Running SymPy in a SageBlock
SymPy 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}
Hello, 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
For 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): $\sage{maxima(limit((3**(1/x)+5**(1/x))**x, x, 0,minus))}$,
right (from above): $\sage{maxima(limit((3**(1/x)+5**(1/x))**x, x, 0,plus))}$.
Axiom Reference
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
Some or all expressions may not have rendered properly,
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