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RootFinding

  

HasRealRoots

  

check for real roots

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

HasRealRoots(sys)

HasRealRoots(sys, vars)

Parameters

sys

-

list or set of polynomial equations with rational coefficients

vars

-

list of names; the indeterminates

Description

• 

The function HasRealRoots tests if the system of equations defined in sys has real roots.

• 

It returns a boolean, true if sys has real zeroes and false otherwise.

• 

The equations in sys must be polynomial with rational coefficients. Any polynomial p appearing in sys is interpreted as the equation p=0.

• 

When the list of names vars is provided, it must contain all the indeterminates appearing in sys. The order in the list is used for internal computations.

Examples

withRootFinding:

HasRealRootsx2+y2+2

false

(1)

HasRealRootsx2+y2,zx3,x,y,z

true

(2)

HasRealRootsx2+y122

true

(3)

HasRealRootsx44x2+4=1

false

(4)

See Also

Isolate

RootFinding

WitnessPoints

 


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