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MathGroup Archive 1995

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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]
>

How about:

In[1]:=
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[2]:=
DPoly[12 x^2+3 x-2, x, f, b]

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

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

Out[3]=
                (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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