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
RegularChains[ConstructibleSetTools][Difference] - compute the difference of two constructible sets
RegularChains[SemiAlgebraicSetTools][Difference] - compute the difference of two semi-algebraic sets
Calling Sequence
Difference(cs1, cs2, R)
Difference(lrsas1, lrsas2, R)
Parameters
cs1, cs2
-
constructible sets
lrsas1
list of regular semi-algebraic systems
lrsas2
R
polynomial ring
Description
This command computes the set-theoretic difference of two constructible sets or two semi-algebraic sets, depending on the input type.
A constructible set must be encoded as an constructible_set object; see the type definition in ConstructibleSetTools.
A semi-algebraic set must be encoded by a list of regular_semi_algebraic_system, see the type definition of RealTriangularize.
The command Difference(cs1, cs2, R) returns a constructible set which is the set theoretic difference of two constructible sets. The polynomial ring may have characteristic zero or a prime characteristic.
The command Difference(lrsas1, lrsas2, R) returns a list of regular semi-algebraic systems, encoding the set-theoretic difference of two semi-algebraic sets. The polynomial ring must have characteristic zero.
The output may contain certain redundancy among the defining regular systems.
This command is available once RegularChains[ConstructibleSetTools] submodule or RegularChains[SemiAlgebraicSetTools] submodule have been loaded. It can always be accessed through one of the following long forms: RegularChains:-ConstructibleSetTools:-Difference or RegularChains:-SemiAlgebraicSetTools:-Difference.
Compatibility
The RegularChains[SemiAlgebraicSetTools][Difference] command was introduced in Maple 16.
The lrsas1 and lrsas2 parameters were introduced in Maple 16.
For more information on Maple 16 changes, see Updates in Maple 16.
Examples
First, define a polynomial ring.
Use Triangularize to solve the polynomial equations given by and below.
Now remove points which cancel the following .
First, build the common solution set of and as a constructible set and also build one with .
Then use Difference to find a new constructible set which encodes those points that cancel and , but do not cancel .
You can check the result using the Info command: cs2 consists of six points, and five of them cancel .
The set cs3 consists of a single point which does not cancel .
An example on semi-algebraic set difference: to check whether or not two formula/conditions are equivalent. # Semi-algebraic Difference, verifying results
Verify dec1 = dec2 as set of points by Difference.
See Also
ConstructibleSet, ConstructibleSetTools, GeneralConstruct, Intersection, IsContained, IsEmpty, MakePairwiseDisjoint, Projection, RealTriangularize
References
Chen, C.; Golubitsky, O.; Lemaire, F.; Moreno Maza, M.; and Pan, W. "Comprehensive Triangular Decomposition". Proc. CASC 2007, LNCS, Vol. 4770: 73-101. Springer, 2007.
Chen, C.; Davenport, J.-D.; Moreno Maza, M.; Xia, B.; and Xiao, R. "Computing with semi-algebraic sets represented by triangular decomposition". Proceedings of 2011 International Symposium on Symbolic and Algebraic Computation (ISSAC 2011), ACM Press, pp. 75--82, 2011.
Download Help Document
