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

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg1282] Re: [Q] Differential operators <--> polynomials
• From: beretta at ATHENA.MIT.EDU (Robert K Beretta)
• Date: Wed, 31 May 1995 04:45:45 -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]
>>

I responded to Ozan's query with the fairly obviously flawed function,

>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]}]

which has Ozan's original polynomial hard-coded into it.  Let's see if I can
copy and paste off of the right part of my screen this time:

Try:

In:=
DPoly[poly_, xvar_, func_, dvar_]:=
CoefficientList[poly, xvar] .
Table[D[func[dvar], {dvar, i}], {i, 0, Exponent[poly, xvar]}]

In:=
DPoly[x y^3 + 41 z - x^4, x, f, b]

Out=
3          (4)
41 z f[b] + y  f'[b] - f   [b]

Apologies for the waste of net-space.

Bob Beretta
beretta at mit.edu

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