Re: Self-teaching snag

*To*: mathgroup at smc.vnet.net*Subject*: [mg74572] Re: [mg74556] Self-teaching snag*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Tue, 27 Mar 2007 03:54:56 -0500 (EST)*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst*References*: <200703260704.CAA11373@smc.vnet.net>*Reply-to*: murray at math.umass.edu

The trouble is that each and every time Mathematica calculates charge[day] for some particular value of day, it must recurse all the way back the initial value. That is, once a value of charge is calculated, Mathematica forgets it. Look at the following, for example: charge[0]=1.0 (* 100% *); charge[day_]:=(charge[day-1]-(0.05*charge[day-1])); charge[20] 0.358486 ?charge (* what does Mathematica know about charge? *) Global`charge charge[0]=1. charge[day_]:=charge[day-1]-0.05 charge[day-1] Indeed, Mathematica knows nothing more about charge than the original definitions, even though it calculated charge[20] -- and hence in the process had to calculate charge[19], charge[18], ..., charge[2], charge[1]. Now force Mathematica to "remember" any value of charge already calculated -- in technical terms, "cache" the calculated values -- by changing the definition to the following: charge[0]=1.0 (*100%*); charge[day_] := charge[day] = (charge[day-1]-(0.05*charge[day-1])); Watch what happens now when, say, you calculate charge[4] (to keep the output here short): charge[4] 0.814506 ?charge Global`charge charge[0]=1. charge[1]=0.95 charge[2]=0.9025 charge[3]=0.857375 charge[4]=0.814506 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 > -- Murray Eisenberg murray at math.umass.edu Mathematics & Statistics Dept. Lederle Graduate Research Tower phone 413 549-1020 (H) University of Massachusetts 413 545-2859 (W) 710 North Pleasant Street fax 413 545-1801 Amherst, MA 01003-9305

**References**:**Self-teaching snag***From:*Todd Allen <genesplicer28@yahoo.com>