Final comments on CoefficientList

*Subject*: [mg2516] Final comments on CoefficientList*From*: sherod at boussinesq.Colorado.EDU (Scott Herod)*Date*: Wed, 15 Nov 1995 07:01:53 GMT*Approved*: usenet@wri.com*Distribution*: local*Newsgroups*: wri.mathgroup*Organization*: University of Colorado at Boulder*Sender*: daemon at wri.com ( )

I'm pretty sure that CoefficientList has a bug in it. The simplest example is In[1]:= CoefficientList[0,x] Out[1]= {} But, In[2]:= PolynomialQ[0,x] Out[2]= True This causes more problems when you try to create the list of coefficients of a polynomial in multiple variables. In[4]:= CoefficientList[ x y + x y^2, {y,x}] Out[4]= {{}, {0, 1}, {0, 1}} In[5]:= CoefficientList[x y + x y^2, {x,y}] Out[5]= {{}, {0, 1, 1}} Below are two functions which (I think) act correctly. Neither makes use of caching as discussed by David Wagner in the most recent Mathematica Journal but such could be added easily. I would appreciate comments on improvements of these because I need to run them MANY times. myCoefList[eqn_, x_Symbol] := myCoefList[eqn,{x}]; myCoefList[{eqn_}, x__] := myCoefList[eqn, x]; myCoefList[{eqn1_, eqn2__}, x__] := {myCoefList[eqn1, x], myCoefList[{eqn2}, x]}; myCoefList[eqn_, {x_}] := Table[Coefficient[eqn,x,i], {i,0, Max[Exponent[eqn, x],0]}]; myCoefList[eqn_, {x_, y__}] := Table[Coefficient[myCoefList[eqn,y],x,i], {i,0,Max[Exponent[eqn,x],0]}]; myCoefList2[eqn_, var_] := Module[{coef, spam, a, b, c}, myCoefList::polynomial = "The equation is not a polynomial in the variables"; coef[spam_, {a_, b_}] := Coefficient[spam, a, b]; coef[spam_, {a_, b_}, c__] := Coefficient[coef[spam, c], a, b]; If[PolynomialQ[eqn, var], Array[ coef[eqn, Inner[List, var, List[##], Sequence]] &, (Exponent[eqn,#] + 1 &) /@ var, 0] , Message[myCoefList::polynomial]; ] ] Scott A. Herod Applied Mathematics University of Colorado, Boulder