# Revision history [back]

It should work:

sage: NumberField(x^8-2*x^7+4*x^5-4*x^4+3*x^2-2*x+1,'b').subfields()
[
(Number Field in b0 with defining polynomial x, Ring morphism:
From: Number Field in b0 with defining polynomial x
To:   Number Field in b with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
Defn: 0 |--> 0, None),
(Number Field in b1 with defining polynomial x^2 + 1, Ring morphism:
From: Number Field in b1 with defining polynomial x^2 + 1
To:   Number Field in b with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
Defn: b1 |--> -b^7 + 2*b^6 - 3*b^4 + 3*b^3 - 2*b + 1, None),
(Number Field in b2 with defining polynomial x^4 - 2*x^3 + x^2 + 1, Ring morphism:
From: Number Field in b2 with defining polynomial x^4 - 2*x^3 + x^2 + 1
To:   Number Field in b with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
Defn: b2 |--> -b^7 + 2*b^6 - 4*b^4 + 3*b^3 + b^2 - 2*b + 1, None),
(Number Field in b3 with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1, Ring morphism:
From: Number Field in b3 with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
To:   Number Field in b with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
Defn: b3 |--> b, Ring morphism:
From: Number Field in b with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
To:   Number Field in b3 with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
Defn: b |--> b3)
]


If your home is sufficiently large, i suggest to install your own recent version of Sagemath until your institution updates it. You do not need to have root access for that. What is the output of the following commands (from a terminal):

uname -a
cat /etc/issue


It should work:

sage: NumberField(x^8-2*x^7+4*x^5-4*x^4+3*x^2-2*x+1,'b').subfields()
[
(Number Field in b0 with defining polynomial x, Ring morphism:
From: Number Field in b0 with defining polynomial x
To:   Number Field in b with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
Defn: 0 |--> 0, None),
(Number Field in b1 with defining polynomial x^2 + 1, Ring morphism:
From: Number Field in b1 with defining polynomial x^2 + 1
To:   Number Field in b with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
Defn: b1 |--> -b^7 + 2*b^6 - 3*b^4 + 3*b^3 - 2*b + 1, None),
(Number Field in b2 with defining polynomial x^4 - 2*x^3 + x^2 + 1, Ring morphism:
From: Number Field in b2 with defining polynomial x^4 - 2*x^3 + x^2 + 1
To:   Number Field in b with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
Defn: b2 |--> -b^7 + 2*b^6 - 4*b^4 + 3*b^3 + b^2 - 2*b + 1, None),
(Number Field in b3 with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1, Ring morphism:
From: Number Field in b3 with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
To:   Number Field in b with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
Defn: b3 |--> b, Ring morphism:
From: Number Field in b with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
To:   Number Field in b3 with defining polynomial x^8 - 2*x^7 + 4*x^5 - 4*x^4 + 3*x^2 - 2*x + 1
Defn: b |--> b3)
]


If your home directory is sufficiently large, i suggest to install your own recent version of Sagemath until your institution updates it. You do not need to have root access for that. What is the output of the following commands (from a terminal):

uname -a
cat /etc/issue