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Re: How to Enable Automatic Recalculation

• To: mathgroup at smc.vnet.net
• Subject: [mg109899] Re: How to Enable Automatic Recalculation
• From: Victor Roberts <xxx at lighting-research.com>
• Date: Sat, 22 May 2010 00:40:28 -0400 (EDT)
• References: <ht5oau$179$1@smc.vnet.net>

Murray,

You are correct.  The example I gave is somewhat simpler
than the problem I am working on.

The problem is a definite integral of a piecewise function,
where that piecewise function depends upon the value of one
variable. 

Based on prior experience with a different math program, I
had expected that after the integral was calculated, I could
go back and change the value of the variable and have the
value of the integral change automatically. 

As I have said elsewhere, this was all based on a
misunderstanding of the design of the Mathematica interface,
and I now see that I can just change the value of the
variable, and then reevaluate the integral.

Thanks for your help.

--
Vic Roberts
Replace xxx with vdr in e-mail address.

On Fri, 21 May 2010 10:46:54 +0000 (UTC), Murray Eisenberg
<murray at math.umass.edu> wrote:

>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.
>>>>
>>>
>>
>>