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2017-07-05 07:23:22 +0100 | asked a question | Plotting geodesics in $SL_2(\mathbb{Z})\backslash\mathbb{H}$ In here there are functions that allow to plot geodesics in the upper half plane (namely, half circles perpendicular to the x axis and vertical lines). Are there similar functions that do the same thing but only in the fundamental domain of $SL_2(\mathbb{Z})$, so that the geodesic is folded up into the domain $|x|<\frac{1}{2}$ and $x^2+y^2>1$? What I would like to have is something like the picture in page 5 of this paper. |

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2015-07-30 07:38:53 +0100 | asked a question | The lattice of number fields Let $L$ be some number field, and $\sigma_1,...,\sigma_{(r+s)}$ its embeddings in the real\complex field. Given an element $a$ in a $L$, how can I produce the vector $(\sigma_1(a),...,\sigma_{(r+s)}(a))$ , or better yet, is there a function returning the lattice embedding of $\mathcal{O}_L$ inside $\mathbb{R}^r \times \mathbb{C}^s $? Similarly, after computing the units group is there some function that returns $(\log |\sigma_i(u) |)$ for a given unit $u$ or the corresponding unit lattice? |

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