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I want to compute the different ideal for $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$ where $\zeta_3$ is a $n$-th root of unity.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code?

I want to compute the different ideal for $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$ where $\zeta_3$ is a $n$-th root of unity.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code?

I want to compute the different ideal for $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$ where $\zeta_3$ $\zeta_n$ is a $n$-th root of unity.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code?

I want to compute the different ideal for $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$ where $\zeta_n$ is a $n$-th root of unity.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code?

I want to compute the different ideal $\mathfrak{d}$ for $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$ and check the formula of $N_{\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})} (\mathfrak{d})=\delta_{\mathfrak{d}}$ where $\zeta_n$ is a $n$-th root of unity.unity and $\delta_{\mathfrak{d}}$ is relative discriminat of $$\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code?

I want to compute the different ideal $\mathfrak{d}$ for $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$ and check the formula of $N_{\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})} (\mathfrak{d})=\delta_{\mathfrak{d}}$ where $\zeta_n$ is a $n$-th root of unity and $\delta_{\mathfrak{d}}$ $\Delta_{\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})}$ is relative discriminat of $$\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$.$\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code?

I want to compute the different ideal $\mathfrak{d}$ for $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$ and check the formula of $N_{\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})} (\mathfrak{d})=\delta_{\mathfrak{d}}$ (\mathfrak{d})=\Delta$ where $\zeta_n$ is a $n$-th root of unity and $\Delta_{\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})}$ $\Delta:=\Delta_{\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})}$ is relative discriminat of $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code?

Let $K/F$ be $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$. I want to compute the different ideal $\mathfrak{d}$ for $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$ $K/F$ and check the formula of $N_{\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})} $N_{K/F} (\mathfrak{d})=\Delta$ where $\zeta_n$ is a $n$-th root of unity and $\Delta:=\Delta_{\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})}$ $\Delta:=\Delta_{K/F}$ is relative discriminat of $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$.$K/F$.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code?

Let $K/F$ be $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$. I want to compute the different ideal $\mathfrak{d}$ for $K/F$ and check the formula of $N_{K/F} (\mathfrak{d})=\Delta$ (\mathfrak{d})=\Delta_{K/F}$ where $\zeta_n$ is a $n$-th root of unity and $\Delta:=\Delta_{K/F}$ $\Delta_{K/F}$ is relative discriminat of $K/F$.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code?

Let $K/F$ be $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$. I want to compute the different ideal $\mathfrak{d}$ for $K/F$ and check the formula of $N_{K/F} (\mathfrak{d})=\Delta_{K/F}$ where $\zeta_n$ is a $n$-th root of unity and $\Delta_{K/F}$ is the relative discriminat of $K/F$.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code?code for this and for original setting?

Let $K/F$ be $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$. I want to compute the different ideal $\mathfrak{d}$ for $K/F$ and check the formula of $N_{K/F} (\mathfrak{d})=\Delta_{K/F}$ where $\zeta_n$ is a $n$-th root of unity and $\Delta_{K/F}$ is the relative discriminat of $K/F$.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code for this and for original setting?

Let $K/F$ be $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$. I want to compute the different ideal $\mathfrak{d}$ for $K/F$ and check the formula of $N_{K/F} (\mathfrak{d})=\Delta_{K/F}$ where $\zeta_n$ is a $n$-th root of unity and $\Delta_{K/F}$ is the relative discriminat of $K/F$.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$.$(2\sqrt{-5})$ since $\Dalta_{\mathbb{Q}(\sqrt{-5})/\mathbb{Q}}=(20)$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code for this and for original setting?

Let $K/F$ be $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$. I want to compute the different ideal $\mathfrak{d}$ for $K/F$ and check the formula of $N_{K/F} (\mathfrak{d})=\Delta_{K/F}$ where $\zeta_n$ is a $n$-th root of unity and $\Delta_{K/F}$ is the relative discriminat of $K/F$.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$ since $\Dalta_{\mathbb{Q}(\sqrt{-5})/\mathbb{Q}}=(20)$.$\Delta_{\mathbb{Q}(\sqrt{-5})/\mathbb{Q}}=(20)$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code for this and for original setting?

Let $K/F$ be $\mathbb{Q}(\sqrt[3]{2},\zeta_3)/\mathbb{Q}(\sqrt[3]{2})$. I want to compute the different ideal $\mathfrak{d}$ for $K/F$ and check the formula of $N_{K/F} (\mathfrak{d})=\Delta_{K/F}$ where $\zeta_n$ is a $n$-th root of unity and $\Delta_{K/F}$ is the relative discriminat of $K/F$.

But, at first, I tried to compute one more easier case for $\mathbb{Q}(\sqrt{-5})/\mathbb{Q}$. It might be $(2\sqrt{-5})$ $\mathfrak{d}_{\mathbb{Q}(\sqrt{-5})/\mathbb{Q}}=(2\sqrt{-5})$ since $\Delta_{\mathbb{Q}(\sqrt{-5})/\mathbb{Q}}=(20)$.

My attempt is following:

x=polygen(ZZ, 'x')
K.<a>=NumberField(x^2+5)
gp(K.diff)

But this makes an error. Could you show me the correct code for this and for original setting?