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 | 1 | initial version |
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?)
| | 2 | No.2 Revision |
If you want the (smallest) number field containing the corners of the unit regular n-gon, you can do:
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?)
