sentence-transformers How to use hyunjongkimmath/notation_linking_rag_sentence_transformers_all_MiniLM_L6_v2 with sentence-transformers:
from sentence_transformers import SentenceTransformer
model = SentenceTransformer("hyunjongkimmath/notation_linking_rag_sentence_transformers_all_MiniLM_L6_v2")
sentences = [
"latex_in_original_or_summarized: K(M, n)\n\n[SEP]\n\nsummarized: $K(M, n)$\n\n[SEP]\n\nmain_note_content: Chain complexes and spaces. [59], that for simplicial sheaf $\\text{X}$ we denote by $C_{*}(\\mathcal{X})$ the (normalized) chain complex $C_{*}(\\mathcal{A}$ associated to the sheaf abelian groups $\\mathbb{X}$. This defines a functor\n\n$$ C_{*}: \\Delta^{o p} S h v_{N i s}\\left(S m_{k}\\right) C_{*}(\\text{A} b(k)) $$$ ^f7eebc\n\nwhich is well (see $[44,59]$ instance) to have a right adjoint\n\n6.2 \\mathbb{A}^{1}$-Derived Category Spaces\n161\n\n$$ K: C_{*}(\\mathcal{A} b(k)) \\rightarrow \\phi^{o p} S h v_{N i s}\\left(S $$ \n\n\ncalled the space \n\nFor an abelian $M b(k)$ and an integer $n$ we define the pointed simplicial sheaf $K(M, n)$ (see [59, page 56]) $K$ to the shifted complex $M[n]$, the complex $M$ placed in degree 0 . If n< 0, the space $K(M, n)$ is a point. If $n \\geq 0$ then $K(M, n)$ has only one non-trivial sheaf which is the and which is canonically isomorphic to $M$. More generally, for a chain $C_{*}$, $K C_{*}$ has homotopy sheaf 0 $n< 0$, and the $n$-th homology sheaf $H_{n}\\left(C_{*}\\right)$ for $n \\geq 0$.\n\nIt is clear that $C_{*}: \\Delta^{o p} S h i s}\\left(S m_{k}\\right) \\rightarrow b(k))$ sends simplicial weak equivalences to quasi-isomorphisms and $K: C_{*}(A b(k)) \\rightarrow \\Delta^{o p} S h v_{N i s}\\left(S m_{k}\\right)$ maps quasi-isomorphisms to simplicial equivalences. If $C_{*}$ fibrant, it follows that $K\\left(C_{*}\\right)$ is simplicially Thus the two functors induce a pair of adjoint functors\n\n$$ C_{*}: \\mathcal{H}{s}(k) \\rightarrow D(\\mathcal{A} b(k)) $$ ^c4a825\n\n\n\n$$ K: D(\\mathrm{A} b(k)) \\rightarrow \\mathcal{H}_{s}(k) $$ \n\nAs a consequence it is clear that is an $\\mathscr{A}^{1}$-local complex, space $K\\left(C_{*}\\right)$ is an $\\mathbb{A}^{1}$-local space. Thus $C_{}: \\mathbf{H}_{s}(k) \\rightarrow maps $\\mathcal{A}^{1}$-weak to $\\mathrm{A}^{1}$-quasi and induces a functor\n\n \\rightarrow D_{\\mathbb{A}^{1}}(A b(k)) $$ \n\nwhich in concrete terms, maps a space $\\operatorname{X}$ to the $\\mathbb{A}^{1}$-localization of $C_{*}(\\mathcal{X})$. We denote the latter by $C_{*}^{A^{1}}(\\mathbb{X})$ and call it the $\\mathbb{A}^{1}$-chain of $\\mathcal{X}$. functor $C_{*}^{\\operatorname{A}^{1}}: \\mathfrak{H}(k) \\rightarrow b(k))$ admits as right adjoint the functor $K^{\\mathbb{A}^{1}}: D_{\\mathbb{A}^{1}}(\\mathcal{A} b(k)) \\rightarrow \\mathcal{H}(k)$ induced by $C_{*} \\mapsto K\\left(L_{\\mathbb{A}^{1}}\\left(C_{*}\\right)\\right)$. We that for an $\\mathbb{A}^{1}$-local complex the space $K\\left(C_{*}\\right)$ is automatically $\\mathbb{A}^{1}$-local and thus simplicially equivalent to the space \n\n\n[SEP]\n\nprocessed_content: the pointed simplicial where $M$ \\in b(k)$ and $n$ is integer. It is defined by applying to the complex $M[n]$, of the complex degree 0 .",
