1off echo,msg; 2 3\documentstyle{article} 4\begin{document} 5\begin{displaymath} 6\frac{a^{5}+5 a^{4} b+10 a^{3} b^{2}+10 a^{2} b^{3}+5 a b^{4}+b^{5}}{a^{4}-4 a 7^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}} 8\end{displaymath} 9\begin{displaymath} 10x=a^{3}+3 a^{2} b+3 a b^{2}+b^{3} 11\end{displaymath} 12\begin{displaymath} 13\left\{ 14a^{3}+3 a^{2} b+3 a b^{2}+b^{3} , 3 \left(a^{2}+2 a b+b^{2}\right) , 6 \left(a 15+b\right) 16\right\} 17\end{displaymath} 18\begin{displaymath} 19\left\{ 20\left\{ 21a , a^{3}+3 a^{2} b+3 a b^{2}+b^{3} 22\right\} , a^{3}+3 a^{2} b+3 a b^{2}+b^{3} 23\right\} 24\end{displaymath} 25\begin{verbatim} 26REDUCE Input: 27 28solve(a^7-13*a+5); 29 30 31Unknown: a 32 33\end{verbatim} 34\begin{displaymath} 35\left\{ 36a={\rm root\_of} \left(a\_^{7}-13 a\_+5,a\_,tag\_1\right) 37\right\} 38\end{displaymath} 39\begin{verbatim} 40REDUCE Input: 41 42solve(a**(2*y)-3*a**y+2,y); 43 44 45\end{verbatim} 46\begin{displaymath} 47\left\{ 48y=\left(2 {\rm arbint} _{2} i \pi +\log \,2\right)/\log \,a , y=\left(2 49{\rm arbint} _{1} i \pi \right)/\log \,a 50\right\} 51\end{displaymath} 52\begin{verbatim} 53REDUCE Input: 54 55off verbatim; 56 57 58\end{verbatim} 59\begin{displaymath} 603 \left(\frac{{\rm d}^{2}a}{{\rm d}c^{2}} a^{2}+2 \frac{{\rm d}^{2}a}{{\rm d}c 61^{2}} a b+\frac{{\rm d}^{2}a}{{\rm d}c^{2}} b^{2}+2 \left(\frac{{\rm d}\,a}{ 62{\rm d}\,c}\right)^{2} a+2 \left(\frac{{\rm d}\,a}{{\rm d}\,c}\right)^{2} b 63\right) 64\end{displaymath} 65\begin{displaymath} 66\cos ^{2}\,\alpha +\sin ^{2}\,\alpha =1 67\end{displaymath} 68\begin{displaymath} 69\sin \left(\alpha +\beta \right)=\cos \,\alpha \: \sin \,\beta \:+\cos \, 70\beta \: \sin \,\alpha \: 71\end{displaymath} 72\begin{displaymath} 73\frac{\partial \,{\bf \tilde{u}}^{e}}{\partial \,t}+c \frac{\partial ^{2}{\bf 74\tilde{u}}^{e}}{\partial x^{2}}+b \frac{\partial \,{\bf \tilde{u}}^{i}}{ 75\partial \,x}={\bf f}^{e} 76\end{displaymath} 77\begin{displaymath} 78\frac{{\bf \tilde{u}}^{e}_{j+1,k}-{\bf \tilde{u}}^{e}_{jk}}{\delta \,t}+c 79\frac{{\bf \tilde{u}}^{e}_{j,k+1}-2 {\bf \tilde{u}}^{e}_{jk}+{\bf \tilde{u}}^{ 80e}_{j,k-1}}{\delta ^{2}\,x}+b \frac{{\bf \tilde{u}}^{i}_{j,k+1/2}-{\bf \tilde{ 81u}}^{i}_{j,k-1/2}}{\delta \,x}={\bf f}^{e} 82\end{displaymath} 83\begin{verbatim} 84REDUCE Input: 85 86product(k=1,2*n+1,f(2*i k+1)\(i(2*k+1)-1)); 87 88 89\end{verbatim} 90\begin{displaymath} 91\prod _{k=1}^{2 n+1}\frac{{\bf f}^{2 i_{k}+1}}{i_{2 k+1}-1} 92\end{displaymath} 93\begin{verbatim} 94REDUCE Input: 95 96int(u(e,j,k,x)*f(e,x),x); 97 98 99\end{verbatim} 100\begin{displaymath} 101\int {\bf \tilde{u}}^{e}_{jk}\left(x\right) {\bf f}^{e}\left(x\right)\:d\,x 102\end{displaymath} 103\begin{verbatim} 104REDUCE Input: 105 106sum(i=0,n,sqrt u(e,i)); 107 108 109\end{verbatim} 110\begin{displaymath} 111\sum _{i=0}^{n}\sqrt {{\bf \tilde{u}}^{e}_{i}} 112\end{displaymath} 113\begin{verbatim} 114REDUCE Input: 115 116off latex,verbatim; 117 118 119\end{verbatim} 120\end{document} 121 122Tested on x86_64-pc-windows CSL 123Time (counter 1): 0 ms plus GC time: 16 ms 124 125End of Lisp run after 0.00+0.06 seconds 126real 0.21 127user 0.04 128sys 0.06 129