Re: How to Enable Automatic Recalculation

*To*: mathgroup at smc.vnet.net*Subject*: [mg109895] Re: How to Enable Automatic Recalculation*From*: Murray Eisenberg <murray at math.umass.edu>*Date*: Fri, 21 May 2010 06:47:06 -0400 (EDT)

Method 1's final result as I showed it is indeed dead wrong, due to an unfortunate copy-and-paste; thanks for catching that. But I see nothing "wrong" in method 2. I just checked the results against evaluation of the input lines shown (one per input cell) in a fresh Mathematica 7.0.1 notebook. But I don't deny there are potential pitfalls. I suspected that the O.P. was interested in something more complicated than the simple arithmetic example he used in his query. So I wanted to suggest the possibility that the sort of thing he was looking for could be treated by Dynamic, and not just SetDelayed. On 5/20/2010 6:39 AM, dh wrote: > Hi, > there seems to be two pitfalls in method 2 and 3. > Dynamic is thought to update screen outputs, not to recalculate > variables. If nothing is printed, Dynamic is not even evaluated. > Let's look at method2: > (* method 2: use Dynamic *) > Clear[a,b] > Dynamic[a] > a > a = 3; (* preceding output changes to 3 *) > b = 3 + a > 6 > a = Pi; > b > 3 + Pi > The last answer is WRONG. b is definitly set to 6 and is NEVER > recalculated when a is changed. This is so because we use a un-delayed > assign. > > Method 3 is even more dangerous: > (* method 3: another way to use Dynamic *) > Clear[a,b] > a = 3; > Dynamic[b = 3 + a] > 6 > a = Pi; (* preceding ouptput changes to 3 + Pi *) > b > 3 + Pi > > The last answer is again wrong in a devious way. The correct value is 6. > However, if you reevaluate b again, it is suddenly 3+Pi. The reason is, > that the Dynamic statement is evaluated AFTER b has been printed. > Therefore, b obtains its new value too late. > > What can we learn from this is that Dynamic should be used for display > jobs and not anything else. The right thing to do here is to use an > delayed assign as in method 1. > cheers, Daniel > > Am 20.05.2010 02:15, schrieb Murray Eisenberg: >> There IS a "simple" answer. Actually, two answers. it used to be that >> the only way to do this was to use SetDelayed ( := ) for the symbol you >> wanted to be recalculated whenever you changed another variable whose >> values was specified by Set ( = ). Since Mathematica 6, you also have >> the more sophisticated method of using Dynamic quantities. >> >> (* method 1: use SetDelayed instead of Set for b *) >> a = 5; >> b := 3 + a >> b >> 8 >> a = Pi; >> b >> 3 + Pi >> >> >> (* method 2: use Dynamic *) >> Clear[a,b] >> Dynamic[a] >> a >> a = 3; (* preceding output changes to 3 *) >> b = 3 + a >> 6 >> a = Pi; >> b >> 3 + Pi >> >> (* method 3: another way to use Dynamic *) >> Clear[a,b] >> a = 3; >> Dynamic[b = 3 + a] >> 6 >> a = Pi; (* preceding ouptput changes to 3 + Pi *) >> b >> 3 + Pi >> >> >> >> On 5/19/2010 7:01 AM, Victor Roberts wrote: >>> I'm new to Mathematica, so perhaps there is a simple answer >>> to this question. >>> >>> How to I set Mathematica so that when I change the value >>> assigned to a variable it will automatically change all >>> later calculations that use that variable. >>> >>> For example, if I set >>> >>> a = 5 >>> >>> and >>> >>> b = 3 + a >>> >>> I would like the value of b updated each time I change the >>> value of a. >>> >>> Right how, I need to recalculate each and every expression >>> that uses the variable a if I change its value. There must >>> be a better way. >>> >>> >>> -- >>> Vic Roberts >>> Replace xxx with vdr in e-mail address. >>> >> > > -- 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