Re: Self-teaching snag

• To: mathgroup at smc.vnet.net
• Subject: [mg74600] Re: Self-teaching snag
• From: David Bailey <dave at Remove_Thisdbailey.co.uk>
• Date: Tue, 27 Mar 2007 04:10:05 -0500 (EST)
• References: <eu7re0\$b6p\$1@smc.vnet.net>

```Todd Allen wrote:
> Hi All,
>
>    I am trying to refresh my skills in basic problem
> solving using Mathematica, but am running into some
> difficulties which are beginning to make me suspicious
> of Mathematica itself.  (I probably should be
> suspicious of my own brain...but you know how that is
> :-)
>
> Here is the scenario:  I have written a basic function
> to tell me what percentage of battery power will
> remain in a battery after x number of days, provided
> that we start with a full charge and lose 5% of that
> charge per day.
>
> If you execute the following code in Mathematica
> (V5.1):
>
> charge[0]=1.0 (* 100% *);
> charge[day_]:=(charge[day-1]-(0.05*charge[day-1]));
> charge[20]
>
> I receive an output of 0.358486 for my query at the 20
> day mark.....so, no problem so far.
>
> However, when I try to ask for the output at
> charge[35], mathematica seems to enter an endless
> calculation.  I've let the computer run for as long as
> 5 minutes without getting an answer.  Is there
> something wrong with my function, my version of
> Mathematica or something else I haven't considered?
>
>
>
> When I try the following:
>
> In[145]:=
> Solve[charge[day]==0.15,day];
>
> Mathematica gives me the error:
> "\$RecursionLimit::reclim: Recursion depth of 256
> exceeded."
>
> I am trying to ask Mathematica to tell my how many
> days it takes to reduce the battery power to 15
> percent, but I must be messing something up??
>
> If anyone has any pointers, I'd certainly appreciate
> it, because I am a little stuck right now.
>
> Best regards,
> Todd Allen
>
>
>
> ____________________________________________________________________________________
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>
Hello,

Your definition of charge is recursive - i.e. the value for N days is
computed from the value at N-1 days. This would be OK (provided you
always use a positive integer as argument) but your definition uses two
calls to charge[N-1], which involves four calls to charge[N-2] .... etc.
2^35 function calls take a lot of time, even in Mathematica! A slight
change will fix this:

charge[0] = 1.0 (*100%*);
charge[day_] := (0.95 charge[day - 1]);

You might think that Mathematica would make this simplification
automatically, but Simplify is not applied automatically on the contents
of a function definition.

Solve works on mathematical equations - not functions defined as
Mathematica code. Even NSolve will flounder because your definition will
enter an infinite recursive loop in its argument is anything other than
a positive integer.