compute the union of two constructible sets - Maple Help

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RegularChains[ConstructibleSetTools][Union] - compute the union of two constructible sets

Calling Sequence

Union(cs1, cs2, R)

Parameters

cs1, cs2

-

constructible sets

R

-

polynomial ring

Description

• 

The command Union(cs1, cs2, R) returns a constructible set, the union of cs1 and cs2.

• 

There might be redundancy in the output.

• 

This command is part of the RegularChains[ConstructibleSetTools] package, so it can be used in the form Union(..) only after executing the command with(RegularChains[ConstructibleSetTools]).  However, it can always be accessed through the long form of the command by using RegularChains[ConstructibleSetTools][Union](..).

Examples

withRegularChains:

withConstructibleSetTools:

Define a polynomial ring R first.

R:=PolynomialRingx,y

R:=polynomial_ring

(1)

Consider the following polynomials of R.

F:=2x2+3xy+y23x3y

F:=2x2+3xy+y23x3y

(2)

G:=xy2x

G:=xy2x

(3)

H:=y3y

H:=y3y

(4)

Let cs1 be the solution set of F and G, and cs2 be the solution set of G and H.

cs1:=GeneralConstructF,G,1,R

cs1:=constructible_set

(5)

cs2:=GeneralConstructG,H,1,R

cs2:=constructible_set

(6)

Use the command Union to obtain the union of these two solution sets.

cs3:=Unioncs1,cs2,R:Infocs3,R

x2,y+1,1,x1,y1,1,x+1,y1,1,x,y3,1,x1,y+1,1,y1,1,y+1,1,x,y,1

y1,1,y+1,1,x,y,1,x,y3,1,x2,y+1,1,x1,y1,1,x1,y+1,1,x+1,y1,1

(7)

The Union command is not guaranteed to remove all the redundant components, for efficiency consideration.  Use the MakePairwiseDisjoint command to remove them.

cs3:=MakePairwiseDisjointcs3,R

cs3:=constructible_set

(8)

Infocs3,R

x,y3,1,x,y,1,y+1,1,y1,1

y1,1,y+1,1,x,y,1,x,y3,1

(9)

See Also

Complement, ConstructibleSet, ConstructibleSetTools, GeneralConstruct, Intersection, MakePairwiseDisjoint, RegularChains


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