Checking whether elements are conjugates

### 25.15.14 Checking whether elements are conjugates

The is_conjugate command determines whether or not two objects are conjugates of each other.

- To check for conjugates with respect to a circle, is_conjugate takes three arguments:
  - C, a circle.
  - P,Q, each of which is a point or a line.
- is_conjugate(C,P,Q) returns 1 if P and Q are conjugate with respect to C, otherwise it returns 0.
- To check for conjugates with respect to two points or two lines, is_conjugate takes three arguments:
  - L1,L2, two lines or two points.
  - P,Q, each of which is a point or a line.
- is_conjugate(L1,L2,P,Q) returns 1 if P and Q are conjugate with respect to L1 and L2, otherwise it returns 0.

#### Examples

is_conjugate(circle(0,1+i),point(1-i),point(3+i))

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is_conjugate(circle(0,1),point((1+i)/2),line(1+i,2))

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is_conjugate(circle(0,1),line(1+i,2),line((1+i)/2,0))

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is_conjugate(point(1+i),point(3+i),point(i),point(3/2+i))

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is_conjugate(line(0,1+i),line(2,3+i),line(3,4+i),line(3/2,5/2+i))

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