[math-fun] conjugation of algebraic numbers

A curiosity: sqrt 6 + sqrt 10 + sqrt 15 is NOT a conjugate of - sqrt 6 - sqrt 10 - sqrt 15. The minimal polynomial of the first expression is X^4 - 62 X^2 - 240 X - 239. (Yet another property of 239.) On the other hand, sqrt 2 + sqrt 3 + sqrt 5 IS a conjugate of - sqrt 2 - sqrt 3 - sqrt 5. and the minimal polynomial is degree 8. Rich