Physics Features in Maple - Physics Software

Updates to the Physics Package

Substantial improvements to the Physics Package are made continually!

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Download the Latest Updates to the Maple Physics Package

The current version of Maple includes the latest official release of Physics, and improvements are ongoing. You can take advantage of this ongoing work by downloading the research version of Physics as it is updated with improvements, fixes, and the very latest new developments.

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Vector Analysis	Quantum state vector calculus (Dirac’s notation)
Projected vectors Non-projected abstract vectors Cartesian, cylindrical, and spherical algebraic unit vectors Projected vectorial differential operators (e.g. Nabla) Abstract vectorial differential operators Scalar and cross product operators for vectors that handle projected and abstract vectors Differentiation taking into account relationships between geometrical coordinates Supporting vectorial routines for changing basis, representing components of abstract vectors, etc.	Anticommutative and noncommutative variables and functions Bras and Kets Projectors Annihilation/Creation operators Orthonormal discrete and continuous bases Hermitian and non-Hermitian operators, possibly tensorial Pauli and Dirac matrices including their commutator algebras and the computation of traces of products Commutators and anticommutators Customizable commutator and anticommutator algebra rules Simplification taking everything into account (fixed and customizable algebra rules, Einstein's sum rule, etc.)
Tensor Analysis (n-dimensional Geometry, Special and General Relativity)	Field Theories (Classical and Quantum)
User defined tensors (under addition, multiplication, differentiation, simplification, and transformation of coordinates) Distinction between covariant and contravariant indices User defined systems of coordinates, possibly many at the same time Coordinate transformation of tensorial expressions taking into account covariant and contravariant indices Computation of components of arbitrary tensorial expressions Determination of free and repeated indices, simplification and differentiation using Einstein's sum rule Complete set of general relativity tensors Searchable database of solutions to Einstein's equations	Ability to represent Lagrangians and Hamiltonians involving anticommutative and noncommutative variables, functions and operators Ability to compute field equations using standard and functional differentiation Ability to compute the analytic structure of the Feynman Diagrams of a model
Product Operators	Differentiation Operators
Standard multiplication operator (*) handling commutative, anticommutative and noncommutative variables in equal footing Automatic normal form for products involving commutative, anticommutative, and noncommutative variables Scalar and cross product operators for 3-D vectors and vectorial functions or vectorial differential operators Scalar product operator for Bras and Kets and related quantum state (Dirac notation) vector calculus	Differentiation with respect to anticommutative variables, scalar and tensor functions Functional differentiation with respect to commutative and anticommutative scalar and tensor functions The d’Alembertian , the galilean and covariant tensorial differentiation operators
Differential Equations Support	Differential Geometry Support
Computation of Poincare sections for dynamical systems Reducing, triangularizing, and/or solving DE systems, possibly involving anticommutative variables and functions Symmetry analysis for ODEs and PDEs, possibly including anticommutative variables and functions	Calculus on manifolds (vector fields, differential forms and transformations) Tensor analysis in advanced general relativity Calculus on jet spaces Lie algebras Lie and transformation groups Computations can be performed in user-specified frames Computations can be performed with abstract differential forms (coordinate-free)