I am new to Mathematica and I have what I am sure is a basic question, which I unfortunately have not been able to figure out. I am trying to keep terms in a polynomial that are of the same degree only. For example, if I have a polynomial in the variables x and y like the following
poly = ax^2*y - bx*y - cx*y^2 + dx + ey
what could I do to extract, for example, only the terms of third order, i.e the terms
ax^2*y-cx*y^2
poly = a x^2*y - b x*y - c x*y^2 + d x + e y;
var = {x, y};
FromCoefficientRules[Select[CoefficientRules[poly, var], Total@#[[1]] == 3 &], var]
a x^2 y - c x y^2
Another route:
d = 3;
poly = a x^2*y - b x*y - c x*y^2 + d x + e y;
var = {x, y};
Fold[Dot, CoefficientArrays[poly, var][[d + 1]], ConstantArray[var, d]]
x (a x y - c y^2)
Easiest is to use a new variable to collect powers in the ones of interest, then set it to 1.
poly = a*x^2*y - b*x*y - c*x*y^2 + d*x + e*y;
vars = {x, y};
Coefficient[poly /. Thread[vars -> t*vars], t^3] /. t -> 1
(* Out[1086]= a x^2 y - c x y^2 *)
axis a distinct entity froma x; if you want to multiply different variables, separate them with a space or explicitly use an asterisk. – J. M.'s missing motivation Dec 13 '16 at 14:29CoefficientListand then take out the elements you want, e.g. by usingIntegerPartitionsbut I'm sure there are better methods. – AndreasP Dec 13 '16 at 14:33