スライドを作るときに、圏論・代数幾何でよく使いそうなLaTex記法を書き残しました。
もしネットからたどり着いた方がいらっしゃったら、お役立てください。
図(コードは下段!)：
![K_{LD} (p \vert \vert q) = \displaystyle \int q(x) \log \frac{q(x)}{p(x|D)} dx \\K_{LD} (p \vert \vert q) = 0 \\\zeta (z) = \int K_{LD} (p (x \vert \theta) \vert \vert q)^{z} p(\theta) d \theta \\E[F(D^n)] = \lambda \log n - (m-1) \log \log n + R(D^n) \\K_{LD} (p (x \vert D^n) \vert \vert q) = E[ \Delta F ] = E[ F(D^{n+1}) ] - E[F(D^n)] \\Y \longrightarrow X_N \longrightarrow \cdots \longrightarrow X \\\normalfont\textbf{Top} \longrightarrow \normalfont\textbf{Ab} \\\normalfont\textbf{Ring} \longrightarrow \normalfont\textbf{Top} \\\exists s \in \mathcal{F}(U) \quad s.t. \quad r_{U_{\lambda} \cap U_{\mu} , U_{\lambda}} (s_{\lambda}) = r_{U_{\lambda} \cap U_{\mu} , U_{\lambda}} (s_{\mu}) \\\mathcal{F}_p = \varinjlim_{p \in U} \mathcal{F}(U) \\\mathbb{C}[x_1, \dots , x_n] \\Spec \mathbb{C}[x_1, \dots , x_n] \\U(I(f)) = \{p \in Spec \mathbb{C}[x_1, \dots , x_n] \vert f \not\in p \} \\\mathcal{F}(U(I(f))) = \mathbb{C}(x_1, \dots , x_n) = \\\{ \displaystyle\frac{h_1}{h_2} \, \vert \, h_1, h_2 \in \mathbb{C}[x_1, \dots , x_n], h_2 \in U(I(f)) \} \\Spec \mathbb{C}[x_1, \dots , x_n] / I \\\mathbb{C}[x, y, z] / (x+z^2, y-z^3) \\\mathbb{C}[x, y] / (x^3 + y^2) \\\normalfont\textbf{Ring} \longrightarrow \normalfont\textbf{Af-Sch} \\Spec A \\Spec A/I \\(X, O_X) \\O^m_X = \bigoplus^m O_X \\O^m_X \rightarrow O^n_X \rightarrow \mathcal{F} \rightarrow 0 \\\Omega^1_X = d(O_X) \\\omega_X = \Omega^n_X \\](http://l.wordpress.com/latex.php?latex=K_%7BLD%7D%20%28p%20%5Cvert%20%5Cvert%20q%29%20%3D%20%5Cdisplaystyle%20%5Cint%20q%28x%29%20%5Clog%20%5Cfrac%7Bq%28x%29%7D%7Bp%28x%7CD%29%7D%20dx%20%5C%5CK_%7BLD%7D%20%28p%20%5Cvert%20%5Cvert%20q%29%20%3D%200%20%5C%5C%5Czeta%20%28z%29%20%3D%20%5Cint%20K_%7BLD%7D%20%28p%20%28x%20%5Cvert%20%5Ctheta%29%20%5Cvert%20%5Cvert%20q%29%5E%7Bz%7D%20p%28%5Ctheta%29%20d%20%5Ctheta%20%5C%5CE%5BF%28D%5En%29%5D%20%3D%20%5Clambda%20%5Clog%20n%20-%20%28m-1%29%20%5Clog%20%5Clog%20n%20%2B%20R%28D%5En%29%20%5C%5CK_%7BLD%7D%20%28p%20%28x%20%5Cvert%20D%5En%29%20%5Cvert%20%5Cvert%20q%29%20%3D%20E%5B%20%5CDelta%20F%20%5D%20%3D%20E%5B%20F%28D%5E%7Bn%2B1%7D%29%20%5D%20-%20E%5BF%28D%5En%29%5D%20%5C%5CY%20%5Clongrightarrow%20X_N%20%5Clongrightarrow%20%5Ccdots%20%5Clongrightarrow%20X%20%5C%5C%5Cnormalfont%5Ctextbf%7BTop%7D%20%5Clongrightarrow%20%5Cnormalfont%5Ctextbf%7BAb%7D%20%5C%5C%5Cnormalfont%5Ctextbf%7BRing%7D%20%5Clongrightarrow%20%5Cnormalfont%5Ctextbf%7BTop%7D%20%5C%5C%5Cexists%20s%20%5Cin%20%5Cmathcal%7BF%7D%28U%29%20%5Cquad%20s.t.