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.Visualization improvements in Maple 2023 include enhanced plotting tools and significant performance enhancements. In Maple 2023, this package can now deal with multivariate Puiseux series and univariate polynomials over multivariate Puiseux series. The MultivariatePowerSeries package deals with multivariate power series in a lazy fashion, meaning that extra terms for a given result can be computed quickly.The collocation method in intsolve has been improved, resulting in more and better approximations to solutions of integral equations.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 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.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 IntegerHull command in the PolyhedralSets package has been extended to support both bounded and unbounded higher dimensional polyhedral sets.The simplify command has been significantly improved, with a particular focus on trigonometric simplification.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.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 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. Assumption handling for integration has been enhanced.It is now possible to directly call the integration by parts routine Parts and a parallel version of the Risch algorithm ParallelRisch, if desired. The int command now exposes more internal routines for indefinite integration through the method option.This technique results in much simpler, much more compact answers to integration problems that are easier to understand and work with. This improvement is achieved through the use of the Blake’s heuristic method, which expresses some algebraic integrands in more elementary forms. 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.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 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.
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