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? > > > Additionally, > > 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 > > > > ____________________________________________________________________________________ > We won't tell. Get more on shows you hate to love > (and love to hate): Yahoo! TV's Guilty Pleasures list. > http://tv.yahoo.com/collections/265 > 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. How about writing your function as charge[n_] := 0.95^n David Bailey http://www.dbaileyconsultancy.co.uk