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