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Re: Solve never calls Equal?
On 16 Jul 2011, at 11:41, Richard Fateman wrote:
> (in a different thread, where replacing Equal by SameQ was proposed)
>
>
> On 7/15/2011 2:07 AM, Andrzej Kozlowski wrote:
>> Well, here is one example of what would happen:
>>
>> In[3]:= Unprotect[Equal]
>>
>> Out[3]= {Equal}
>>
>> In[5]:= Equal[a_, b__] := SameQ[a, b]
>>
>> In[6]:= Protect[Equal]
>>
>> Out[6]= {Equal}
>>
>> In[7]:= Solve[3 x == 1, x]
>>
>> Out[7]= {}
>>
>> Doesn't look like a great idea to me.
>>
>> Andrzej Kozlowski
>>
>
> That's because 3*x==1 is immediately changed to False, and
> Solve[False, x] is indeed not a great idea.
>
>
>
> Equal[a_?NumberQ, b_?NumberQ] := SameQ[a, b];
>
> works better. That Solve example works just fine.
>
> Indeed, if one does this..
>
> Equal[a_?NumberQ, b_?NumberQ] := (Print[test[a, b]]; SameQ[a, b]);
>
> one can detect when, if ever, the Solve program calls Equal on two
> numbers. It will print test[...] on such occasions.
>
> When does Solve call Equal on 2 numbers? I poked around a little and
> found -- never. I tried Integrate, Factor, Do, Product, Plot.. =
--never.
>
>
> note that f[x_] := If [x == 0, 1, f[x - 1]*x]; f[5] computes 5! =
and
> calls Equal 6 times... but Factorial[5] does not.
>
>
> Perhaps the internal support routines do not call Equal?
> or calls to it are compiled away and not in reach of redefinition by =
the
> user? Or do they call SameQ? (no, they don't. I tried it).
>
> Cheers
>
>
> RJF
>
>
This may indeed "work", though one would have to check functions such as
NSolve, NSum, Reduce, etc, which I haven't tried (and don't want to).
But it certainly will produce effects like this:
In[1]:= Unprotect[Equal];
In[2]:= Equal[a_?NumberQ, b_?NumberQ] := SameQ[a, b]
In[3]:= Protect[Equal];
In[4]:= eqn = 2 x + 1 == 0;
In[5]:= Solve[eqn, x][[1]] // N
Out[5]= {x->-0.5}
In[6]:= eqn /. %
Out[6]= False
I am not at all convinced that the "naive user" will find this behaviour
much of an improvement, in fact, quite the opposite.
Andrzej Kozlowski
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