%20%5Cquad%20r_%7BU_%7B%5Clambda%7D%20%5Ccap%20U_%7B%5Cmu%7D%20%2C%20U_%7B%5Clambda%7D%7D%20%28s_%7B%5Clambda%7D%29%20%3D%20r_%7BU_%7B%5Clambda%7D%20%5Ccap%20U_%7B%5Cmu%7D%20%2C%20U_%7B%5Clambda%7D%7D%20%28s_%7B%5Cmu%7D%29%20%5C%5C%5Cmathcal%7BF%7D_p%20%3D%20%5Cvarinjlim_%7Bp%20%5Cin%20U%7D%20%5Cmathcal%7BF%7D%28U%29%20%5C%5C%5Cmathbb%7BC%7D%5Bx_1%2C%20%5Cdots%20%2C%20x_n%5D%20%5C%5CSpec%20%5Cmathbb%7BC%7D%5Bx_1%2C%20%5Cdots%20%2C%20x_n%5D%20%5C%5CU%28I%28f%29%29%20%3D%20%5C%7Bp%20%5Cin%20Spec%20%5Cmathbb%7BC%7D%5Bx_1%2C%20%5Cdots%20%2C%20x_n%5D%20%5Cvert%20f%20%5Cnot%5Cin%20p%20%5C%7D%20%5C%5C%5Cmathcal%7BF%7D%28U%28I%28f%29%29%29%20%3D%20%5Cmathbb%7BC%7D%28x_1%2C%20%5Cdots%20%2C%20x_n%29%20%3D%20%5C%5C%5C%7B%20%5Cdisplaystyle%5Cfrac%7Bh_1%7D%7Bh_2%7D%20%5C%2C%20%5Cvert%20%5C%2C%20h_1%2C%20h_2%20%5Cin%20%5Cmathbb%7BC%7D%5Bx_1%2C%20%5Cdots%20%2C%20x_n%5D%2C%20h_2%20%5Cin%20U%28I%28f%29%29%20%5C%7D%20%5C%5CSpec%20%5Cmathbb%7BC%7D%5Bx_1%2C%20%5Cdots%20%2C%20x_n%5D%20%2F%20I%20%5C%5C%5Cmathbb%7BC%7D%5Bx%2C%20y%2C%20z%5D%20%2F%20%28x%2Bz%5E2%2C%20y-z%5E3%29%20%5C%5C%5Cmathbb%7BC%7D%5Bx%2C%20y%5D%20%2F%20%28x%5E3%20%2B%20y%5E2%29%20%5C%5C%5Cnormalfont%5Ctextbf%7BRing%7D%20%5Clongrightarrow%20%5Cnormalfont%5Ctextbf%7BAf-Sch%7D%20%5C%5CSpec%20A%20%5C%5CSpec%20A%2FI%20%5C%5C%28X%2C%20O_X%29%20%5C%5CO%5Em_X%20%3D%20%5Cbigoplus%5Em%20O_X%20%5C%5CO%5Em_X%20%5Crightarrow%20O%5En_X%20%5Crightarrow%20%5Cmathcal%7BF%7D%20%5Crightarrow%200%20%5C%5C%5COmega%5E1_X%20%3D%20d%28O_X%29%20%5C%5C%5Comega_X%20%3D%20%5COmega%5En_X%20%5C%5C&bg=FFFFFF&fg=00000&s=0 "K_{LD} (p \vert \vert q) = \displaystyle \int q(x) \log \frac{q(x)}{p(x|D)} dx \\K_{LD} (p \vert \vert q) = 0 \\\zeta (z) = \int K_{LD} (p (x \vert \theta) \vert \vert q)^{z} p(\theta) d \theta \\E[F(D^n)] = \lambda \log n - (m-1) \log \log n + R(D^n) \\K_{LD} (p (x \vert D^n) \vert \vert q) = E[ \Delta F ] = E[ F(D^{n+1}) ] - E[F(D^n)] \\Y \longrightarrow X_N \longrightarrow \cdots \longrightarrow X \\\normalfont\textbf{Top} \longrightarrow \normalfont\textbf{Ab} \\\normalfont\textbf{Ring} \longrightarrow \normalfont\textbf{Top} \\\exists s \in \mathcal{F}(U) \quad s.t. \quad r_{U_{\lambda} \cap U_{\mu} , U_{\lambda}} (s_{\lambda}) = r_{U_{\lambda} \cap U_{\mu} , U_{\lambda}} (s_{\mu}) \\\mathcal{F}_p = \varinjlim_{p \in U} \mathcal{F}(U) \\\mathbb{C}[x_1, \dots , x_n] \\Spec \mathbb{C}[x_1, \dots , x_n] \\U(I(f)) = \{p \in Spec \mathbb{C}[x_1, \dots , x_n] \vert f \not\in p \} \\\mathcal{F}(U(I(f))) = \mathbb{C}(x_1, \dots , x_n) = \\\{ \displaystyle\frac{h_1}{h_2} \, \vert \, h_1, h_2 \in \mathbb{C}[x_1, \dots , x_n], h_2 \in U(I(f)) \} \\Spec \mathbb{C}[x_1, \dots , x_n] / I \\\mathbb{C}[x, y, z] / (x+z^2, y-z^3) \\\mathbb{C}[x, y] / (x^3 + y^2) \\\normalfont\textbf{Ring} \longrightarrow \normalfont\textbf{Af-Sch} \\Spec A \\Spec A/I \\(X, O_X) \\O^m_X = \bigoplus^m O_X \\O^m_X \rightarrow O^n_X \rightarrow \mathcal{F} \rightarrow 0 \\\Omega^1_X = d(O_X) \\\omega_X = \Omega^n_X \\")
![O_X(-\mathcal{I}) = O_X / O_{\mathcal{I}} \\O_X(-\mathcal{I}) \, s.t. \, O_{\mathcal{I}} = O_X / O_X(-\mathcal{I}) \\\mathcal{I} \cdot O_X = g(f^* \mathcal{I}) \\Pic(X) = Div(X) / \sim \\O_X(D) = \prod O_X(div(h)) / \sim \\O_X(-\mathcal{D}) \\\mathcal{L} \, s.t. \, \mathcal{L} \vert_U = O^1_X \\(X, O_\mathcal{I}) \\\mathbb{P}^{n-1} \\\mathbb{P}^{m-1} \\\cong \mathbb{A}^{n} \\\mathbb{A}^{m} \\X \times \mathbb{P}^{n-1} \\D = \mu^* (X \backslash \{0\}) + E \\(a,b,c,d,e,f,g,h) \rightarrow (a,ab) \cup (cd^2,d) \cup (e^3f, e^2f) \cup (g^2h^3, gh^2) \\K_{Z_1} = (K_{X_1} + Z_1) \vert_{Z_1} \\= (\mu^*_1 K_X + E_1 + \mu^*_1 Z - 2 E_1) \vert_{Z_1} \\= (\mu^*_1 K_X + \mu^*_1 Z - E_1) \vert_{Z_1} \\= \mu^*_1((K_X + Z) \vert_{Z}) - 2P_1 \\= \mu^*_1 K_Z - 2P_1 \\K_{Z_{32}} = \mu^*_3 K_{Z_2} + \mu^{-1}_{3*} P_2 + \mu^{-1}_{3*} \mu^{-1}_{2*} P_1 + \mu^{-1}_{3*} \mu^{-1}_{2*} \mu^{-1}_{1*} P \\Y \displaystyle\xrightarrow[]{\mu_n} X_{n-1} \xrightarrow[]{\mu_{n-1}} \cdots \xrightarrow[]{\mu_1} X \\D_{n+1} = \mu^{-1}_{n+1*} D_{n} + E_{n+1} \leftarrow D_{n} \\D = D_1 + 2 D_2 + 3 D_3 \\K_X \in D/\sim, O_X(D), O_X(-D), Z \subset X \\\mathcal{F/G}(U) = \{ s \in \prod_{P \in U} (\mathcal{F/G})_P \} \\\mathcal{F}_{i-1} \longrightarrow \mathcal{F}_i \longrightarrow \mathcal{F}_{i+1} \\](http://l.wordpress.com/latex.php?latex=O_X%28-%5Cmathcal%7BI%7D%29%20%3D%20O_X%20%2F%20O_%7B%5Cmathcal%7BI%7D%7D%20%5C%5CO_X%28-%5Cmathcal%7BI%7D%29%20%5C%2C%20s.t.