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RootFinding[Parametric]

  

CellsWithSolutions

  

find all cells with a given number of real solutions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

CellsWithSolutions(m, k)

CellsWithSolutions(m, l..r)

Parameters

m

-

solution record, as returned by CellDecomposition

k,l

-

non-negative integers

r

-

non-negative integer or

Description

• 

The CellsWithSolutions(m,k) calling sequence returns the indices of all cells where the system

f=0,g>0fm:Equations,gm:Inequalities

  

has exactly k real solutions.

• 

The CellsWithSolutions(m,l..r) calling sequence returns the indices of all cells where the system above has between l and r (inclusive) real solutions.

• 

If there are no cells with the requested number of solutions, the empty list is returned.

• 

This command is part of the RootFinding[Parametric] package, so it can be used in the form CellsWithSolutions(..) 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][CellsWithSolutions](..).

Examples

withRootFinding[Parametric]:

mCellDecompositionx6+ay2b=0,ax2+y2bxy=0,x,y:

m:-SamplePoints

a=4,b=3,a=2,b=3,a=1,b=3,a=3,b=3,a=2,b=1,a=1,b=1,a=0,b=1,a=1,b=1,a=2,b=1,a=1,b=1,a=0,b=1,a=1,b=1,a=4,b=3,a=2,b=3,a=1,b=3,a=3,b=3

(1)

NumberOfSolutionsm

1,8,2,4,3,0,4,0,5,8,6,4,7,0,8,0,9,4,10,4,11,4,12,0,13,4,14,4,15,4,16,0

(2)

CellsWithSolutionsm,4

2,6,9,10,11,13,14,15

(3)

CellsWithSolutionsm,0..3

3,4,7,8,12,16

(4)

See Also

CellDecomposition

Parametric

RootFinding

 


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