Re: Constant term in polynomial?
- To: mathgroup at smc.vnet.net
- Subject: [mg3345] Re: [mg3326] Constant term in polynomial?
- From: brucec (Bruce Carpenter)
- Date: Thu, 29 Feb 1996 03:23:48 -0500
- Sender: owner-wri-mathgroup at wolfram.com
>Arrgh, I feel stupid asking this question, but I can't think how to do it: >how do I find the constant term in a polynomial in several variables in >Mathematica? For example, the "7" in 7 + 3 x y + y^2 ? > >I suppose one way would be to use > > Coefficient[Coefficient[7 + 3 x y + y^2,x,0],y,0]. > >But that's incredibly clunky, especially since I may have fifty or more >variables in my real-life problem. > >I could evaluate the expression under the rule {x->0, y->0}, with the same >problem: for fifty variables that's awkward. I could build the rule using >Variables[expr], but that's clumsy and seems inefficient. > >First[7 + 3 x y + y^2] will work for this one, since the 7 is present and >appears first in the FullForm representation. But it won't work in >First[3 x y + y^2], which returns 3 x y. > >OK, so I can build a command which computes Variables[First[expr]], and >if that's empty, returns 0; otherwise returns First[expr]. Also clunky >IMHO, but it seems the most workable--unless there's some trap I'm missing? > >Or I can introduce an auxiliary variable "one", refer to the polynomial as >"7 one + 3 x y + y^2", and ask for Coefficient[expr, one]. Gag! If I ever >want to EVALUATE it, I have to remember to use the rule one->1. > >There MUST be a standard way to do this, but I can't think of what it could be! > >--Ron Bruck How about the following? For the multivariate polynominal poly, Select[poly, NumberQ]. For example In[63]:= Short[poly = Expand[(2+Sum[a[i]^i, {i,1,50}])^2],3] Out[63]//Short= 2 2 2 4 4 + 4 a[1] + a[1] + 4 a[2] + 2 a[1] a[2] + a[2] + 48 50 49 50 100 <<1317>> + 2 a[48] a[50] + 2 a[49] a[50] + a[50] In[64]:= Timing[Select[poly, NumberQ]] Out[64]= {0.05 Second, 4} Cheers, Bruce Carpenter ----------------------- Bruce Carpenter Courseware Coordinator phone: (217) 398-0700 Wolfram Research, Inc. fax: (217) 398-0747 100 Trade Centre Drive email: brucec at wolfram.com Champaign, IL 61820 web: http://www.wolfram.com ==== [MESSAGE SEPARATOR] ====