added to the Polynomial Tools package.
• The signum command, the sign function for real and complex expressions, can now handle more problems.
• The Re and Im commands handle more problems than before.
• The max and min commands can now recognize some numbers as real even though they are composed from nonreal ingredients.
• The commands sturm and sturmseq have been extended to support polynomials with real algebraic number coefficients.
• The arctan command now performs more automatic simplifications, and the combine command performs more simplifications on arctan functions.

With a new Calendar package, Maple 2018 makes it easier to work with dates and times, such as analyzing time-dependent data, or calculating the flight duration to your next conference.

• New fundamental Maple objects represent dates, times, and clocks.
• Arithmetic with dates and times is built in, so you can, for example, compute the duration between two dates by subtracting them.
• Time zones and daylight savings time are supported.
• Built-in operations include computing the day of week of a given date, determining if a given date falls on a weekend, calculating the Julian day number, and more.
• The Finance package has been extended so that it can work with date objects seamlessly.

• Properties are available for over 2000 gases, liquids, and crystalline species.
• The data can be to study chemical equilibrium composition, reaction constants and spontaneity, rocket performance, flame temperatures, explosion and detonation pressures, and many other applications.

Each Maple release includes speed and efficiency improvements that make Maple run faster. Performance improvements in Maple 2018 include both broad-based and targeted enhancements. The following operations are all faster in Maple 2018:

• Fundamental operations involving Gröbner bases. Gröbner bases lie at the heart of many higher level computations in Maple, such as solving systems of equations and integration, so performance improvements in Gröbner bases result in faster calculations in many areas of Maple. Maple 2018 includes new optimizations that increase parallel speedup when computing large total degree Gröbner bases. In tests, the new implementation runs 33 percent faster and parallel speedup increases from 1.94x to 2.84x. Maple 2018 also includes a new implementation of the FGLM algorithm for converting total degree Gröbner bases to lexicographical order, with improved performance and lower memory requirements.
• Replacing variables in polynomials with products using subs.
• Type checking tests for detecting polynomials and rational functions, a step found in many math engine algorithms.
• New algorithms for solving sparse linear equations mod p.
• Satisfiability tests in the Logic package.
• Finding the inverse of a matrix whose entries involve trigonometric functions.
• The timelimit command, which is useful for putting a time bound on a computation, now has virtually no overhead.

Maple 2018 includes a new set of drawing tools you can use to annotate images, generate diagrams, and more, all programmatically. These tools are in addition to the interactive drawing tools already available with the Drawing Canvas.

• Supports lines, multi-segment lines, closed shapes, rectangles, circles, and text as drawing primitives.
• Can be used to create images from scratch or add to an existing image.
• Provides control over color, thickness, fill color, line style, fill style, and the appearance of segment ends.
• Allows tapered lines between two points.
• Supports the combination of drawing operations with other image manipulation techniques.
• Uses continuous mathematical coordinates, not discrete pixels.
• Renders using anti-aliasing.
• Enables text annotations using a variety of character sets and customizations, including ASCII, Greek, Cyrillic, many Japanese characters, and a large collection of symbols, with control over font, font size, color, rotation, weight and more.

• In addition to providing code generation to Python, Maple now provides access to a Python interpreter, so you can execute Python scripts and get the results, all within Maple.
• The OpenMaple API for Java includes several new commands, including tools to convert numeric objects to BigInteger and BigDecimal, handling relations such as equalities and inequalities, and representing sets.
• A new Deep Learning package provides an API to a subset of the TensorFlow toolset for machine learning using neural networks.
• File handing tools now include a CanonicalPath command that returns a file path that is independent of the value of the current directory, in which any symbolic links and special directories have been resolved.
• The MapleTA package can now convert IMS Question & Test Interoperability (QTI) files into Maple T.A. and Möbius course modules.
• XML Tools has a new command that formats an XML tree as a nested record.

In addition to substantial improvements to the code editor, Maple 2018 also includes many other enhancements to its language and programming tools.

• You can now add an until clause to loop structures, allowing many variations of a do-while loop.
• The code analysis tool mint, which works on text files, and maplemint, for use inside Maple, have both been improved and consolidated. As a result, maplemint now works on modules and reports a wider class of warnings, and the external tool mint now provides additional warnings.
• The select, remove, and selectremove commands can now perform substitutions in-place with arrays, matrices, vectors, tables, and objects, simplifying many common use cases involving these functions.
• Assignments can now be used as, or embedded within, expressions.
• The String Tools package can decode and encode strings with HTML entities.
• The new SameStructure command compares the value and structure of two expressions.
• The Random Tools package provides new options, including the ability to generate random variable names.

In addition to the new context panel, code editor improvements, tools for encrypting and protecting your content, and other changes detailed elsewhere in this document, Maple 2018 also includes a variety of smaller interface changes that further streamline your workflow. Enhancements include:

• Reorganized and consolidated top level menus that make it easier to find what you need.
• Command completion that helps you enter a string that specifies the path to a file.
• New shortcut keys for opening, navigating, using, and exiting the Maple Help Browser.