RegularChains[SemiAlgebraicSetTools]
RepresentingChain
return the regular chain part of a regular semi-algebraic set/system
Calling Sequence
Parameters
Description
Examples
RepresentingChain(rst, R)
RepresentingChain(rsas, R)
rst
-
a regular semi-algebraic set
rsas
a regular semi-algebraic system
R
a polynomial ring
The command RepresentingChain(rst, R) or the command RepresentingChain(rsas, 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.
withRegularChains:
withChainTools:
withParametricSystemTools:
withSemiAlgebraicSetTools:
f≔ax2+bx+c
F≔f
F≔ax2+bx+c
N≔
P≔
H≔
R≔PolynomialRingx,a,b,c
R≔polynomial_ring
d≔3
rrc≔RealRootClassificationF,N,P,H,d,1..n,R
rrc≔regular_semi_algebraic_set,border_polynomial
rst≔rrc11
rst≔regular_semi_algebraic_set
rc≔RepresentingChainrst,R
rc≔regular_chain
Inforc,R
F≔ax2+bx+c=0,0<x,a≠0
R≔PolynomialRingx,c,b,a
out≔LazyRealTriangularizeF,R,output=list
out≔regular_semi_algebraic_system
mapDisplay,out,R
ax2+bx+c=0x>0−4ca+b2>0andb<0andc>0anda≠0or−4ca+b2>0andb>0andc>0anda<0or−4ca+b2>0andb>0andc<0anda≠0or−4ca+b2>0andb<0andc<0anda>0
P≔PositiveInequalitiesout1,R
P≔x
rc≔RepresentingChainout1,R;Displayrc,R
ax2+bx+c=0a≠0
qff≔RepresentingQuantifierFreeFormulaout1;Displayqff,R
qff≔quantifier_free_formula
−4ca+b2>0andb<0andc>0anda≠0
or−4ca+b2>0andb>0andc>0anda<0
or−4ca+b2>0andb>0andc<0anda≠0
or−4ca+b2>0andb<0andc<0anda>0
Displayout1,R
See Also
IsParametricBox
PositiveInequalities
RealRootClassification
RegularChains
RepresentingBox
RepresentingQuantifierFreeFormula
RepresentingRootIndex
VariableOrdering
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