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