Suppose $K$ is a number field, $\mathfrak{m}$ is a modulus of $K$, and $\mathfrak{a}$ is a given fractional ideal of $K$. SAGE can compute the ray class group $Cl_{\mathfrak{m}}(K)$. However, how can I find what element of the ray class group $\mathfrak{a}$ corresponds to?
Suppose $K$ is a number field, $\mathfrak{m}$ is a modulus of $K$, and $\mathfrak{a}$ is a given fractional ideal of $K$. SAGE can compute the ray class group $Cl_{\mathfrak{m}}(K)$. However, how can I find what element of the ray class group $\mathfrak{a}$ corresponds to?to? More specifically, I need to find the order of $\mathfrak{a}$ in $Cl_{\mathfrak{m}}$.
I can do this in MAGMA only when $\mathfrak{m}=(1)$, but does anyone know of a way to do this in SAGE?