Revision history [back]
 | 1 | initial version |
sage: Qp=pAdicField(7)
sage: R.<x>=Qp[]
sage: K.<a>=Qp.extension(x^2-5)
sage: OK=K.integer_ring()
sage: OK
7-adic Unramified Extension Ring in a defined by x^2 - 5
Note that 15 is a square in $\mathbb{Q}_p$, so $\mathbb{Q}_p(\sqrt{15})$ is just $\mathbb{Q}_p$.
| | 2 | No.2 Revision |
Note that 15 is a square in $\mathbb{Q}_p$, $\mathbb{Q}_7$, so $\mathbb{Q}_p(\sqrt{15})$ $\mathbb{Q}_7(\sqrt{15})$ is just $\mathbb{Q}_p$.$\mathbb{Q}_7$.
| | 3 | No.3 Revision |
| | 4 | No.4 Revision |
| | 5 | No.5 Revision |
| | 6 | No.6 Revision |
| | 7 | No.7 Revision |
| | 8 | No.8 Revision |
Try:
sage: Qp=pAdicField(7)
sage: R.<x>=Qp[]
sage: K.=Qp.extension(x^2-5)
K.<a>=Qp.extension(x^2-5)
sage: OK=K.integer_ring()
sage: OK
7-adic Unramified Extension Ring in a defined by x^2 - 55
Note that 15 is a square in $\mathbb{Q}_7$, so $\mathbb{Q}_7(\sqrt{15})$ is just $\mathbb{Q}_7$.
| | 9 | No.9 Revision |
Try:
sage: Qp=pAdicField(7)
sage: R.<x>=Qp[]
sage: K.<a>=Qp.extension(x^2-5)
sage: OK=K.integer_ring()
sage: OK
7-adic Unramified Extension Ring in a defined by x^2 - 5
Note that 15 is a square in $\mathbb{Q}_7$, so $\mathbb{Q}_7(\sqrt{15})$ $\mathbb{Q}_7(\sqrt{3}.\sqrt{5})$ is just $\mathbb{Q}_7$.$\mathbb{Q}_7(\sqrt{5})$.
| | 10 | No.10 Revision |
Try:
sage: Qp=pAdicField(7)
sage: R.<x>=Qp[]
sage: K.<a>=Qp.extension(x^2-5)
sage: OK=K.integer_ring()
sage: OK
7-adic Unramified Extension Ring in a defined by x^2 - 5
Note that 15 is a square in $\mathbb{Q}_7$, so $\mathbb{Q}_7(\sqrt{3}.\sqrt{5})$ $\mathbb{Q}_7(\sqrt{3},\sqrt{5})$ is just $\mathbb{Q}_7(\sqrt{5})$.
