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

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RegularChains[SemiAlgebraicSetTools][RepresentingChain] - return the regular chain part of a regular semi-algebraic set/system

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:

f:=ax2+bx+c

f:=ax2+bx+c

(1)

F:=f

F:=ax2+bx+c

(2)

N:=

N:=

(3)

P:=

P:=

(4)

H:=

H:=

(5)

R:=PolynomialRingx,a,b,c

R:=polynomial_ring

(6)

d:=3

d:=3

(7)

rrc:=RealRootClassificationF,N,P,H,d,1..n,R

rrc:=regular_semi_algebraic_set,border_polynomial

(8)

rst:=rrc11

rst:=regular_semi_algebraic_set

(9)

rc:=RepresentingChainrst,R

rc:=regular_chain

(10)

Inforc,R

(11)

F:=ax2&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)

R:=PolynomialRingx&comma;c&comma;b&comma;a

R:=polynomial_ring

(13)

out:=LazyRealTriangularizeF&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)

P:=PositiveInequalitiesout1&comma;R

P:=x

(16)

rc:=RepresentingChainout1&comma;R&semi;Displayrc&comma;R

rc:=regular_chain

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

(17)

qff:=RepresentingQuantifierFreeFormulaout1&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


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