# Revision history [back]

If you want the (smallest) number field containing the corners of the unit regular n-gon, you can do:

sage: F = CyclotomicField(n)

If you want the (smallest) number field containing real and imaginary parts of the first corner of the unit regular n-gon, you can do:

sage: F = number_field_elements_from_algebraics([ca, sa], minimal=True)
sage: F
(Number Field in a with defining polynomial y^16 - 17*y^14 + 119*y^12 - 442*y^10 + 935*y^8 - 1122*y^6 + 714*y^4 - 204*y^2 + 17,
[1/2*a^14 - 15/2*a^12 + 45*a^10 - 275/2*a^8 + 225*a^6 - 189*a^4 + 70*a^2 - 15/2,
1/2*a],
Ring morphism:
From: Number Field in a with defining polynomial y^16 - 17*y^14 + 119*y^12 - 442*y^10 + 935*y^8 - 1122*y^6 + 714*y^4 - 204*y^2 + 17
To:   Algebraic Real Field
Defn: a |--> 0.7224833323743059?)


If you want the (smallest) number field containing the corners of the unit regular n-gon, you can do:

sage: F = CyclotomicField(n)CyclotomicField(n)


If you want the (smallest) number field containing real and imaginary parts of the first corner of the unit regular n-gon, you can do:

sage: F = number_field_elements_from_algebraics([ca, sa], minimal=True)
sage: F
(Number Field in a with defining polynomial y^16 - 17*y^14 + 119*y^12 - 442*y^10 + 935*y^8 - 1122*y^6 + 714*y^4 - 204*y^2 + 17,
[1/2*a^14 - 15/2*a^12 + 45*a^10 - 275/2*a^8 + 225*a^6 - 189*a^4 + 70*a^2 - 15/2,
1/2*a],
Ring morphism:
From: Number Field in a with defining polynomial y^16 - 17*y^14 + 119*y^12 - 442*y^10 + 935*y^8 - 1122*y^6 + 714*y^4 - 204*y^2 + 17
To:   Algebraic Real Field
Defn: a |--> 0.7224833323743059?)