       Re: gives

• To: mathgroup at smc.vnet.net
• Subject: [mg125910] Re: gives
• From: Bob Hanlon <hanlonr357 at gmail.com>
• Date: Fri, 6 Apr 2012 06:00:52 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com
• References: <201204050952.FAA13197@smc.vnet.net>

```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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