Intersection - Maple Help
For the best experience, we recommend viewing online help using Google Chrome or Microsoft Edge.

Online Help

All Products    Maple    MapleSim


RegularChains

  

ConstructibleSetTools[Intersection]

  

compute the intersection of two constructible sets

  

SemiAlgebraicSetTools[Intersection]

  

compute the intersection of two semi-algebraic sets

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

Intersection(cs1, cs2, R)

Intersection(lrsas1, lrsas2, R)

Parameters

cs1, cs2

-

constructible sets

lrsas1, lrsas2

-

lists of regular semi-algebraic systems

R

-

polynomial ring

Description

• 

This command computes the set-theoretic intersection of two constructible sets, or two semi-algebraic set, depending on the input type of its arguments.

• 

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 in RealTriangularize.

• 

The command Intersection(cs1, cs2, R) returns the intersection of two constructible sets.  The polynomial ring may have characteristic zero or a prime characteristic.

• 

The command Intersection(lrsas1, lrsas2, R) returns the intersection of two semi-algebraic sets, encoded by list of regular_semi_algebraic_system. The polynomial ring must have characteristic zero.

• 

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:-Intersection or RegularChains:-SemiAlgebraicSetTools:-Intersection.

Examples

First, define the polynomial ring  and two polynomials of .

(1)

(2)

(3)

Using the GeneralConstruct command and adding one inequality, you can build a constructible set. Using the polynomials  and  for defining inequations, the two constructible sets cs1 and cs2 are different.

(4)

(5)

The intersection of cs1 and cs2 is a new constructible set cs.

(6)

Check the result in another way.

(7)

(8)

The results are as desired.

Consider now the semi-algebraic case:

(9)

(10)

(11)

(12)

Verify the results

(13)

(14)

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.

Compatibility

• 

The RegularChains[SemiAlgebraicSetTools][Intersection] command was introduced in Maple 16.

• 

The lrsas1 parameter was introduced in Maple 16.

• 

For more information on Maple 16 changes, see Updates in Maple 16.

See Also

Complement

ConstructibleSet

ConstructibleSetTools

Difference

GeneralConstruct

RealTriangularize

RegularChains

RegularChains

SemiAlgebraicSetTools

 


Download Help Document