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Re: List-Operations on Heads other than List

• To: mathgroup at smc.vnet.net
• Subject: [mg29739] Re: List-Operations on Heads other than List
• From: "Allan Hayes" <hay at haystack.demon.co.uk>
• Date: Fri, 6 Jul 2001 03:24:34 -0400 (EDT)
• References: <9i068k$h0i$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Detlef Mueller" <dmueller at mathematik.uni-kassel.de> wrote in message
news:9i068k$h0i$1 at smc.vnet.net...
> Hello,
>
> The Help Browser says:
>
> Select[list, crit] picks out all elements ...
>
> Now this works fin for other Haeders thal List
> too.
>
> Select[Expand[P], ! NumberQ[#] &] removes the
> absolute Part of the Poynomial P
> (in my Version).
>
> Is this a dangerous Way of Programming?
>
> Greetings
>   Detlef

This is fine as long as
1) the expanded polynomial has more than one term
2) the absolute part is a number.

Re 1)
    x+3 has full form Plus[x,3] and so is the same shape as  {x,3} (which
has full form List[x,3]
But x and 3 are not of this form.

Re 2)  If the polynomial is in the variables x we could use
        Select[Expand[P], ! FreeQ[#,x] &]
 but we still run into the problem 1); and we have to use  Alternatives[x,y,
...] in place of x for a polynomial in variables x,y, ...

One way out of both 1) and 2) is .

Select[Expand[P]+Unique[], ! FreeQ[#, Alternatives[x,y...]] &]

Another way is

        (# - #/. {x->0,y->0, ...})&P

For dealing with many variables note that

    Thread[{x,y,...}->0]  gives {x->0, y->0, ...}

--
Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565