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geom3d

  

AreConjugate

  

test if a pair of points is conjugate with respect to a sphere

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

AreConjugate(A, B, s, cond)

Parameters

s

-

a sphere

A, B

-

two points

cond

-

(optional) name

Description

• 

Two points A and B are said to be conjugate with respect to the sphere s if the points of intersection P and Q divide A and B harmonically.

• 

The routine returns true if A and B are conjugate with respect to s; false if they are not; and FAIL if it is unable to reach a conclusion.

• 

If FAIL is returned, and the optional argument cond is given, the condition that makes the points conjugate is assigned to this argument.

• 

The command with(geom3d,AreConjugate) allows the use of the abbreviated form of this command.

Examples

withgeom3d:

For what values of ``a'' are the points (-a,2,a), (a,2,3) conjugate with respect to the sphere x2+y2+z26x+2y4z+4=0.

pointA,a,2,a,pointB,a,2,3:

spheres,x2+y2+z26x+2y4z+4=0,x,y,z:

AreConjugateA,B,s,cond

AreConjugate:   "unable to determine if -a^2+a is zero"

FAIL

(1)

cond

a2+a=0

(2)

Hence, the values of ``a'' are

solvecond

0,1

(3)

check:

assumecond

AreConjugateA,B,s

true

(4)

See Also

geom3d[HarmonicConjugate]

 


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