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changed: -The resulting SymPy expression is: - -\begin{verbatim} -print e -\end{verbatim} The resulting SymPy expression is:: print e
Running SymPy in a SageBlockSymPy initialization:
\begin{sageblock} #sys.path.append("/home/page/sympy") import sympy # the follow command is only needed because we are running SymPy inside Sage Integer = int \end{sageblock}
We are running SymPy version: $\sage{sympy.__version__}$
First simple confidence test:
\begin{sageblock} from sympy import Symbol a=Symbol(
a
) b=Symbol(b
) c=Symbol(c
) e=( abb+2bab )*c \end{sageblock}The resulting SymPy expression is:
print e\begin{equation} \label{eq1} \sage{e} \end{equation}
Limits
Here is a simple limit in SymPy?
This used to work by now it fails in sympy-0.5.3.
test:
\begin{sageblock} from sympy import limit x = Symbol("x") e=limit((3**(1/x)+5**(1/x))**x, x, 0) \end{sageblock}and the result is:
\begin{equation} \sage{e} \end{equation}Unfortunately for this limit Axiom gives: $\sage{axiom(
limit((3**(1/x)+5**(1/x))**x, x=0)::OutputForm
)}$.And Maxima gives: $\sage{maxima(
limit((3**(1/x)+5**(1/x))**x, x, 0)
)}$.So the Axiom and Maxima developers have some more work to do!
But worse, Reduce actually gets it wrong... \begin{reduce} limit((3(1/x)+5(1/x))**x, x,0); \end{reduce}
question about limit --robert.dodier, Fri, 20 Apr 2007 15:22:26 -0500 replyHello, about this limit problem, limit((3^(1/x) + 5^(1/x))^x, x, 0), I seem to find that the limit is different depending on whether 0 is approached from above or below. (I get 5 as the limit from above, and 3 as the limit from below.) So either "failed" or "und" (undetermined) seems like an acceptable response, and 5 is OK only with qualification; it doesn't seem right to return 5 unqualified. Very likely, the implementation computes by default the limit from above. I guess that Gruntz' algorithm is restricted to the real case, but I do not know.Martin
left and right limits can be different (not two-sided) but ... --billpage, Fri, 20 Apr 2007 17:59:01 -0500 replyFor this limit, approaching from the right, Axiom gives: $\sage{axiom(limit((3**(1/x)+5**(1/x))**x, x=0,"right")::OutputForm
)}$ and from the left: $\sage{axiom(limit((3**(1/x)+5**(1/x))**x, x=0,"left")::OutputForm
)}$;while Maxima gives: left (from below): $\sage{maxima(
Axiom Referencelimit((3**(1/x)+5**(1/x))**x, x, 0,minus)
)}$, right (from above): $\sage{maxima(limit((3**(1/x)+5**(1/x))**x, x, 0,plus)
)}$.On Computing Limits in a Symbolic Manipulation System; Dominik Gruntz. ETH Diss 11432 abstract postscript , 1996.
Some or all expressions may not have rendered properly, because REDUCE returned the following error:Error: export PATH=/usr/local/bin:$PATH; ulimit -t 240; reduce < /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/1626299353486179848-25px.run
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