From: Chris Dams <Chris.Dams@mi.infn.it>
Date: Thu, 1 Feb 2007 16:15:02 +0000 (+0000)
Subject: Added a proof for our new simplification rule for powers.
X-Git-Tag: release_1-4-0~35
X-Git-Url: https://www.ginac.de/ginac.git//ginac.git?a=commitdiff_plain;h=a35c58dffed76bd9991af62eb88aa1138782d0ef;p=ginac.git

Added a proof for our new simplification rule for powers.
---

diff --git a/doc/powerlaws.tex b/doc/powerlaws.tex
index 1943957a..ade0547d 100644
--- a/doc/powerlaws.tex
+++ b/doc/powerlaws.tex
@@ -151,7 +151,19 @@ Hence
 & = & x^{ab} \mbox{ q.e.d.}
 \end{eqnarray}
 
-proof contributed by Adam Strzebonski from Wolfram Research
-({\tt adams@wolfram.com}) in newsgroup {\tt sci.math.symbolic}.
+Proof contributed by Adam Strzebonski ({\tt adams@wolfram.com}) from
+Wolfram Research in newsgroup {\tt sci.math.symbolic}.
 
-\end{document}
\ No newline at end of file
+\subsubsection{$x$ positive, $a$ real and $b$ arbitrary complex}
+We have
+\begin{equation}
+(x^a)^b = e^{b\log e^{a\log x}}.
+\end{equation}
+Because $a$ is real and $x$ is positive, $a\log x$ is real. From this
+it follows that $\log e^{a\log x} = a\log x$. I.e, we see that
+\begin{equation}
+(x^a)^b = e^{ba\log x} = x^{ab}.
+\end{equation}
+Qed.
+
+\end{document}