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 Topics FrontPage AboutSage SandBoxSage ... SandBox SandBoxSage SandBoxSymPy <-- You are here. 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: $$\sage{e}$$ 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. see Gruntz --kratt6, Fri, 20 Apr 2007 15:56:42 -0500 replyVery 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): $\sage{maxima(limit((3**(1/x)+5**(1/x))**x, x, 0,minus))}$, 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 replyAxiom Reference On Computing Limits in a Symbolic Manipulation System; Dominik Gruntz. ETH Diss 11432 abstract postscript , 1996. 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