"latex_in_original_or_summarized: \\gamma_1=(m_1,N_1,a_1)\n\n[SEP]\n\nsummarized: $\\gamma_1=(m_1,N_1,a_1)$\n\n[SEP]\n\nmain_note_content: \\begin{notation}\\label{Dep1}\nLet $\\gamma_1=(m_1,N_1,a_1)$, $\\gamma_2=(m_2,N_2,a_2)$ be an ordered pair of \n(generalized) monodromy data which hypothesis (A). Assume that $m_1|m_2$.\nSet $d:=m_2/m_1$ and $r:=\\gcd(m_1, a_1(N_1))$. \nThen, \\eqref{Dep} to \n$\\epsilon=d(r-1)$ and $g_3=dg_1+g_2+\\epsilon$.\nIn particular, $\\epsilon=0$ if and if $r=1$. \n\\end{notation}\n\n\n[SEP]\n\nprocessed_content: ",
"latex_in_original_or_summarized: \\langle u\\rangle G W(F)\n\n[SEP]\n\nsummarized: $\\langle u\\rangle \\in G W(F)$\n\n[SEP]\n\nmain_note_content: Let us denote (in characteristic) by $G W(F)$ the Grothendieck-Witt ring of isomorphism classes of non-degenerate symmetric bilinear forms [48]: this is the group completion of the commutative monoid of isomorphism classes of non-degenerate symmetric forms for the direct sum.\n\nFor $u \\in F^{\\times}$, we denote by $\\langle u\\rangle G W(F)$ the form on vector space of rank one given by $F^{2} F,(x, \\mapsto u x y .$ By the results of loc. \\langle u\\rangle$ generate $G as a group. The following Lemma is (essentially) [48, Lemma (1.1) Chap. IV]:\n\n\n[SEP]\n\nprocessed_content: ",
"latex_in_original_or_summarized: $\\varepsilon_{\\infty}$\n\n[SEP]\n\nsummarized: $\\varepsilon_{\\infty}$\n\n[SEP]\n\nmain_note_content: To compute the genus of $X(\\kappa)$, further specialize to $\\Gamma_{1}=\\Gamma$ and $\\Gamma_{2}=$ $\\mathfrak{SL}_{2}(\\mathbb{Z}) . Let $y_{2}=\\mathrm{SL}_{2}(\\mathbb{Z}) i, y_{3}=\\mathrm{SL}_{2}(\\mathbb{Z}) \\mu_{3}$, and $y_{\\infty}=\\mathfrak{SL}_{2}(\\mathbb{Z}) \\infty$ be the elliptic point of period 2, the elliptic point of period 3, and the cusp of $X(1)=$ SL_{2}(\\mathbb{Z}) \\backslash \\mathcal{H}^{*} .$ Let $\\varepsilon_{2}$ and $\\varepsilon_{3}$ be the number of elliptic points of $\\Gamma$ in $f^{-1}\\left(y_{2}\\right)$$ and of^{-1}\\left(y_{3}\\right)$, i.e., the number of elliptic points of period 2 and 3 in $X(\\Gamma)$, and let $\\varepsilon_{\\infty}$ be the number of cusps of X(\\Gamma) .$ Then recalling that $d=\\operatorname{deg}(f)$ and letting $h=2$ or $h=3$, the formula for $d$ at the beginning of the section and then the formula for $e_{\\pi_{1}(\\tau)}$ at the nonelliptic points and the elliptic points over $\\mathrm{SL}_{2}(\\mathscr{Z}) y_{h}$ show that (Exercise 3.1.3(a))\n\n$$ d=\\sum_{x \\in f^{-1}\\left(y_{h}\\right)} e_{x}=h \\cdot\\left(\\left|f^{-1}\\left(y_{h}\\right)\\right|-\\varepsilon_{h}\\right)+1 \\cdot \\varepsilon_{h} $$\n\nand using these equalities twice gives\n$$ \\sum_{x \\in f^{-1}\\left(y_{h}\\right)}\\left(e_{x}-1\\right)=(h-1)\\left(\\left|f^{-1}\\left(y_{h}\\right)\\right|-\\varepsilon_{h}\\right)=\\frac{h-1}{h}\\left(d-\\varepsilon_{h}\\right) $$\n\n$68 \\quad 3$ Dimension Formulas\n\nAlso.\n$$ \\sum_{x \\in f^{-1}\\left(y_{\\infty}\\right)}\\left(e_{x}-1\\right)=d-\\varepsilon_{\\infty} $$\nSince $X(1)$ has genus 0, the Riemann-Hurwitz formula now shows\n\n\n[SEP]\n\nprocessed_content: "
]
embeddings = model.encode(sentences)
similarities = model.similarity(embeddings, embeddings)
print(similarities.shape)
# [4, 4] 
