Re: Generate polynomial of specified degree
- To: mathgroup at smc.vnet.net
- Subject: [mg60660] Re: Generate polynomial of specified degree
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Fri, 23 Sep 2005 04:20:09 -0400 (EDT)
- Organization: The University of Western Australia
- References: <dgtj9q$28g$1@smc.vnet.net> <dgtuja$6ni$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <dgtuja$6ni$1 at smc.vnet.net>, dh <dh at metrohm.ch> wrote:
> it is not too hard:
>
> f[x_Symbol,n_Integer]:= Array[c,{n+1},0].x^Range[0,n]
Personally, I think it is better to separate parameters from variables,
and also to localise the coefficient name:
f[n_Integer,c_:c][x_Symbol]:= With[{p = Range[0, n]}, (c /@ p) . x^p]
f[0, c_:c][x_Symbol]:= c[0]
Now try
f[0][x]
f[3][x]
f[3,a][x]
Sometimes using pure functions is advantageous:
Clear[f]
f[n_Integer,c_:c] := Function[x, (c /@ Range[0, n]) . x^Range[0, n]]
f[0, c_:c]:= Function[x, c[0]]
As a particular advantage of this syntax, try
f[2]'[x]
Cheers,
Paul
> Renan wrote:
> > Hello,
> >
> > Sorry if this may seem a silly question, but I readed the Mathematica
> > help and found no references.
> >
> > Is there any function that can generate a polynomial of a given degree?
> >
> > e.g.
> >
> > For degree 1, f[x] would return a x + b
> > For degree 2, f[x] would return a x^2 + b x + c (quadratic equation)
> > For degree 3, f[x] would return a x^3 + b x^2 + c x + d (quadratic equation)
> >
> > Thanks,
> > Renan - Canoas, RS, Brazil
> >
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