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I thought they are complex by default. But even when I try to force the domain to be complex, I always get x.conjugate().simplify() == x. Why? See also below:

sage: t1,t2,t4 = var("t1 t2 t4")
sage: t2.conjugate().simplify()
t2
sage: t1,t2,t4 = var("t1 t2 t4", domain="complex")
sage: t2
t2
sage: t2.is_real()
False
sage: t2.conjugate().simplify()
t2

I thought they are complex by default. But even when I try to force the domain to be complex, I always get x.conjugate().simplify() == x. Why? See also below:

sage: t1,t2,t4 = var("t1 t2 t4")
sage: t2.conjugate().simplify()
t2
sage: t1,t2,t4 = var("t1 t2 t4", domain="complex")
sage: t2
t2
sage: t2.is_real()
False
sage: t2.conjugate().simplify()
t2
sage: (t2.real()*2 - t2).simplify()
t2

I thought they are complex by default. But even when I try to force the domain to be complex, I always get x.conjugate().simplify() == x. Why? See also below:

sage: t1,t2,t4 = var("t1 t2 t4")
sage: t2.conjugate().simplify()
t2
sage: t1,t2,t4 = var("t1 t2 t4", domain="complex")
sage: t2
t2
sage: t2.is_real()
False
sage: t2.conjugate().simplify()
t2
sage: (t2.real()*2 - t2).simplify()
t2
sage: t2.real().simplify()
t2

I thought they are complex by default. But even when I try to force the domain to be complex, I always get x.conjugate().simplify() == x. Why? See also below:

sage: t1,t2,t4 = var("t1 t2 t4")
sage: t2.conjugate().simplify()
t2
sage: t1,t2,t4 = var("t1 t2 t4", domain="complex")
sage: t2
t2
sage: t2.is_real()
False
sage: t2.conjugate().simplify()
t2
sage: (t2.real()*2 - t2).simplify()
t2
sage: t2.real().simplify()
t2
sage: t2.imag().simplify()
0