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Re: gives wrong result
*To*: mathgroup at smc.vnet.net
*Subject*: [mg125890] Re: gives wrong result
*From*: Yi Wang <tririverwangyi at gmail.com>
*Date*: Fri, 6 Apr 2012 05:53:54 -0400 (EDT)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
Dear Bob,
Thanks a lot for your reply! Your suggestion indeed works but I am
still curious about it:
Because I used Replace instead of ReplaceAll by purpose. This is to
mean, in the rule I want Mathematica to match the entire expression
instead of part of it. For example, if I am not using Simplify, but
instead use the rule directly:
Replace[aa PDD[z, d], aa_. PDD[bb_, cc_] :> -bb PDD[aa, cc]]
I get the (correct) non-zero result. Thus there is still something I
don't understand in Simplify[].
Thanks again,
Yi
PS: I am new to this discussion group. Thus I am not sure if directly
reply to your personal email and cc to the group is appropriate. If
not, sorry, and let me know so that I will stop doing it to you and
others.
On Thu, Apr 5, 2012 at 7:38 AM, Bob Hanlon <hanlonr357 at gmail.com> wrote:
> ClearAll[PDD, try, t, z, aa];
>
> PDD[a_?NumericQ, idx_] := 0;
>
> t = aa PDD[z, d];
>
> try[expr_] := Replace[expr, aa_. PDD[bb_, cc_] :> -bb PDD[aa, cc]];
>
> Simplify[t, TransformationFunctions :> {try}]
>
> 0
>
> The default value for aa in aa_. PDD[bb_, cc_] is one. Consequently,
> PDD[z, d] by itself matches the LHS of the rule and becomes -z PDD[1,
> d] which evaluates to zero. Note the behavior if the default is
> removed:
>
> try[expr_] := Replace[expr, aa_ PDD[bb_, cc_] :> -bb PDD[aa, cc]];
>
> Simplify[t, TransformationFunctions :> {try}]
>
> aa PDD[z, d]
>
>
> Bob Hanlon
>
>
> On Thu, Apr 5, 2012 at 5:52 AM, Yi Wang <tririverwangyi at gmail.com> wrote:
>> Hi, all,
>>
>> I met a problem when using the TransformationFunctions option in Simplify:
>>
>> ClearAll[PDD,try,t,z,aa];
>> PDD[a_?NumericQ, idx_] := 0;
>> t = aa PDD[z, d];
>> try[expr_] := Replace[expr, aa_. PDD[bb_, cc_] :> -bb PDD[aa, cc]];
>> Simplify[t, TransformationFunctions :> {try}]
>>
>> I expect Simplify to do nothing, because the replace rule in try[] does not make the function simpler in this special case. However, Simplify[...] returns 0.
>>
>> If I delete the line " PDD[a_?NumericQ, idx_] := 0; ", Simplify will give the correct result. However, z (or N[z]) is not a number thus it seems the above line shouldn't matter.
>>
>> I also tried several other tests. I found a_?NumberQ, a_?IntegerQ both have the above problem, while a_ListQ has the desired behaviour.
>>
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