# Revision history [back]

### (1-i)^(1/3),(1-i)^(1/4) is algebra interger?

I try http://www.wolframalpha.com/input/?i=Is+cbrt%281%2Bi%29+an+algebraic+integer%3F answer:UNKNOW

but sagemath :true,why?which is right?

Number Field in a with defining polynomial x^10 - 2*x^5 + 2 [0, 1, 0, 0, 0, 0, 0, 0, 0, 0] True 2 No.2 Revision

### (1-i)^(1/3),(1-i)^(1/4) is algebra interger?

I try http://www.wolframalpha.com/input/?i=Is+cbrt%281%2Bi%29+an+algebraic+integer%3F answer:UNKNOW

but sagemath :true,why?which is right?

K.

K.<a> = NumberField((x^3-1)^2+1);K;a.list();a.is_integral()  Number Field in a with defining polynomial x^6 - 2*x^3 + 2
[0, 1, 0, 0, 0, 0]
True
K. K.<a> = NumberField((x^4-1)^2+1);K;a.list();a.is_integral()  Number Field in a with defining polynomial x^8 - 2*x^4 + 2
[0, 1, 0, 0, 0, 0, 0, 0]
True
K. K.<a> = NumberField((x^5-1)^2+1);K;a.list();a.is_integral()  Number Field in a with defining polynomial x^10 - 2*x^5 + 2
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
TrueTrue 3 retagged FrédéricC 4815 ●3 ●39 ●101

### (1-i)^(1/3),(1-i)^(1/4) is algebra interger?

I try http://www.wolframalpha.com/input/?i=Is+cbrt%281%2Bi%29+an+algebraic+integer%3F answer:UNKNOW

but sagemath :true,why?which is right?

K.<a> = NumberField((x^3-1)^2+1);K;a.list();a.is_integral()

Number Field in a with defining polynomial x^6 - 2*x^3 + 2
[0, 1, 0, 0, 0, 0]
True
K.<a> = NumberField((x^4-1)^2+1);K;a.list();a.is_integral()

Number Field in a with defining polynomial x^8 - 2*x^4 + 2
[0, 1, 0, 0, 0, 0, 0, 0]
True
K.<a> = NumberField((x^5-1)^2+1);K;a.list();a.is_integral()

Number Field in a with defining polynomial x^10 - 2*x^5 + 2
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
True 4 retagged FrédéricC 4815 ●3 ●39 ●101

### (1-i)^(1/3),(1-i)^(1/4) is algebra interger?

I try http://www.wolframalpha.com/input/?i=Is+cbrt%281%2Bi%29+an+algebraic+integer%3F answer:UNKNOW

but sagemath :true,why?which is right?

K.<a> = NumberField((x^3-1)^2+1);K;a.list();a.is_integral()

Number Field in a with defining polynomial x^6 - 2*x^3 + 2
[0, 1, 0, 0, 0, 0]
True
K.<a> = NumberField((x^4-1)^2+1);K;a.list();a.is_integral()

Number Field in a with defining polynomial x^8 - 2*x^4 + 2
[0, 1, 0, 0, 0, 0, 0, 0]
True
K.<a> = NumberField((x^5-1)^2+1);K;a.list();a.is_integral()

Number Field in a with defining polynomial x^10 - 2*x^5 + 2
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0]
True