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last edited 16 years ago by page |
Edit detail for SandBoxSymPy revision 2 of 4
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Editor: page
Time: 2007/09/19 00:58:03 GMT-7 |
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changed: -\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} 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}
Running SymPy? in a SageBlock?
SymPy? initialization:
We are running SymPy? version: 
First simple confidence test:
The resulting SymPy? expression is:
 | (1) |
Limits
Here is a simple limit in SymPy?
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:
.
And Maxima gives:
.
So the Axiom and Maxima developers have some more work to do!
But worse, Reduce actually gets it wrong...
limit((3**(1/x)+5**(1/x))**x, x,0); | 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:
and from the left:
;
while Maxima gives:
left (from below): 
,
right (from above): 
.
On Computing Limits in a Symbolic Manipulation System; Dominik Gruntz. ETH Diss 11432 abstract postscript , 1996.