RegularChains[SemiAlgebraicSetTools] - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Factorization and Solving Equations : RegularChains : SemiAlgebraicSetTools Subpackage : RegularChains/SemiAlgebraicSetTools/RepresentingChain

RegularChains[SemiAlgebraicSetTools]

  

RepresentingChain

  

return the regular chain part of a regular semi-algebraic set/system

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

RepresentingChain(rst, R)

RepresentingChain(rsas, R)

Parameters

rst

-

a regular semi-algebraic set

rsas

-

a regular semi-algebraic system

R

-

a polynomial ring

Description

• 

The command RepresentingChain(rst, R) or the command RepresentingChain(rst, R) returns the regular chain part of its first argument.

  

See the page SemiAlgebraicSetTools for the definition of a regular semi-algebraic system and that of a regular semi-algebraic set.

Examples

withRegularChains:

withChainTools:

withParametricSystemTools:

withSemiAlgebraicSetTools:

fax2+bx+c

f:=ax2+bx+c

(1)

Ff

F:=ax2+bx+c

(2)

N

N:=

(3)

P

P:=

(4)

H

H:=

(5)

RPolynomialRingx,a,b,c

R:=polynomial_ring

(6)

d3

d:=3

(7)

rrcRealRootClassificationF,N,P,H,d,1..n,R

rrc:=regular_semi_algebraic_set,border_polynomial

(8)

rstrrc11

rst:=regular_semi_algebraic_set

(9)

rcRepresentingChainrst,R

rc:=regular_chain

(10)

Inforc,R

(11)

Fax2&plus;bx&plus;c&equals;0&comma;0<x&comma;a0

F:=ax2&plus;bx&plus;c&equals;0&comma;0<x&comma;a0

(12)

RPolynomialRingx&comma;c&comma;b&comma;a

R:=polynomial_ring

(13)

outLazyRealTriangularizeF&comma;R&comma;output&equals;list

out:=regular_semi_algebraic_system

(14)

mapDisplay&comma;out&comma;R

&lcub;ax2+bx+c=0x>0&lcub;4ca+b2>0andb<0andc>0anda0or4ca+b2>0andb>0andc>0anda<0or4ca+b2>0andb>0andc<0anda0or4ca+b2>0andb<0andc<0anda>0

(15)

PPositiveInequalitiesout1&comma;R

P:=x

(16)

rcRepresentingChainout1&comma;R&semi;Displayrc&comma;R

rc:=regular_chain

&lcub;ax2&plus;bx&plus;c&equals;0a0

(17)

qffRepresentingQuantifierFreeFormulaout1&semi;Displayqff&comma;R

qff:=quantifier_free_formula

4ca+b2>0andb<0andc>0anda0

or4ca+b2>0andb>0andc>0anda<0

or4ca+b2>0andb>0andc<0anda0

or4ca+b2>0andb<0andc<0anda>0

(18)

Displayout1&comma;R

&lcub;ax2+bx+c=0x>0&lcub;4ca+b2>0andb<0andc>0anda0or4ca+b2>0andb>0andc>0anda<0or4ca+b2>0andb>0andc<0anda0or4ca+b2>0andb<0andc<0anda>0

(19)

See Also

IsParametricBox

PositiveInequalities

RealRootClassification

RegularChains

RepresentingBox

RepresentingChain

RepresentingQuantifierFreeFormula

RepresentingRootIndex

VariableOrdering

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam