Re: Patterns_ to define linear operators?

• To: mathgroup at smc.vnet.net
• Subject: [mg71441] Re: Patterns_ to define linear operators?
• From: Peter Pein <petsie at dordos.net>
• Date: Sat, 18 Nov 2006 04:41:11 -0500 (EST)
• Organization: 1&1 Internet AG
• References: <ejgvpf\$8tm\$1@smc.vnet.net>

```W. Craig Carter schrieb:
> Hello,
> I'd like to implement a rule that will factor out constants from
> linear operators such as FourierTransform; i.e.,
> FourierTransform[a*f[x], x, k]  to a*FourierTransform[f[x],x,k]
>
> Here is a method that seems sensible at first, but is potentially
> dangerous:
>
> MyRule1 =
> FourierTransform[a_ f_[y_], x_, k_] :-> a FourierTransform[f[y],x,k]
> (which would fail if a was not free of x)
>
> An improvement is:
>
> MyRule2 =
> FourierTransform[a_?(FreeQ[#,x]&), f_[y_], x_, k_] :-> a FourierTransform[f[y],x,k]
> (which would fail if a were a product, say b x)
>
> Does anybody have advice on a robust way to implement this rule?
>
> Thanks, Craig Carter
>

Hi Craig,

I recommend essentially the same as Dimitris does, but use ReplaceRepeated
instead!

myrule=
lintrans_[a_. * b_,x_,w_] :>
a*lintrans[b,x,w] /; FreeQ[a,x] && MemberQ[b,x,Infinity];

and compare

ft[3*x*g[y]*y*h[x],x,w] /. myrule
--> 3 ft[x y g[y] h[x],x,w]

with

ft[3*x*g[y]*y*h[x],x,w] //. myrule
--> 3 y ft[x h[x],x,w] g[y]

I guess, the second one is what you expect.

Cheers,
Peter

```

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