Description
In Macaulay2, the degree of a polynomial is a list of integers. This is to accommodate polynomial rings having multigradings. The usual situation is when the ring has the usual grading: each variable has length 1.
i1 : R = QQ[a..d];

i2 : degree (a^3b1)^2
o2 = {6}
o2 : List

When not dealing with multigraded rings, obtaining the degree as a number is generally more convenient:
i3 : first degree (a^3b1)^2
o3 = 6

i4 : S = QQ[a..d,Degrees=>{1,2,3,4}];

i5 : first degree (a+b+c^3)
o5 = 9

i6 : T = QQ[a..d,Degrees=>{{0,1},{1,0},{1,1},{3,4}}];

i7 : degree c
o7 = {1, 1}
o7 : List

In a multigraded ring, the degree of a polynomial whose terms have different degrees is perhaps nonintuitive: it is the maximum (in each of the component degree) over each term:
i8 : degree c^5
o8 = {5, 5}
o8 : List

i9 : degree d
o9 = {3, 4}
o9 : List

i10 : degree (c^5+d)
o10 = {3, 5}
o10 : List
