Checking if elements are conjugates: is_conjugate

### 13.16.14 Checking if elements are conjugates: is_conjugate

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

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.

Examples.

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

  1

- Input:
  is_conjugate(circle(0,1),point((1+i)/2), line(1+i,2))
  Output:

  1

- Input:
  is_conjugate(circle(0,1), line(1+i,2), line((1+i)/2,0))
  Output:

  1

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.

- Input:
  is_conjugate(point(1+i),point(3+i),point(i),point(3/2+i))
  Output:

  1

- Input:
  is_conjugate(line(0,1+i),line(2,3+i),line(3,4+i),line(3/2,5/2+i))
  Output:

  1