Revision history [back]

Let $B$ be the quaternion algebra over $\mathbb{Q}$ ramified at prime $p$ and $\infty$ and $\mathcal{O}\subset B$ be a maximal order. How do you compute all integral right ideals $I \subseteq \mathcal{O}$ of a given norm?

You know BrandtModule(p).hecke_matrix(l) returns l-Brandt matrix of B and we can draw the l-Brandt graph from it, then $\mathcal{O}$ is a vertex and there are $l+1$ integral right $\mathcal{O}$-ideals of norm $l$ representing each of edge from $\mathcal{O}$ in general. I'd like to compute these $\ell$-neighbors of $\mathcal{O}$.

Let $B$ be the quaternion algebra over $\mathbb{Q}$ ramified at prime $p$ and $\infty$ and $\mathcal{O}\subset B$ be a maximal order. How do you compute all integral right ideals $I \subseteq \mathcal{O}$ of a given norm?norm? Say $l$ is prime.

You know BrandtModule(p).hecke_matrix(l) returns l-Brandt matrix of B and we can draw the l-Brandt graph from it, then $\mathcal{O}$ is a vertex and there are $l+1$ integral right $\mathcal{O}$-ideals of norm $l$ representing each of edge from $\mathcal{O}$ in general. I'd like to compute these $\ell$-neighbors of $\mathcal{O}$.

Let $B$ be the quaternion algebra over $\mathbb{Q}$ ramified at prime $p$ and $\infty$ and $\mathcal{O}\subset B$ be a maximal order. How do you compute all integral right ideals $I \subseteq \mathcal{O}$ of a given norm? Say $l$ is prime.

Say $l$ is prime. You know BrandtModule(p).hecke_matrix(l) returns l-Brandt matrix of B and we can draw the l-Brandt graph from it, then $\mathcal{O}$ is a vertex and there are $l+1$ integral right $\mathcal{O}$-ideals of norm $l$ representing each of edge from $\mathcal{O}$ in general. I'd like to compute these $\ell$-neighbors of $\mathcal{O}$.

Let $B$ be the quaternion algebra over $\mathbb{Q}$ ramified at prime $p$ and $\infty$ and $\mathcal{O}\subset B$ be a maximal order. How do you compute all integral right ideals $I \subseteq \mathcal{O}$ of a given norm?

Say $l$ is prime. You know BrandtModule(p).hecke_matrix(l) returns l-Brandt $l$-Brandt matrix of B and we can draw the l-Brandt $l$-Brandt graph from it, then $\mathcal{O}$ is a vertex and there are $l+1$ integral right $\mathcal{O}$-ideals of norm $l$ representing each of edge from $\mathcal{O}$ in general. I'd like to compute these $\ell$-neighbors of $\mathcal{O}$.

Let $B$ be the quaternion algebra over $\mathbb{Q}$ ramified at prime $p$ and $\infty$ and $\mathcal{O}\subset B$ be a maximal order. How do you compute all integral right ideals $I \subseteq \mathcal{O}$ of a given norm?

Say $l$ is prime. You know BrandtModule(p).hecke_matrix(l) returns $l$-Brandt matrix of B and we can draw the $l$-Brandt graph from it, then $\mathcal{O}$ is a vertex and there are $l+1$ integral right $\mathcal{O}$-ideals of norm $l$ representing each of edge from $\mathcal{O}$ in general. I'd like to compute these $\ell$-neighbors $\l$-neighbors of $\mathcal{O}$.

Let $B$ be the quaternion algebra over $\mathbb{Q}$ ramified at prime $p$ and $\infty$ and $\mathcal{O}\subset B$ be a maximal order. How do you compute all integral right ideals $I \subseteq \mathcal{O}$ of a given norm?

Say $l$ is prime. You know BrandtModule(p).hecke_matrix(l) returns $l$-Brandt matrix of B and we can draw the $l$-Brandt graph from it, then $\mathcal{O}$ is a vertex and there are $l+1$ integral right $\mathcal{O}$-ideals of norm $l$ representing each of edge from $\mathcal{O}$ in general. I'd like to compute these $\l$-neighbors $l$-neighbors of $\mathcal{O}$.

Let $B$ be the quaternion algebra over $\mathbb{Q}$ ramified at prime $p$ and $\infty$ and $\mathcal{O}\subset B$ be a maximal order. How do you compute all integral right ideals $I \subseteq \mathcal{O}$ of a given norm?

Say $l$ is prime. You know BrandtModule(p).hecke_matrix(l) BrandtModule(p).hecke_matrix(l) returns $l$-Brandt matrix of B and we can draw the $l$-Brandt graph from it, then $\mathcal{O}$ is a vertex and there are $l+1$ integral right $\mathcal{O}$-ideals of norm $l$ representing each of edge from $\mathcal{O}$ in general. I'd like to compute these $l$-neighbors of $\mathcal{O}$.