XyJax Test Page


\[ \xymatrix{A \ar@{}[dr]|{=} \ar[d] \ar[r] & B \ar[d] \\ B \ar[r] & C } \] \[ \begin{xy} \xyimport(3.7, 3.7)(1.4, 1.4){\includegraphics[width=15em, height=15em]{ellip.png}} ,!D+<2pc, -1pc>*+!U\txt{Rathinal points on the elliptic curve: $x^3+y^3=7$.} ,(1,0)*+!U{1}, ,(-1,0)*+!U{-1} ,(0,1)*+!R{1}, ,(0,-1)*+!R{-1} ,(2,-1)*+!RU{P} ,(-1,2)*+!RU{-P} ,(1.3333,1.6667)*+!UR{-2P} ,(1.6667,1.3333)*!DL{\;2P} ,(-.5,1.9)*++!DL{3P} ,(1.9,-.5)*!DL{\;-3P} ,(-1,2.3)*+++!D{\infty}*=0{},{\ar+(-.2,.2)} ,(.5,2.3)*+++!D{\infty}*=0{},{\ar+(-.2,.2)} ,(2.3,-1)*+++!L{\infty}*=0{},{\ar+(.2,-.2)} \end{xy} \] \[ A\xymatrix{ (f_1)_*x_1 \ar[r]_a \ar[d]_{(f_1)_*b_1} & (f_2)_*x_2 \ar[d]^{(f_2)_*b_2} \\ (f_1)_*x'_1 \ar[r]^{a'} & (f_2)_*x'_2. }B \] \[ A\begin{xy} \xymatrix{ R \ar@<1ex>[r] \ar@<-1ex>[r] & U \ar[r]^{a} & F } \end{xy}B \]