       Re: [Q] Differential operators <--> polynomials

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1277] Re: [Q] Differential operators <--> polynomials
• From: beretta at ATHENA.MIT.EDU (Robert K Beretta)
• Date: Wed, 31 May 1995 03:55:43 -0400
• Organization: Massachusetts Institute of Technology

```In article <3q3m05\$mc5 at news0.cybernetics.net> ozan at matematik.su.se (Ozan \Vktem) writes:
>
>  I would like to be able to "convert" a polynomial to its associated
>differential operator. I am pretty sure that this is done, but I could not
>find it anywhere. A package that works like the example below would be
>very nice to have.
>
>Example: The package provides the command "DPoly" and
>
>  DPoly[12 x^2+3 x-2,f[b,s],b]
>
>  should be equivalent to
>
>  12 D[f[b,s],{b,2}]+3 D[f[b,2],b]-2 f[b,s]
>

In:=
DPoly[poly_, xvar_, func_, dvar_]:=
CoefficientList[12 x^2 + 3 x - 2, xvar] .
Table[D[func[dvar], {dvar, i}], {i, 0, Exponent[poly, xvar]}]

In:=
DPoly[12 x^2+3 x-2, x, f, b]

Out=
-2 f[b] + 3 f'[b] + 12 f''[b]

In:=
DPoly[12 x^2+3 x-2, x, f[#, s]&, b]

Out=
(1,0)             (2,0)
-2 f[b, s] + 3 f     [b, s] + 12 f     [b, s]

Hope this helps,

Bob Beretta
beretta at mit.edu

```

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