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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}

question about limit --robert.dodier, Fri, 20 Apr 2007 15:22:26 -0500 reply
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

left and right limits can be different (not two-sided) but ... --billpage, Fri, 20 Apr 2007 17:59:01 -0500 reply
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): $\sage{maxima(limit((3**(1/x)+5**(1/x))**x, x, 0,plus))}$.

Dominik Gruntz --billpage, Fri, 20 Apr 2007 18:26:50 -0500 reply
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


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