query: Computing Class Group of $\mathbb{R}[x, y] / \langle x^2+y^2 -1 \rangle$
positive_passages.docid: 145630
positive_passages.text: What is the ideal class group of the ring $\mathbb{R}[x,y]/(x^2+y^2-1)$?
negative_passages.docid: 23517
negative_passages.text: Presentation $\langle x,y,z\mid xyx^{-1}y^{-2},yzy^{-1}z^{-2},zxz^{-1}x^{-2}\rangle$ of group equal to trivial group
negative_passages.docid: 134872
negative_passages.text: Generators of $\text{GL}_{2}(\mathbb{Z})$ group, good reference book?
negative_passages.docid: 98352
negative_passages.text: If $k|n$, then $D_{2n}/\langle{r^k}\rangle\cong D_{2k}$
negative_passages.docid: 9422
negative_passages.text: Computing the Galois group of polynomials $x^n-a \in \mathbb{Q}[x]$
negative_passages.docid: 60946
negative_passages.text: Find the matrix of $\langle f, g \rangle = \displaystyle\int_0^1 f(t) g(t) \, \mathrm dt$ with respect to the basis $\{1,t,\dots,t^n\}$
negative_passages.docid: 37414
negative_passages.text: Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$
negative_passages.docid: 87946
negative_passages.text: Proving that the unities of a ring form a group under multiplication
negative_passages.docid: 147158
negative_passages.text: Galois group of a non-separable polynomial
negative_passages.docid: 58135
negative_passages.text: Quotient group $SL(2,\mathbb{R})/SO(2,\mathbb{R})$
negative_passages.docid: 12698
negative_passages.text: Orthonormal basis for $\mathcal{L}^2([0,1])$
negative_passages.docid: 78075
negative_passages.text: Why can I apply $HS^\dagger$ and then measure in the computational basis to measure $Y$?
negative_passages.docid: 120594
negative_passages.text: $\mathbb Z[i]/ \langle 1+2i \rangle \cong \mathbb Z_5$
negative_passages.docid: 106911
negative_passages.text: Square root of $-1$ in the ring $\mathbb{R}[x]/\langle(x^2+1)^2\rangle$
negative_passages.docid: 122665
negative_passages.text: Help finding the fundamental group of $S^2 \cup \{xyz=0\}$
negative_passages.docid: 67768
negative_passages.text: How to determine the group structure of $E(\mathbb{R})$ for an elliptic curve $E/\mathbb{R}$
negative_passages.docid: 85299
negative_passages.text: computing the orbits for a group action