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RootFinding[Parametric]

  

SampleSolutions

  

solve a system for given parameter values

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

SampleSolutions(m, s, options)

SampleSolutions(m, p, options)

SampleSolutions(m, k, options)

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

k

-

positive integer; the index of a cell

options

-

(optional) solver options, see RootFinding[Isolate] 

Description

• 

The SampleSolutions command computes all real solutions of the system

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

  

when the parameters are evaluated at the given point.

• 

Solutions are returned as a list of lists of equations of the form variable=number, or variable=[number,number] when the output=interval option is specified.

• 

The point can be specified in three different formats:

– 

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

– 

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

– 

as a cell index k, in which case the point is taken to be the kth sample point in m:-SamplePoints.

• 

Any optional arguments are passed directly to RootFinding[Isolate].

• 

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

Examples

withRootFinding[Parametric]:

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

m:-SamplePoints

a&equals;14&comma;b&equals;1&comma;a&equals;1&comma;b&equals;1&comma;a&equals;14&comma;b&equals;1&comma;a&equals;1&comma;b&equals;1

(1)

The following three calling sequences are equivalent:

SampleSolutionsm&comma;a&equals;1&comma;b&equals;1

x&equals;1.&comma;y&equals;0.&comma;x&equals;0.&comma;y&equals;1.

(2)

SampleSolutionsm&comma;1&comma;1

x&equals;1.&comma;y&equals;0.&comma;x&equals;0.&comma;y&equals;1.

(3)

SampleSolutionsm&comma;2

x&equals;1.&comma;y&equals;0.&comma;x&equals;0.&comma;y&equals;1.

(4)

You can request the output in the form of isolating intervals instead of floating-point approximations using the option output=interval recognized by RootFinding[Isolate].

SampleSolutionsm&comma;a&equals;1&comma;b&equals;1&comma;output&equals;interval

x&equals;1&comma;1&comma;y&equals;0&comma;0&comma;x&equals;0&comma;0&comma;y&equals;1&comma;1

(5)

Solve the non-parametric system by substituting parameter values not corresponding to a sample point, and by requesting 15 digits of precision instead of the default of 10.

SampleSolutionsm&comma;1&comma;12&comma;digits&equals;15

x&equals;0.411437827766148&comma;y&equals;0.911437827766148&comma;x&equals;0.911437827766148&comma;y&equals;0.411437827766148

(6)

See Also

CellDecomposition

Parametric

RootFinding

RootFinding[Isolate]

 


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