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[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]}]
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[1]:=
DPoly[poly_, xvar_, func_, dvar_]:=
CoefficientList[poly, xvar] .
Table[D[func[dvar], {dvar, i}], {i, 0, Exponent[poly, xvar]}]
In[2]:=
DPoly[x y^3 + 41 z - x^4, x, f, b]
Out[2]=
3 (4)
41 z f[b] + y f'[b] - f [b]
Apologies for the waste of net-space.
Bob Beretta
beretta at mit.edu