find the cell index of a given point
solution record, as returned by CellDecomposition
list of equations of the form parameter=rational number representing a point in parameter space
list of rational numbers representing a point in parameter space
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](..).
m ≔ CellDecomposition⁡x2+y2=a,x−y=b,0<a,x,y
m ≔ Equations=⁢x2+y2−a,x−y−bInequalities=⁢aFilter=⁢0≠1Variables=⁢x,yParameters=⁢a,bDiscriminantVariety=⁢a,−b2+2⁢aProjectionPolynomials=⁢b,a,−b2+2⁢aSamplePoints=⁢a=14,b=−1,a=1,b=−1,a=14,b=1,a=1,b=1
The point 12,1 lies on the discriminant variety and therefore not in any open cell.
The point −1,1 violates the inequality 0<a, and m does not contain any cells in the negative half plane for a.
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