In particular, Maple 2021 includes several improvements to streamline the workflow when using Document Mode. In addition to the changes described elsewhere, Maple 2021 includes a variety of other enhancements to the interface that support your work in Maple. The new Student ODEs package covers the material in a standard first course in ODEs, and provides step-by-step tools for solving ODEs as well as interactive visualization.For ODEs and PDEs, the Lie Algebras of Vector Fields package has a new command for analyzing the possible linearization of polynomially nonlinear equations and determining the corresponding mapping when it exists, allowing for the computation of more approximate and exact solutions.The algorithms implemented are at the frontier of the understanding of this problem, and handle classes of extended equations with apparent singularities as well as the most common linear equations with four and five singularities. There are significant improvements in dsolve for finding exact solutions of second order linear ODEs using hypergeometric functions.In addition, Maple 2021 includes tools to help students just starting out with their first ODE course. Maple 2021 extends that lead even further with new algorithms and techniques for solving more ODEs and PDEs. Maple is the world leader in finding exact solutions to ordinary and partial differential equations. Two new commands in the Generic subpackage of the Linear Algebra package can be used for addition and scalar multiplication of matrices and vectors over a specified domain of computation.The Linear Recurrence Equations Tools package has been enhanced with the addition of several commands related to recurrence factorization and recognition, including GuessRecurrence, GCRD, LCLM, RightDivision, OperatorToRecurrence, RecurrenceToOperator, MinimalRecurrence, and others.The intsolve command has been updated to recognize some integral equations that contain integral transforms, and the method of collocation is now available to provide approximate solutions for certain types of integral equations.After a finite Galois field has been constructed using the GF package, there is now an easy syntax to create new field elements.The asympt command can now compute asymptotic expansions of the logarithmic integral.A new and faster algorithm for checking for redundant constraints is available when projecting a polyhedral set to a lower coordinate dimension using the Polyhedral Sets package.You can now numerically solve differential equations that are collected together in vectors, easily.
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A new Multivariate Power Series package provides functionality for doing lazy computations with multivariate power series at high speed and high precision.The limit command has been improved for the multivariate case of quotients of analytic functions, finding solutions to more problems than before.Integration has been enhanced with improved algorithms for indefinite integration, and the ability to easily specify which integration method should be used and to compare the results from different methods.