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[GenerateForms]
Calling Sequence
GenerateForms(Omega, deg)
Parameters
Omega
-
a list of lists of differential 1-forms
deg
a list of positive integers
Description
Let Omega = [Omega_1, Omega_2, Omega_3, ...] and let deg = [p_1, p_2, p_3, ...]. Then GenerateForm(Omega, deg) returns a list of differential forms of degree p = p_1 + p_2 + p_3 + ..., where each form omega in the list is of the form omega = omega_1 &w omega_2 &w omega_3 .... and where omega_i is a p_i-fold wedge product of forms in Omega_i.
The command GenerateForms is part of the DifferentialGeometry:-Tools package, and so can be used in the form GenerateForms(...) only after executing the commands with(DifferentialGeometry) and with(Tools) in that order. It can always be used in the long form DifferentialGeometry:-Tools:-GenerateForms.
Examples
Define a 6-dimensional manifold M with coordinates [x1, x2, y1, y2, y3, z1]. (This choice of coordinate names is simply to help understand the output of the commands that follow).
Example 1.
Find all 2 -forms generated from [dy1, dy2, dy3].
Example 2.
Find all 2-forms obtained by choosing 1 from [dx1, dx2] and 1 from [dy1, dy2, dy3].
Example 3.
Find all 5-forms obtained by choosing 2 from [dx1, dx2] and 3 from [dy1, dy2, dy3].
Example 4.
Find all 3-forms obtained by choosing 1 from [dx1, dx2], 1 from [dy1, dy2], and 1 from [dz1].
See Also
DifferentialGeometry, Tools, JetCalculus, GenerateSymmetricTensors
Download Help Document