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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
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