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