multiple algebraic extension
I'm looking for a way to formulate a number field which can express corners of a given regular $n$-gon exactly, but which might be faster than
AA. I need to be able to check signs of elements of that number field. Here is what I tried:
n = 17 z = QQbar.zeta(n) ca = z.real() sa = z.imag() QQ[ca, sa]
However I get the error message
ValueError: defining polynomial (x^16 - 17/4*x^14 + 119/16*x^12 - 221/32*x^10 + 935/256*x^8 - 561/512*x^6 + 357/2048*x^4 - 51/4096*x^2 + 17/65536) must be irreducible
How can I avoid this?