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Calling Sequence
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CellDescription(m, k)
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Parameters
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Description
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The CellDescription command returns a list of lists of the form where
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p and q are polynomials in the parameters
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i and j are non-negative integers
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The CellDescription() calling sequence returns a description of the th cell in in terms of real roots of some projection polynomials.
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The solution record m must have been computed with the option output=cad or without using the output keyword.
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Each inner list, , in the result is to be interpreted as follows: the -coordinate of a point lying in the interior of the th cell is greater than the th real root of the polynomial and less than the th real root of the polynomial .
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If an inner list is of the form , then this means that the -coordinate is unbounded from above, and similarly, if an inner list is of the form , then the -coordinate is unbounded from below.
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The polynomials and in each inner list contain only the parameters from the current and all earlier lists. So the polynomials in the first inner list are univariate, the ones in the second inner list are bivariate, etc.
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The result, [[], [], ...], can be used to sample a cell as follows: Compute the th real root of the univariate polynomial and the th real root of the univariate polynomial (for example, using RootFinding[Isolate]), and pick a value for the -coordinate between those two roots. Then substitute that value of into and , turning these into univariate polynomials in . In the same way as above, compute their th and th roots, respectively, and pick a value for the -coordinate in between those two roots. Continue in a similar fashion.
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This command is part of the RootFinding[Parametric] package, so it can be used in the form CellDescription(..) 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][CellDescription](..).
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Examples
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This result is to be interpreted as follows: a point in the parameter space belongs to the th cell if and only if
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is greater than the st (and only) real root of , that is, ; and
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is greater than the first (and only) real root of and less than the first (and only) real root of , that is,
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Similarly, a point belongs to the th cell if and only if
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