RootFinding[Parametric] - Maple Programming Help

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RootFinding[Parametric]

  

CellLocation

  

find the cell index of a given point

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

CellLocation(m, s)

CellLocation(m, p)

Parameters

m

-

solution record, as returned by CellDecomposition

s

-

list of equations of the form parameter=rational number representing a point in parameter space

p

-

list of rational numbers representing a point in parameter space

Description

• 

The CellLocation command returns a non-negative integer, the index of the open cell in which the point lies, or 0 if the point does not lie in any of the open cells of m.

• 

The CellLocation command determines the cell of m in which the given point lies.

• 

The point can be specified in two different formats:

– 

as a list s of equations of the form parameter=rational number, or

– 

as a list p of rational numbers, in which case the ith parameter in m:-Parameters gets replaced by pi, for all i.

• 

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

Examples

withRootFinding[Parametric]:

mCellDecompositionx2&plus;y2&equals;a&comma;xy&equals;b&comma;0<a&comma;x&comma;y

m:=Equations&equals;x2+y2a&comma;xybInequalities&equals;aFilter&equals;01Variables&equals;x&comma;yParameters&equals;a&comma;bDiscriminantVariety&equals;a&comma;b2+2aProjectionPolynomials&equals;b&comma;a&comma;b2+2aSamplePoints&equals;a=14&comma;b=−1&comma;a=1&comma;b=−1&comma;a=14&comma;b=1&comma;a=1&comma;b=1

(1)

CellPlotm&comma;&apos;samplepoints&apos;

CellLocationm&comma;a&equals;12&comma;b&equals;3

3

(2)

CellLocationm&comma;1&comma;1

2

(3)

The point 12&comma;1 lies on the discriminant variety and therefore not in any open cell.

CellLocationm&comma;a&equals;12&comma;b&equals;1

0

(4)

The point 1&comma;1 violates the inequality 0<a, and m does not contain any cells in the negative half plane for a.

CellLocationm&comma;1&comma;1

0

(5)

See Also

CellDecomposition

CellPlot

Parametric

RootFinding

 


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