%20%5C%2C%20O_%7B%5Cmathcal%7BI%7D%7D%20%3D%20O_X%20%2F%20O_X%28-%5Cmathcal%7BI%7D%29%20%5C%5C%5Cmathcal%7BI%7D%20%5Ccdot%20O_X%20%3D%20g%28f%5E%2A%20%5Cmathcal%7BI%7D%29%20%5C%5CPic%28X%29%20%3D%20Div%28X%29%20%2F%20%5Csim%20%5C%5CO_X%28D%29%20%3D%20%5Cprod%20O_X%28div%28h%29%29%20%2F%20%5Csim%20%5C%5CO_X%28-%5Cmathcal%7BD%7D%29%20%5C%5C%5Cmathcal%7BL%7D%20%5C%2C%20s.t.%20%5C%2C%20%5Cmathcal%7BL%7D%20%5Cvert_U%20%3D%20O%5E1_X%20%5C%5C%28X%2C%20O_%5Cmathcal%7BI%7D%29%20%5C%5C%5Cmathbb%7BP%7D%5E%7Bn-1%7D%20%5C%5C%5Cmathbb%7BP%7D%5E%7Bm-1%7D%20%5C%5C%5Ccong%20%5Cmathbb%7BA%7D%5E%7Bn%7D%20%5C%5C%5Cmathbb%7BA%7D%5E%7Bm%7D%20%5C%5CX%20%5Ctimes%20%5Cmathbb%7BP%7D%5E%7Bn-1%7D%20%5C%5CD%20%3D%20%5Cmu%5E%2A%20%28X%20%5Cbackslash%20%5C%7B0%5C%7D%29%20%2B%20E%20%5C%5C%28a%2Cb%2Cc%2Cd%2Ce%2Cf%2Cg%2Ch%29%20%5Crightarrow%20%28a%2Cab%29%20%5Ccup%20%28cd%5E2%2Cd%29%20%5Ccup%20%28e%5E3f%2C%20e%5E2f%29%20%5Ccup%20%28g%5E2h%5E3%2C%20gh%5E2%29%20%5C%5CK_%7BZ_1%7D%20%3D%20%28K_%7BX_1%7D%20%2B%20Z_1%29%20%5Cvert_%7BZ_1%7D%20%5C%5C%3D%20%28%5Cmu%5E%2A_1%20K_X%20%2B%20E_1%20%2B%20%5Cmu%5E%2A_1%20Z%20-%202%20E_1%29%20%5Cvert_%7BZ_1%7D%20%5C%5C%3D%20%28%5Cmu%5E%2A_1%20K_X%20%2B%20%5Cmu%5E%2A_1%20Z%20-%20E_1%29%20%5Cvert_%7BZ_1%7D%20%5C%5C%3D%20%5Cmu%5E%2A_1%28%28K_X%20%2B%20Z%29%20%5Cvert_%7BZ%7D%29%20-%202P_1%20%5C%5C%3D%20%5Cmu%5E%2A_1%20K_Z%20-%202P_1%20%5C%5CK_%7BZ_%7B32%7D%7D%20%3D%20%5Cmu%5E%2A_3%20K_%7BZ_2%7D%20%2B%20%5Cmu%5E%7B-1%7D_%7B3%2A%7D%20P_2%20%2B%20%5Cmu%5E%7B-1%7D_%7B3%2A%7D%20%5Cmu%5E%7B-1%7D_%7B2%2A%7D%20P_1%20%2B%20%5Cmu%5E%7B-1%7D_%7B3%2A%7D%20%5Cmu%5E%7B-1%7D_%7B2%2A%7D%20%5Cmu%5E%7B-1%7D_%7B1%2A%7D%20P%20%5C%5CY%20%5Cdisplaystyle%5Cxrightarrow%5B%5D%7B%5Cmu_n%7D%20X_%7Bn-1%7D%20%5Cxrightarrow%5B%5D%7B%5Cmu_%7Bn-1%7D%7D%20%5Ccdots%20%5Cxrightarrow%5B%5D%7B%5Cmu_1%7D%20X%20%5C%5CD_%7Bn%2B1%7D%20%3D%20%5Cmu%5E%7B-1%7D_%7Bn%2B1%2A%7D%20D_%7Bn%7D%20%2B%20E_%7Bn%2B1%7D%20%5Cleftarrow%20D_%7Bn%7D%20%5C%5CD%20%3D%20D_1%20%2B%202%20D_2%20%2B%203%20D_3%20%5C%5CK_X%20%5Cin%20D%2F%5Csim%2C%20O_X%28D%29%2C%20O_X%28-D%29%2C%20Z%20%5Csubset%20X%20%5C%5C%5Cmathcal%7BF%2FG%7D%28U%29%20%3D%20%5C%7B%20s%20%5Cin%20%5Cprod_%7BP%20%5Cin%20U%7D%20%28%5Cmathcal%7BF%2FG%7D%29_P%20%5C%7D%20%5C%5C%5Cmathcal%7BF%7D_%7Bi-1%7D%20%5Clongrightarrow%20%5Cmathcal%7BF%7D_i%20%5Clongrightarrow%20%5Cmathcal%7BF%7D_%7Bi%2B1%7D%20%5C%5C&bg=FFFFFF&fg=00000&s=0 "O_X(-\mathcal{I}) = O_X / O_{\mathcal{I}} \\O_X(-\mathcal{I}) \, s.t. \, O_{\mathcal{I}} = O_X / O_X(-\mathcal{I}) \\\mathcal{I} \cdot O_X = g(f^* \mathcal{I}) \\Pic(X) = Div(X) / \sim \\O_X(D) = \prod O_X(div(h)) / \sim \\O_X(-\mathcal{D}) \\\mathcal{L} \, s.t. \, \mathcal{L} \vert_U = O^1_X \\(X, O_\mathcal{I}) \\\mathbb{P}^{n-1} \\\mathbb{P}^{m-1} \\\cong \mathbb{A}^{n} \\\mathbb{A}^{m} \\X \times \mathbb{P}^{n-1} \\D = \mu^* (X \backslash \{0\}) + E \\(a,b,c,d,e,f,g,h) \rightarrow (a,ab) \cup (cd^2,d) \cup (e^3f, e^2f) \cup (g^2h^3, gh^2) \\K_{Z_1} = (K_{X_1} + Z_1) \vert_{Z_1} \\= (\mu^*_1 K_X + E_1 + \mu^*_1 Z - 2 E_1) \vert_{Z_1} \\= (\mu^*_1 K_X + \mu^*_1 Z - E_1) \vert_{Z_1} \\= \mu^*_1((K_X + Z) \vert_{Z}) - 2P_1 \\= \mu^*_1 K_Z - 2P_1 \\K_{Z_{32}} = \mu^*_3 K_{Z_2} + \mu^{-1}_{3*} P_2 + \mu^{-1}_{3*} \mu^{-1}_{2*} P_1 + \mu^{-1}_{3*} \mu^{-1}_{2*} \mu^{-1}_{1*} P \\Y \displaystyle\xrightarrow[]{\mu_n} X_{n-1} \xrightarrow[]{\mu_{n-1}} \cdots \xrightarrow[]{\mu_1} X \\D_{n+1} = \mu^{-1}_{n+1*} D_{n} + E_{n+1} \leftarrow D_{n} \\D = D_1 + 2 D_2 + 3 D_3 \\K_X \in D/\sim, O_X(D), O_X(-D), Z \subset X \\\mathcal{F/G}(U) = \{ s \in \prod_{P \in U} (\mathcal{F/G})_P \} \\\mathcal{F}_{i-1} \longrightarrow \mathcal{F}_i \longrightarrow \mathcal{F}_{i+1} \\")
コード：
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K_{LD} (p \vert \vert q) = \displaystyle \int q(x) \log \frac{q(x)}{p(x|D)} dx \\ K_{LD} (p \vert \vert q) = 0 \\ \zeta (z) = \int K_{LD} (p (x \vert \theta) \vert \vert q)^{z} p(\theta) d \theta \\ E[F(D^n)] = \lambda \log n - (m-1) \log \log n + R(D^n) \\ K_{LD} (p (x \vert D^n) \vert \vert q) = E[ \Delta F ] = E[ F(D^{n+1}) ] - E[F(D^n)] \\ Y \longrightarrow X_N \longrightarrow \cdots \longrightarrow X \\ \normalfont\textbf{Top} \longrightarrow \normalfont\textbf{Ab} \\ \normalfont\textbf{Ring} \longrightarrow \normalfont\textbf{Top} \\ \exists s \in \mathcal{F}(U) \quad s.t. \quad r_{U_{\lambda} \cap U_{\mu} , U_{\lambda}} (s_{\lambda}) = r_{U_{\lambda} \cap U_{\mu} , U_{\lambda}} (s_{\mu}) \\ \mathcal{F}_p = \varinjlim_{p \in U} \mathcal{F}(U) \\ \mathbb{C}[x_1, \dots , x_n] \\ Spec \mathbb{C}[x_1, \dots , x_n] \\ U(I(f)) = \{p \in Spec \mathbb{C}[x_1, \dots , x_n] \vert f \not\in p \} \\ \mathcal{F}(U(I(f))) = \mathbb{C}(x_1, \dots , x_n) = \\ \{ \displaystyle\frac{h_1}{h_2} \, \vert \, h_1, h_2 \in \mathbb{C}[x_1, \dots , x_n], h_2 \in U(I(f)) \} \\ Spec \mathbb{C}[x_1, \dots , x_n] / I \\ \mathbb{C}[x, y, z] / (x+z^2, y-z^3) \\ \mathbb{C}[x, y] / (x^3 + y^2) \\ \normalfont\textbf{Ring} \longrightarrow \normalfont\textbf{Af-Sch} \\ Spec A \\ Spec A/I \\ (X, O_X) \\ O^m_X = \bigoplus^m O_X \\ O^m_X \rightarrow O^n_X \rightarrow \mathcal{F} \rightarrow 0 \\ \Omega^1_X = d(O_X) \\ \omega_X = \Omega^n_X \\ O_X(-\mathcal{I}) = O_X / O_{\mathcal{I}} \\ O_X(-\mathcal{I}) \, s.t. \, O_{\mathcal{I}} = O_X / O_X(-\mathcal{I}) \\ \mathcal{I} \cdot O_X = g(f^* \mathcal{I}) \\ Pic(X) = Div(X) / \sim \\ O_X(D) = \prod O_X(div(h)) / \sim \\ O_X(-\mathcal{D}) \\ \mathcal{L} \, s.t. \, \mathcal{L} \vert_U = O^1_X \\ (X, O_\mathcal{I}) \\ \mathbb{P}^{n-1} \\ \mathbb{P}^{m-1} \\ \cong \mathbb{A}^{n} \\ \mathbb{A}^{m} \\ X \times \mathbb{P}^{n-1} \\ D = \mu^* (X \backslash \{0\}) + E \\ (a,b,c,d,e,f,g,h) \rightarrow (a,ab) \cup (cd^2,d) \cup (e^3f, e^2f) \cup (g^2h^3, gh^2) \\ K_{Z_1} = (K_{X_1} + Z_1) \vert_{Z_1} \\ = (\mu^*_1 K_X + E_1 + \mu^*_1 Z - 2 E_1) \vert_{Z_1} \\ = (\mu^*_1 K_X + \mu^*_1 Z - E_1) \vert_{Z_1} \\ = \mu^*_1((K_X + Z) \vert_{Z}) - 2P_1 \\ = \mu^*_1 K_Z - 2P_1 \\ K_{Z_{32}} = \mu^*_3 K_{Z_2} + \mu^{-1}_{3*} P_2 + \mu^{-1}_{3*} \mu^{-1}_{2*} P_1 + \mu^{-1}_{3*} \mu^{-1}_{2*} \mu^{-1}_{1*} P \\ Y \displaystyle\xrightarrow[]{\mu_n} X_{n-1} \xrightarrow[]{\mu_{n-1}} \cdots \xrightarrow[]{\mu_1} X \\ D_{n+1} = \mu^{-1}_{n+1*} D_{n} + E_{n+1} \leftarrow D_{n} \\ D = D_1 + 2 D_2 + 3 D_3 \\ K_X \in D/\sim, O_X(D), O_X(-D), Z \subset X \\ \mathcal{F/G}(U) = \{ s \in \prod_{P \in U} (\mathcal{F/G})_P \} \\ \mathcal{F}_{i-1} \longrightarrow \mathcal{F}_i \longrightarrow \mathcal{F}_{i+1} \\ |
おまけ mathematicaコード
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ContourPlot[x^2+y^3==0, {x, -4,4}, {y, -4,4}] ParametricPlot3D[{{z^2,-z^3, z}, {z^2,-z^3, 0} }, {z, -1,1}] ContourPlot[x^2== y -y^3 / x^2, {x, -0.45, 0.45}, {y, -0.25, 0.25}] ContourPlot[1 + x^1*y^3==0, {x, -4,4}, {y, -4,4}] ContourPlot[x^2 + y^1==0, {x, -4,4}, {y, -4,4}] ContourPlot[x^1 + y^1==0, {x, -4,4}, {y, -4,4}] ContourPlot[1 + x^2*y^1==0, {x, -4,4}, {y, -4,4}] ContourPlot[1 + x^3*y^1==0, {x, -4,4}, {y, -4,4}] ContourPlot[(1 + x^1)*y^1==0, {x, -4,4}, {y, -4,4}] |