Maple Professional
Maple Academic
Maple Student Edition
Maple Personal Edition
Maple Player
Maple Player for iPad
MapleSim Professional
MapleSim Academic
Maple T.A. - Testing & Assessment
Maple T.A. MAA Placement Test Suite
Möbius - Online Courseware
Machine Design / Industrial Automation
Aerospace
Vehicle Engineering
Robotics
Power Industries
System Simulation and Analysis
Model development for HIL
Plant Modeling for Control Design
Robotics/Motion Control/Mechatronics
Other Application Areas
Mathematics Education
Engineering Education
High Schools & Two-Year Colleges
Testing & Assessment
Students
Financial Modeling
Operations Research
High Performance Computing
Physics
Live Webinars
Recorded Webinars
Upcoming Events
MaplePrimes
Maplesoft Blog
Maplesoft Membership
Maple Ambassador Program
MapleCloud
Technical Whitepapers
E-Mail Newsletters
Maple Books
Math Matters
Application Center
MapleSim Model Gallery
User Case Studies
Exploring Engineering Fundamentals
Teaching Concepts with Maple
Maplesoft Welcome Center
Teacher Resource Center
Student Help Center
DifferentialGeometry:-Tools[DGbifom, DGform, DGtensor, DGvector]
Calling Sequence
DGbiform(x, M)
DGform(x, M)
DGtensor(x, indexType, M)
DGvector(y, M)
Parameters
x
-
a positive integer, a list of positive integers, a coordinate variable, or a list of coordinate variables
M
(optional) the name of defined frame
indexType
specifying the index type of the tensor
y
a positive integer or a coordinate variable
Description
The command DGform will create a single term differential form. Let Theta = [theta_1, theta_2, theta_3, ...] denote the coframe for the current frame or, if the optional argument M is given, the frame M. The list Theta can be obtained from the command DGinfo with the keyword "frameBaseForms" or "frameJetForms". Let V = [x_1, x_2, x_3, ...] denote the local coordinates for the current frame or, if the optional argument M is given, the frame M. The list V can be obtained from the command DGinfo with the keyword "frameIndependentVariables" or "frameJetVariables". If the integer i or coordinate x_i is given, the command returns the corresponding 1-form theta_i. If a list of p integers [i, j, k, ...] or coordinates [x_i, x_j, x_k, ...] is given, the command returns the p-form theta_i &w theta_j &w theta_k...
The commands DGbiform, DGtensor, and DGvector work in a similar fashion.
The command DGform is part of the DifferentialGeometry:-Tools package and so can be used in the form DGform(...) only after executing the commands with(DifferentialGeometry) and with(Tools) in that order. It can always be used in the long form DifferentialGeometry:-Tools:-DGform. DGbiform, DGtensor, and DGvector work in the same way.
Examples
Example 1.
Define a manifold M with coordinates [x, y, z, w].
Example 2.
Define a rank 3 vector bundle E with coordinates [x, y, u, v, w] over a two dimensional base with coordinates [x, y].
Define the jet space J^2(R^2, R^2) for two functions u and v of 2 independent variables x and y.
See Also
DifferentialGeometry, Tools, evalDG, DGinfo, DGzip
Download Help Document