reduce-historical/r38/log/rlfi.rlg

Tue Apr 15 00:34:22 2008 run on win32
off echo,msg;

\documentstyle{article}
\begin{document}
\begin{displaymath}
\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
^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}}
\end{displaymath}
\begin{displaymath}
x=a^{3}+3 a^{2} b+3 a b^{2}+b^{3}
\end{displaymath}
\begin{displaymath}
\left\{
a^{3}+3 a^{2} b+3 a b^{2}+b^{3} , 3 \left(a^{2}+2 a b+b^{2}\right) , 6 \left(a
+b\right)
\right\}
\end{displaymath}
\begin{displaymath}
\left\{
\left\{
a , a^{3}+3 a^{2} b+3 a b^{2}+b^{3}
\right\} , a^{3}+3 a^{2} b+3 a b^{2}+b^{3}
\right\}
\end{displaymath}
\begin{verbatim}
REDUCE Input:

solve(a^7-13*a+5);


Unknown: a

\end{verbatim}
\begin{displaymath}
\left\{
a={\rm root\_of} \left(a\_^{7}-13 a\_+5,a\_,tag\_1\right)
\right\}
\end{displaymath}
\begin{verbatim}
REDUCE Input:

solve(a**(2*y)-3*a**y+2,y);


\end{verbatim}
\begin{displaymath}
\left\{
y=\left(2 {\rm arbint} _{2} i \pi +\log \,2\right)/\log \,a , y=\left(2 
{\rm arbint} _{1} i \pi \right)/\log \,a
\right\}
\end{displaymath}
\begin{verbatim}
REDUCE Input:

off verbatim;


\end{verbatim}
\begin{displaymath}
3 \left(\frac{{\rm d}^{2}a}{{\rm d}c^{2}} a^{2}+2 \frac{{\rm d}^{2}a}{{\rm d}c
^{2}} a b+\frac{{\rm d}^{2}a}{{\rm d}c^{2}} b^{2}+2 \left(\frac{{\rm d}\,a}{
{\rm d}\,c}\right)^{2} a+2 \left(\frac{{\rm d}\,a}{{\rm d}\,c}\right)^{2} b
\right)
\end{displaymath}
\begin{displaymath}
\cos ^{2}\,\alpha +\sin ^{2}\,\alpha =1
\end{displaymath}
\begin{displaymath}
\sin \left(\alpha +\beta \right)=\cos \,\alpha \: \sin \,\beta \:+\cos \,
\beta \: \sin \,\alpha \:
\end{displaymath}
\begin{displaymath}
\frac{\partial \,{\bf \tilde{u}}^{e}}{\partial \,t}+c \frac{\partial ^{2}{\bf 
\tilde{u}}^{e}}{\partial x^{2}}+b \frac{\partial \,{\bf \tilde{u}}^{i}}{
\partial \,x}={\bf f}^{e}
\end{displaymath}
\begin{displaymath}
\frac{{\bf \tilde{u}}^{e}_{j+1,k}-{\bf \tilde{u}}^{e}_{jk}}{\delta \,t}+c 
\frac{{\bf \tilde{u}}^{e}_{j,k+1}-2 {\bf \tilde{u}}^{e}_{jk}+{\bf \tilde{u}}^{
e}_{j,k-1}}{\delta ^{2}\,x}+b \frac{{\bf \tilde{u}}^{i}_{j,k+1/2}-{\bf \tilde{
u}}^{i}_{j,k-1/2}}{\delta \,x}={\bf f}^{e}
\end{displaymath}
\begin{verbatim}
REDUCE Input:

product(k=1,2*n+1,f(2*i k+1)\(i(2*k+1)-1));


\end{verbatim}
\begin{displaymath}
\prod _{k=1}^{2 n+1}\frac{{\bf f}^{2 i_{k}+1}}{i_{2 k+1}-1}
\end{displaymath}
\begin{verbatim}
REDUCE Input:

int(u(e,j,k,x)*f(e,x),x);


\end{verbatim}
\begin{displaymath}
\int {\bf \tilde{u}}^{e}_{jk}\left(x\right) {\bf f}^{e}\left(x\right)\:d\,x
\end{displaymath}
\begin{verbatim}
REDUCE Input:

sum(i=0,n,sqrt u(e,i));


\end{verbatim}
\begin{displaymath}
\sum _{i=0}^{n}\sqrt {{\bf \tilde{u}}^{e}_{i}}
\end{displaymath}
\begin{verbatim}
REDUCE Input:

off latex,verbatim;


\end{verbatim}
\end{document}


Time for test: 6 ms, plus GC time: 8 ms